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The canonical scenario of cross-flow vortex-induced vibration (VIV) of a circular cylinder in the turbulent regime, which has been studied by several physical experiments in the literature, is reexamined in this study through high-fidelity large-eddy simulations (LES) at a Reynolds number 104. The VIV response (including vibration amplitude and frequency) and hydrodynamic coefficients predicted by the present LES agree with the experimental results better than previous numerical attempts. In addition, several phenomena reported by previous experimental studies are confirmed numerically for the first time. After validating against the experiments, new VIV characteristics and physical mechanisms are explored with confidence. First, a collective analysis on the frequency spectra of the displacement, lift, and velocity signals provides a complete picture of the frequency response of the system. In contrast, the use of a single signal may miss certain aspects of the frequency response, so that caution should be exercised. Second, spanwise correlation of primary vortex shedding is examined, where relatively low correlations in the upper and lower branches are likely because the vortex shedding patterns involve complex vortex generation and interaction. Third, the effect of mass ratio (m*) of the cylinder on the VIV response is analyzed with a range of m* (=1.4–3.4) relevant to cylindrical structures used in offshore engineering (such as subsea pipelines). The variations in the amplitude response, frequency response, and hydrodynamic coefficients with m* and reduced velocity are examined in detail. The present results suggest that a lighter pipeline is more susceptible to the onset of VIV. [ABSTRACT FROM AUTHOR]

In this study, we consider the connection of the hydrodynamic force with vortex shedding behind a stationary sphere in an unbounded fluid at several Reynolds numbers, covering the range of critical transition from plane-symmetric to non-symmetric flow. A principal spectrum analysis (PSA) is employed/proposed to obtain the spectral representation (SR) modes for each time-varying force coefficient; this enables us to identify (i) one single characteristic frequency at R e = 300 , 350, and 380, i.e., the fast frequency f V S which represents the frequency of vortex shedding and (ii) two characteristic frequencies at R e = 390 , 400, and 420: one is the first fast frequency f 1 = f V S , representing the frequency of vortex shedding, and the other is the second fast frequency f 2 , representing the frequency of side oscillations of the vortex flow in the transverse flow direction. In the situations of the latter set of Reynolds numbers, the SR modes indicate that not only the strength but also the phase of shed vortex varies slightly at each successive vortex shedding, and most notably, we have identified rotation of the vorticity pattern in the near wake about the central axis. The PSA-SR mode analysis reveals that these three vortex activities all co-operate at the integer multiples of the greatest common-divisor of the two characteristic frequencies ( f 1 , f 2 ). In other words, the intricate subtlety of vortex shedding behind a stationary sphere can well be uncovered through the PSA-SR mode analysis for establishing the close connections between the force coefficients and the vorticity activities behind the sphere. The present work represents a sequel to our previous study: A spectral force representation and its physical implication for vortex shedding past a stationary or an oscillating circular cylinder at low Reynolds numbers [Lu et al., "A spectral force representation and its physical implication for vortex shedding past a stationary or an oscillating circular cylinder at low Reynolds number," Phys. Fluids 35(5), 053606 (2023)], where we initially proposed the PSA-SR analysis to establish the connections between the force coefficients and the vortex shedding of the circular cylinder under pre-, sub-, and normal synchronization. [ABSTRACT FROM AUTHOR]

This study explores the effects of bubble distribution parameters on the noise spectrum of bubble clusters through direct numerical simulations across volume fractions from 0.005% to 40%. Three types of bubble cluster distributions were analyzed: layered (uniformly sized bubbles with layered positioning), random (uniformly sized bubbles with random positioning), and lognormal (log-normally distributed bubble sizes with random positioning). Using the Ffowcs Williams–Hawkings (FW–H) method, we evaluated the sound pressure levels of the clusters. We found that the arrangement of bubble positions has little impact on the collapse times of bubble clusters. At volume fractions greater than 0.5%, bubble size also shows minimal effect on collapse times. However, when the volume fraction is less than 0.5%, the collapse times gradually approach the collapse time of the largest bubble in the cluster in a free field. Noise spectrum analyses showed that the arrangement of bubble positions significantly influences the noise spectra within the volume fraction range of 0.5%–25%, but has minimal impact outside this range. Importantly, the distribution of bubble sizes shows negligible effects on the noise spectrum, demonstrated by the nearly identical sound pressure level octave decay rates for random and lognormal clusters at the same volume fractions. This consistency can be mathematically described by the fitting formula: decay rate (dB/octave) = 18.192 × α − 0.047 −16.264. These findings enhance our understanding of the noise spectrum across varied bubble cluster distributions and provide new insights into the mechanisms of cavitation noise. [ABSTRACT FROM AUTHOR]

Fluidized beds are favored for their high efficiency in material and heat exchange. However, a limited understanding of two-phase flow dynamics leads to the construction of larger equipment and makes precise control of fluidized beds challenging. Since it is challenging to eliminate the impact of signal noise in experiments, which arises from the inconsistency of particles and measurement methods, a square fluidized bed model has been established for numerical analysis of the chaotic characteristics of two-phase flow. The bubble distribution in the fluidized bed was observed more clearly, the bubble behavior was combined with the chaotic parameters, and the two flow states and the chaotic state were analyzed comprehensively. The results show that the bubbles present a regular arrangement parallel to the diagonal in the early stage of bubbling. At the same time, smooth reconstructed attractors are observed. The increase in fluidization wind speed will make the attractors rough until collapse. The bubbling bed experiences bifurcation into chaos as the fluidization wind speed increases, and we can see this process through the pressure signal. The system state cannot be distinguished by correlation dimension or K-entropy alone. Comprehensive consideration of a variety of chaotic features can be used as a method to identify two-phase flow chaotic states. The method used in this paper combines bubble behavior, pressure signal, power spectrum analysis, phase space reconstruction, correlation dimension, and Kolmogorov entropy to distinguish the state of the fluidized bed more accurately. [ABSTRACT FROM AUTHOR]

The atomization characteristics of impinging jets with high-frequency jet velocity perturbations is studied numerically based on the volume of fluid method. Three typical perturbation modes are considered to mimic the velocity discrepancies of jet flow in real engine conditions. Both the perturbation amplitude and frequency are investigated independently. Results show that the liquid sheet structure and atomization characteristics are significantly changed under the intrinsic perturbation frequency. The spectrum analysis is performed to reveal the specific phenomenon and explore the mechanism of different velocity perturbation modes. The analyses show that the atomization process is sensitive to perturbation frequency but its effectiveness diminishes significantly at excessively high frequencies. Additionally, when the frequency of velocity perturbation approaches the natural intrinsic frequency of sheet waves, resonance occurs within the liquid sheet for certain perturbation mode, leading to dramatic varies in breakup length and spray angle because the velocity superposition of the intrinsic and perturbed flow and its dynamics. [ABSTRACT FROM AUTHOR]

In this study, two individual dam-break induced surge impact pressure datasets are analyzed using the Hilbert–Huang transform method, which is capable of adaptively decomposing the impulsive, oscillatory, and quasi-steady pressure components from the measured raw pressure data. Time-frequency characteristics of these three pressure components are analyzed. Applying the empirical mode decomposition method, the intrinsic mode function (IMF) series extract the local periodic features, including the impulsive and oscillatory pressures, whereas the non-periodic residual series reveal the general variation characteristics of the surge impact pressure, i.e., the quasi-steady pressure. Subsequently, the Hilbert spectrum analysis is conducted to the individual IMF series. The impulsive pressure components are found to be high-frequency (over 5 Hz in this study), and the oscillatory pressure components have frequency ranging from 20 to 60 Hz. It is confirmed that the quasi-steady pressure contributes the dominant amount of the total surge impact energy in both the bottom impact zone and the upper outer zone on the wall. The impulsive pressure-induced instantaneous energy is large in the bottom impact zone shortly after the impact, whereas the oscillatory pressures only lead to a small local instantaneous energy peak. In addition, the impulsive pressure impulses are calculated, which are more test-stable than those of peak pressures. These findings indicate that impulsive pressures induced by surge impact can be rather destructive, especially near the toe of the structure, thus deserve particular attention in the safe design of coastal structures. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) is a type of fluid–solid coupling vibration with a complex flow-field structure. Herein, the wall pressures around a 5:1 rectangular cylinder in the stationary and vibration states are studied via wind tunnel tests. By conducting the spectrum analysis, a novel method is proposed to divide the flow-field of the side surface into recirculation, main vortex, and reattachment regions. The method proposed can be used as a reference for partitioning the flow-field. Based on the partition results, the effects of the maximum amplitudes and development VIV stages on the spanwise correlations of the aerodynamic forces in different subregions are investigated. The results show that the correlation coefficients of the aerodynamic forces in all three subregions increase with the value of maximum amplitude, while the correlation coefficients in the stationary state are all the smallest. Additionally, the spanwise correlations are most affected by the maximum amplitude in the recirculation region and least affected in the main vortex region. Moreover, the maximum spanwise correlation coefficients in the three subregions do not appear at the maximum amplitude, but in the VIV rising stage, owing to the interaction between the self-excited force and vortex shedding force. [ABSTRACT FROM AUTHOR]

This study explores the effects of wear and shaft-shape error defects on the tribo-dynamic responses of water-lubricated bearings under nonlinear propeller disturbance using a numerical model. The model proposed in this paper is verified by comparing the results from experiments and simulations in published studies. Numerical simulation studies reveal the effects of nonlinear propeller disturbance on the dynamic behavior and lubrication performance, such as hydrodynamic force, contact force, and journal trajectory, of the water-lubricated bearings with wear and shaft-shape errors. In addition, the effects of the critical factors for wear and shaft-shape errors, including wear depth, deviation angle, magnitude, and waviness order, on the tribo-dynamic responses of water-lubricated bearings are identified. The results of numerical spectrum analyses show that the nonlinear disturbance significantly affects the dynamic behavior (shown as the fluctuation range of the journal trajectory increases), and reasonable wear parameters can improve the lubrication performance of the water-lubricated bearing. Moreover, the effects of shaft-shape errors on the transient hydrodynamic force, contact force, film thickness, pressure, and journal trajectory are greater than that of wear. [ABSTRACT FROM AUTHOR]

Shock-induced finite-thickness fluid layer evolution is investigated numerically and theoretically. Specifically, two-dimensional helium layers consisting of two interfaces owning diverse perturbation phases are considered to explore the interface-coupling on the Richtmyer–Meshkov instability (RMI). A general linear model is first established to quantify the phase effect on the RMI of the two interfaces of an arbitrary fluid layer. The linear model is validated with the present numerical results. As the phase difference between the two interfaces' perturbations increases, the linear amplitude growth rates of the two interfaces are larger. The influences of diverse parameters on the interface-coupling are concerned. Moreover, the nonlinearity of the RMI of the two interfaces is dependent on the phase difference. Finally, spectrum analysis is performed to investigate the phase effect on perturbation growths of the first three-order harmonics of the two interfaces. [ABSTRACT FROM AUTHOR]

The present work explores the spanwise logarithmic decay of the turbulence intensity for wall-attached eddies per Townsend's attached eddy hypothesis. Within the dataset spanning a friction Reynolds number range R e τ ∼ O (10 3) − O (10 6) , the coherence between the turbulence in the logarithmic region along the spanwise direction and that at a near-wall reference location is used to assess the scale-dependent coherence. Linear coherence spectrum analysis is applied as a filter to separate the coherent and incoherent portions. After this separation procedure, the turbulence intensity decay for wall-attached eddies in the spanwise direction is described in a log-linear manner, which also identifies how the scaling parameter increases with the Reynolds number. This variation is parametrized and consequently can be used to improve existing near-wall models. [ABSTRACT FROM AUTHOR]

Experimental and theoretical investigations are performed to explore the development of Richtmyer–Meshkov (RM) instability for a minimum-surface featured (3D-) interface. The exact mathematical expression of 3D-interface perturbation is obtained for the first time by the spectrum analysis, describing as a superposition of transverse two-dimensional (2D) single-mode with three-dimensional (3D) multi-mode. In particular, the normalized 3D-interface profile is found to be solely determined by one dimensionless parameter related to the 3D-interface initial spectrum. The shock tube experiments are performed by varying the interface height to change the mode-composition of 3D-interfaces under weak shock conditions. It is found that the 3D multi-mode component of a 3D-interface promotes/suppresses the RM instability at the transverse boundary/symmetry plane in comparison with the classical 2D single-mode case. At the linear regime, the 3D perturbation growth can be well predicted by combining the amplitude growth of a 2D single-mode and a 3D dual-mode. At the nonlinear regime, as the interface height reduces, the nonlinear effect on the RM instability at the boundary plane becomes stronger. A generalized nonlinear model is established to predict the interface amplitude by considering the interface spectrum and the mode-coupling of 3D modes. It is found that the mode-coupling has an evident influence on the bubble evolution, and the first-order 3D mode leads to different behaviors for the bubble and spike width growths. This work may provide great insight into the physical mechanism of the 3D RM instability existing in practical applications. [ABSTRACT FROM AUTHOR]

A data-fusion approach is reported to reconstruct missing data and is applied to particle image velocimetry (PIV) measurements. This approach departs from the existing ones in that the datasets involved in its operation are incomplete. Two sets of incomplete but complementary data with fault regions, obtained using different measurement setups, are combined to yield a complete dataset by reconstructing the missing data. In this report, the capability of the current approach is first demonstrated by using three fabricated scalar patterns with different frequency spectra. Second, this method is applied to PIV measurements pertaining to the natural wake of a circular cylinder with a Reynolds number ReD = 1.8 × 103. The performance of this approach is also examined under different configurations, size, location, and direction, of the fault regions. For the real-world data with turbulence and fluctuations, this approach encounters an overfitting problem. To employ this approach in real-world applications without ground-truth data, a method is also proposed to avoid the overfitting problem and estimate reconstruction accuracy. Then, the method is applied on a spectrally richer flow, i.e., wake flow of two side-by-side cylinders with different diameters, and a wake flow of a blunt plate at a relatively higher Reynolds number ReD = 1.6 × 104. The errors are observed to be below 6% for the velocity and fluctuating components. [ABSTRACT FROM AUTHOR]

We derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function m(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H(τ), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, h (γ) = 1 + A γ 2 + O γ 4 . Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = −1/6, and any LVE relaxation spectrum could be used. [ABSTRACT FROM AUTHOR]

The numerical simulation of incompressible turbulent flow at Re = 11 800 (equivalent Reynolds number Rem = 10 030) inside lid-driven cavities with varying spanwise aspect ratio and depthwise aspect ratio (DAR) has been carried out using the dynamic Smagorinsky model. A better comparison of central line averaged velocities and second order turbulent properties is obtained with the existing experimental result of Prasad and Koseff [“Reynolds number and end-wall effects on a lid-driven cavity flow,” Phys. Fluids A 1, 208–218 (1989)] than with the one provided by Leriche and Gavrilakis [“Direct numerical simulation of the flow in a lid-driven cubical cavity,” Phys. Fluids 12, 1363–1376 (2000)]. It is noticed that the size of the downstream secondary vortex increases with an increase in the aspect ratio. Lower DAR cavities are found to be having the maximum turbulent kinetic energy (TKE) and turbulent production, which is further confirmed by the TKE spectra shown at the point of maximum turbulent production on the symmetrical mid-plane. The power spectra maintain a slope of − 5 3 in the inertial subrange as proposed by Kolmogorov and show a steeper slope in the dissipating range. The time integral scale shows that in low DAR cavities, eddies are formed and undergo complete distortion more frequently. The joint probability density function confirms the anisotropy in turbulence, and the anisotropy invariant map (Lumley triangle) shows the type of turbulent anisotropy which shows whether the turbulence is either one-component or two-component near the walls. [ABSTRACT FROM AUTHOR]

Cavity arrays have been previously identified to disrupt the sweep events and consequently the bursting cycle in the boundary layer by capturing the structures responsible for the Reynolds stresses. In the present study, the sensitivity of a flushed-surface cavity array in reducing the turbulent energy production has been investigated. Two plates of varying thicknesses and four different backing cavity volumes were considered, at three different Reynolds numbers. The volume of the backing cavity was shown to be the most important characteristic in determining the attenuation of streamwise velocity fluctuations within the logarithmic region of the turbulent boundary layer. However, the results also demonstrated that the orifice length of the cavity array had negligible effect in modifying the reduction of the turbulent energy by the cavity array in this investigation. The results show that the maximum reduction in turbulence generation achieved for this study occurs when the backing volume is 3.1 × 106 times greater than the viscous length scale at Reθ = 3771. The reduction in turbulence intensity, sweep intensity, and energy spectrum were shown to be 5.6%, 6.3%, and 13.4%, respectively. By decreasing the cavity volume to zero, no change in the turbulent boundary layer turbulence statistics was found. The results suggest a larger reduction in turbulence intensity, sweep intensity, and energy spectrum that can be achieved with a larger backing volume. [ABSTRACT FROM AUTHOR]

Kraichnan's seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt- Vaisala frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, 1=2 ≤ N=f ≤ 2.We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker. [ABSTRACT FROM AUTHOR]

A two-point, two-time similarity solution is derived for homogeneous decaying turbulence. This is the first known solution which includes the temporal decay at two-different times. It assumes that the turbulence is homogeneous in all three space dimensions, and finds that homogeneity holds across time. The solutions show that time is logarithmically "stretched" while the homogeneous spatial scales grow. This solution reduces to the two point, single time equation when the two times are set equal. The turbulence initially decays exponentially, then asymptotically as t-n where n ≥ 1 and equality is possible only if the initial energy is infinite. The methodology should be applicable to other non-equilibrium homogeneous turbulent flows. [ABSTRACT FROM AUTHOR]

The decomposition proposed by Lumley in 1966 is applied to a high Reynolds number turbulent boundary layer. The experimental database was created by a hot-wire rake of 143 probes in the Laboratoire de Mecanique de Lille wind tunnel. The Reynolds numbers based on momentum thickness (Reg) are 9800 and 19 100. Three-dimensional decomposition is performed, namely, proper orthogonal decomposition (POD) in the inhomogeneous and bounded wall-normal direction, Fourier decomposition in the homogeneous spanwise direction, and Fourier decomposition in time. The first POD modes in both cases carry nearly 50% of turbulence kinetic energy when the energy is integrated over Fourier dimensions. The eigenspectra always peak near zero frequency and most of the large scale, energy carrying features are found at the low end of the spectra. The spanwise Fourier mode which has the largest amount of energy is the first spanwise mode and its symmetrical pair. Pre-multiplied eigenspectra have only one distinct peak and it matches the secondary peak observed in the log-layer of pre-multiplied velocity spectra. Energy carrying modes obtained from the POD scale with outer scaling parameters. Full or partial reconstruction of turbulent velocity signal based only on energetic modes or non-energetic modes revealed the behaviour of urms in distinct regions across the boundary layer. When urms is based on energetic reconstruction, there exists (a) an exponential decay from near wall to log-layer, (b) a constant layer through the log-layer, and (c) another exponential decay in the outer region. The non-energetic reconstruction reveals that urms has (a) an exponential decay from the near-wall to the end of log-layer and (b) a constant layer in the outer region. Scaling of urms using the outer parameters is best when both energetic and non-energetic profiles are combined. [ABSTRACT FROM AUTHOR]

Data on the frequency-wavenumber spectra and dispersion relation of the dynamic water surface in an open channel flow are very scarce. In this work, new data on the frequency-wavenumber spectra were obtained in a rectangular laboratory flume with a rough bottom boundary, over a range of subcritical Froude numbers. These data were used to study the dispersion relation of the surface waves in such shallow turbulent water flows. The results show a complex pattern of surface waves, with a range of scales and velocities. When the mean surface velocity is faster than the minimum phase velocity of gravity-capillary waves, the wave pattern is dominated by stationary waves that interact with the static rough bed. There is a coherent three-dimensional pattern of radially propagating waves with the wavelength approximately equal to the wavelength of the stationary waves. Alongside these waves, there are freely propagating gravity-capillary waves that propagate mainly parallel to the mean flow, both upstream and downstream. In the flow conditions where the mean surface velocity is slower than the minimum phase velocity of gravitycapillary waves, patterns of non-dispersive waves are observed. It is suggested that these waves are forced by turbulence. The results demonstrate that the free surface carries information about the underlying turbulent flow. The knowledge obtained in this study paves the way for the development of novel airborne methods of non-invasive flow monitoring. [ABSTRACT FROM AUTHOR]

Expressions for the logarithmic variations of the normalized turbulent longitudinal velocity (u2p+)1/p with normalized distance z/δ from a boundary for high-order (p) moments in the intermediate region of wall bounded flows characterized by thickness δ are derived. The ansatz that (u2p+)1/p variation in ln(z/δ) originates from a compound effect of random sweeping and -1 power-law scaling in the longitudinal velocity spectrum Eu(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an Eu(k) ~ k-1 scaling is confirmed for k z < 1 and kδ > 1. The data were then used to analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the k-1 power-law with log-scaling in (u2p+)1/p. It has been found out that while the RSD hypothesis is operationally applicable to scales associated with attached eddies bounded by kz < 1 and kδ > 1, significant interactions among high-order turbulent velocity and velocity increments lead to the conclusion that the RSD hypothesis cannot be exactly valid. Its operational utility stems from the observations that some of the interaction terms among the high-order velocity and velocity increments act in opposite directions thereby canceling their additive effects in RSD. [ABSTRACT FROM AUTHOR]

This paper aims to shed further light on the viscous reconnection phenomenon. To this end, we propose a robust and efficient method in order to quantify the degree of reconnection of two vortex tubes. This method is used to compare the evolutions of two simple initial vortex configurations: orthogonal and antiparallel. For the antiparallel configuration, the proposed method is compared with alternative estimators and it is found to improve accuracy since it can account properly for the formation of looping structures inside the domain. This observation being new, the physical mechanism for the formation of those looping structures is discussed. For the orthogonal configuration, we report results from simulations that were performed at a much higher vortex Reynolds number (ReΓ ≡ circulation/viscosity = 104) and finer resolution (N³ = 1024³) than previously presented in the literature. The incompressible Navier-stokes equations are solved directly (Direct Numerical Simulation or DNS) using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The associated zero-circulation constraint is circumvented by solving the governing equations in a proper rotating frame of reference. Using ideas similar to those behind our method to compute the degree of reconnection, we split the vorticity field into its reconnected and non-reconnected parts, which allows to create insightful visualizations of the evolving vortex topology. It also allows to detect regions in the vorticity field that are neither reconnected nor non-reconnected and thus must be associated to internal looping structures. Finally, the Reynolds number dependence of the reconnection time scale Trec is investigated in the range 500 ≤ ReΓ ≤ 10 000. For both initial configurations, the scaling is generally found to vary continuously as ReΓ is increased from Trec ~ ReΓ-1 to Trec ~ ReΓ-1/2, thus providing quantitative support for previous claims that the reconnection physics of two vortices should be similar regardless of their spatial arrangement. [ABSTRACT FROM AUTHOR]

The dispersion relation of a confined capillary jet with negligible inertia is measured by Fourier analysis of the jet radius. The real part of the dispersion relation, obtained through the spatiotemporal Fourier spectrum, demonstrates that the phase velocity is independent of the perturbation frequency, at least in the accessible range of frequencies. The imaginary part of the dispersion relation, i.e., the spatial growth rate, is frequency dependent. To measure this dependence, an external forcing is used to amplify modes with different frequencies. The spatial growth rate is then obtained from the exponential growth of the corresponding Fourier mode. The phase velocity and the spatial growth rate are found to increase and decrease, respectively, with the capillary number and to depend only weakly on the degree of confinement. These observations are consistent with a spatialinstability that convects the perturbations downstream with velocity proportional to the capillary number. The frequency of the dominant mode in the absence of forcing, on the contrary, depends mainly on the degree of confinement, i.e., on the jet diameter, and only weakly on the capillary number, which is consistent with the mode selection of the Rayleigh-Plateau instability. Experimental measurements are compared to predicted dispersion relations reported in the literature, and good qualitative agreement is observed. [ABSTRACT FROM AUTHOR]

We report results on rotating stratified turbulence in the absence of forcing and with large-scale isotropic initial conditions using direct numerical simulations computed on grids of up to 4096³ points. The Reynolds and Froude numbers are, respectively, equal to Re = 5.4 × 104 and Fr = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f, is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReFr² ≈ 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling. This scaling is also found for geostrophically balanced initial conditions on a run at a lower resolution and hence lower RB 4. Furthermore, we confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow, in the velocity and temperature fields, with local overturning events indicated by small local Richardson numbers and strong localized vortex tangles. Finally, a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed. [ABSTRACT FROM AUTHOR]

Quasigeostrophic turbulence on a β--plane with a finite deformation radius is studied numerically, with particular emphasis on frequency and combined wavenumberfrequency domain analyses. Under suitable conditions, simulations with small-scale random forcing and large-scale drag exhibit a spontaneous formation of multiple zonal jets. The first hint of wave-like features is seen in the distribution of kinetic energy as a function of frequency; specifically, for progressively larger deformation scales, there are systematic departures in the form of isolated peaks (at progressively higher frequencies) from a power-law scaling. Concomitantly, there is an inverse flux of kinetic energy in frequency space which extends to lower frequencies for smaller deformation scales. The identification of these peaks as Rossby waves is made possible by examining the energy spectrum in frequency-zonal wavenumber and frequency-meridional wavenumber diagrams. In fact, the modified Rhines scale turns out to be a useful measure of the dominant meridional wavenumber of the modulating Rossby waves; once this is fixed, apart from a spectral peak at the origin (the steady jet), almost all the energy is contained in westward propagating disturbances that follow the theoretical Rossby dispersion relation. Quite consistently, noting that the zonal scale of the modulating waves is restricted to the first few wavenumbers, the energy spectrum is almost entirely contained within the corresponding Rossby dispersion curves on a frequency-meridional wavenumber diagram. Cases when jets do not form are also considered; once again, there is a hint of Rossby wave activity, though the spectral peaks are quite muted. Further, the kinetic energy scaling in frequency domain follows a -5/3 power-law and is distributed much more broadly in frequency-wavenumber diagrams. [ABSTRACT FROM AUTHOR]

We generalize Batchelor's parameterization of the autocorrelation functions of isotropic turbulence in a form involving a product expansion with multiple small scales. The richer small scale structure acquired this way, compared to the usual Batchelor function, is necessary so that the associated energy spectrum approximate well actual spectra in the universal equilibrium range. We propose that the generalized function provides an approximation of arbitrary accuracy for actual spectra of isotropic turbulence over the universal equilibrium range. The degree of accuracy depends on the number of higher moments which are determinable and it is reflected in the number of small scales involved. The energy spectrum of the generalized function is derived, and for the case of two small scales is compared with data from high-resolution direct numerical simulations. We show that the compensated spectra (which illustrate the bottleneck effect) and dissipation spectra are encapsulated excellently, in accordance with our proposal. [ABSTRACT FROM AUTHOR]

We present the linear stability analysis of experimental measurements obtained from unsteady flexible pitching panels. The analysis establishes the connections among the wake dynamics, propulsor dynamics, and Froude efficiency in flexible unsteady propulsion systems. Efficiency is calculated from direct thrust and power measurements and wake flowfields are obtained using particle image velocimetry. It is found that for flexible propulsors every peak in efficiency occurswhen the driving frequency of motion is tuned to a wake resonant frequency, not a structural resonant frequency. Also, there exists an optimal flexibility that globally maximizes the efficiency. The optimal flexibility is the one where a structural resonant frequency is tuned to a wake resonant frequency. The optimally tuned flexible panels demonstrate an efficiency enhancement of 122%-133% as compared to an equivalent rigid panel and there is a broad spectrum of wake resonant frequencies allowing high efficiency swimming over a wide range of operating conditions. At a wake resonant frequency we find that the entrainment of momentum into the time-averaged velocity jet is maximized. [ABSTRACT FROM AUTHOR]

The subgrid-scale (SGS) modeling in large-eddy simulation (LES) which accounts for the effect of unsteadiness and nonequilibrium state in the SGS is considered. Unsteadiness is incorporated by considering the spectral evolution in the forced homogeneous isotropic turbulence using the transport equation for the SGS energy. As for the unfiltered spectrum, perturbative expansion of the Kovasnay spectral model about the Kolmogorov -5/3 energy spectrum which constitutes a base equilibrium state in the inertial subrange, yields the extra components with -7/3 and -9/3 powers. It is shown that these spectra are actually extracted in the direct numerical simulation (DNS) data and these components govern the unsteady energy transfer. As for the SGS real-space representation of the spectral model, we consider the SGS one-equation model. The perturbation expansion is applied to the one-equation model by setting the base SGS energy as the standard Smagorinsky model, which assumes the equilibrium state in the SGS and its spectral counterpart is the Kolmogorov -5/3 spectrum. The solution yields the terms whose spectral counterparts are the components with -7/3 and -9/3 powers. These additional terms are induced by temporal variations of the base SGS energy. In the temporal variations of the grid-scale energy, SGS energy, SGS production term, and SGS dissipation which are obtained by applying the filter to the DNS data, it is shown that these quantities lag in time in this order. This time-lag is not realized in the standard Smagorinsky model and the one-equation model because the SGS dissipation is defined so that it instantaneously adjusts to the SGS energy. In the one-equation model, the direction of the energy cascade in the initial period is opposite to that obtained in the DNS data. To retrieve correct time-lag and direction of energy transfer, we relax this instantaneous adjustment and propose the nonequilibrium Smagorinsky model. In this nonequilibrium model, the SGS energy incurred by the -7/3 spectrum is added to the base Smagorinsky energy. Assessment in actual LES shows that the time-lag predicted using the standard Smagorinsky and the one-equation models is inaccurate, whereas good agreement with the DNS data is achieved in the nonequilibrium Smagorinsky model. Extraction of the grid-scale nonequilibrium energy spectrum yields the -7/3 and -9/3 components in addition to the base -5/3 spectrum. In the nonequilibrium Smagorinsky model, continuation of the grid-scale spectra into the SGS is established for the -5/3 and -7/3 components. As a result, the unsteady energy transfer is more accurately predicted, whereas the standard Smagorinsky model does not have the SGS counterpart for the -7/3 component. Feasibility of employing the eddy-viscosity approximation to account for the transfer in the period in which -9/3 spectrum prevails is discussed. [ABSTRACT FROM AUTHOR]

Flow and noise predictions for the tandem cylinder benchmark are performed using lattice Boltzmann and Ffowcs Williams-Hawkings methods. The numerical results are compared to experimental measurements from the Basic Aerodynamic Research Tunnel and Quiet Flow Facility (QFF) at NASA Langley Research Center. The present study focuses on two configurations: the first configuration corresponds to the typical setup with uniform inflow and spanwise periodic boundary condition. To investigate installation effects, the second configuration matches the QFF setup and geometry, including the rectangular open jet nozzle, and the two vertical side plates mounted in the span to support the test models. For both simulations, the full span of 16 cylinder diameters is simulated, matching the experimental dimensions. Overall, good agreement is obtained with the experimental surface data, flow field, and radiated noise measurements. In particular, the presence of the side plates significantly reduces the excessive spanwise coherence observed with periodic boundary conditions and improves the predictions of the tonal peak amplitude in the far-field noise spectra. Inclusion of the contributions from the side plates in the calculation of the radiated noise shows an overall increase in the predicted spectra and directivity, leading to a better match with the experimental measurements. The measured increase is about 1 to 2 dB at the main shedding frequency and harmonics, and is likely caused by reflections on the spanwise side plates. The broadband levels are also slightly higher by about 2 to 3 dB, likely due to the shear layers from the nozzle exit impacting the side plates. [ABSTRACT FROM AUTHOR]

In boundary layers, eigenfunctions which belong to the continuous spectrum of the Orr-Sommerfeld equation have been established as a suitable basis for the expansion of general free-stream vortical disturbances. They are oscillatory in the free stream, and attenuate inside the boundary layer due to shear sheltering. The extent of modal penetration into the shear depends on the disturbance frequency and orientation, with the low-frequency, streamwise elongated modes being the most effective triggers of a high-amplitude streak-like response. The influence of introducing a time-periodic, spanwise mean flow on modal sheltering is investigated. The evaluation of the continuous modes in this case requires a Floquet expansion in the fundamental frequency of the base flow. Appropriate treatment of the free-stream boundedness condition is developed, and quantitative measures of modal sheltering are computed. The time-dependent, spanwise motion is shown to significantly enhance shear sheltering, and to change the optimal orientation of the continuous modes for penetration into the shear. An explanation is provided, in the limit of low frequency of the base flow, using asymptotic analyses. [ABSTRACT FROM AUTHOR]

This experimental study addresses late transition stages over a conventional airfoil at Reynolds numbers of several ten thousands. The study is based on extensive volumetric flow measurements using constant temperature anemometry. This technique provided both the time-averaged description of the flow field in the vicinity of the wing and the high fidelity spectral analysis inside the separated boundary layer. Large cellular flow structures were observed above the wing. They resemble the stall cells at Reynolds numbers of a few hundred thousands and separation cells at Reynolds numbers of a few hundred. It is shown that most of the energy of the velocity fluctuations within the boundary layer over the forward half of the wing is concentrated in the low-frequency range of the spectrum, where the chord-based Strouhal number is small as compared with unity. [ABSTRACT FROM AUTHOR]

In this work, the spectral equilibrium theory of Ishihara et al. [Phys. Rev. Lett. 88, 154501 (2002)] is applied to Rayleigh-Taylor turbulence. With the help of Canuto and Dubovikov's model [V. Canuto and M. Dubovikov, Phys. Fluids 8, 571 (1996)] closed expressions for the anisotropic spectra of velocity and density, valid in the inertial range, are derived. Based on this result, the main properties of Rayleigh-Taylor turbulence at small scales are discussed. These theoretical results are compared against a direct numerical simulation of a Rayleigh-Taylor mixing zone. [ABSTRACT FROM AUTHOR]

The Kolmogorov's 4/5 law is often considered as the sole exact relationship of inertial range statistics. Its asymptotic character, however, has been evidenced, investigating the finite Reynolds number (FRN) effect for the third-order structure function S3(r) (e.g., for longitudinal velocity increments with r separation length) using variants of the Kármán-Howarth equation in physical space. Similar semi-empirical fits were proposed for the maximum of the normalized structure function, C3 = -maxrS3(r)/(&eh;r), expressing C3 - 4/5 as a power law of the Taylor-based Reynolds number. One of the most complete studies in this domain is by Antonia and Burratini [J. Fluid Mech. 550, 175 (2006)]. Considering that these studies are based on a model for the unsteady second-order structure function S2(r,t), with no explicit model for the third-order structure function itself, we propose to revisit the FRN effect by a spectral approach, in the line of Qian [Phys. Rev. E 55, 337 (1997), Phys. Rev. E 60, 3409 (1999)]. The spectral transfer term T(k,t), from which S3(r,t) is derived by an exact quadrature, is directly calculated by solving the Lin equation for the energy spectrum E(k,t), closed by a standard triadic (or three-point) theory, here Eddy Damped Quasi Normal Markovian. We show that the best spectral approach to the FRN effect is found by separately investigating the negative (largest scales) and positive (smaller scales) bumps of the transfer term, and not only by looking at the maximum of the spectral flux or [formula]. In the forced case, previous results are well reproduced, with Reynolds numbers as high as Reλ = 5 000 to nearly recover the 4/5 value. In the free decay case, the general trend is recovered as well, with an even higher value of Reλ = 50 000, but the EDQNM plots are systematically below those in Antonia and Burattini [J. Fluid Mech. 550, 175 (2006)]. This is explained by the sensitivity to initial data for E(k) in solving the Lin equation at moderate Reynolds numbers. Accordingly, an ad hoc initialization yields results consistent with the experimental spectrum measurements of Comte-Bellot and Corrsin [J. Fluid Mech. 48(2), 273 (1971)], from which S3(r) are recalculated. Present results show that the dispersion observed in existing data at low Reynolds number may be due to sensitivity to initial spectrum shape, a feature of the flow which is not under control in most of laboratory experiments. [ABSTRACT FROM AUTHOR]

We investigate the influence of uncertainties in the shape of the energy spectrum over the Smagorinsky ['General circulation experiments with the primitive equations. I: The basic experiment,' Mon. Weather Rev. 91(3), 99 (1963)] subgrid scale model constant CS: the analysis is carried out by a stochastic approach based on generalized polynomial chaos. The free parameters in the considered energy spectrum functional forms are modeled as random variables over bounded supports: two models of the energy spectrum are investigated, namely, the functional form proposed by Pope [Turbulent Flows (Cambridge University Press, Cambridge, 2000)] and by Meyers and Meneveau ['A functional form for the energy spectrum parametrizing bottleneck and intermittency effects,' Phys. Fluids 20(6), 065109 (2008)]. The Smagorinsky model coefficient, computed from the algebraic relation presented in a recent work by Meyers and Sagaut ['On the model coefficients for the standard and the variational multi-scale Smagorinsky model,' J. Fluid Mech. 569, 287 (2006)], is considered as a stochastic process and is described by numerical tools streaming from the probability theory. The uncertainties are introduced in the free parameters shaping the energy spectrum in correspondence to the large and the small scales, respectively. The predicted model constant is weakly sensitive to the shape of the energy spectrum when large scales uncertainty is considered: if the large-eddy simulation (LES) filter cut is performed in the inertial range, a significant probability to recover values lower in magnitude than the asymptotic Lilly-Smagorinsky model constant is recovered. Furthermore, the predicted model constant occurrences cluster in a compact range of values: the correspondent probability density function rapidly drops to zero approaching the extremes values of the range, which show a significant sensitivity to the LES filter width. The sensitivity of the model constant to uncertainties propagated in the small scales of the energy spectrum is noticeable and a wide range of possible Smagorinsky model constant values is observed, if the LES filter cut is performed close to the dissipation region. [ABSTRACT FROM AUTHOR]

In a recent paper by C. Bogey, O. Marsden, and C. Bailly ['Large-eddy simulation of the flow and acoustic fields of a Reynolds number 105 subsonic jet with tripped exit boundary layers,' Phys. Fluids 23(3), 035104 (2011)], simulation results were presented for round jets with tripped boundary layers, displaying nozzle-exit conditions typical of initially nominally turbulent, transitional jets, namely laminar mean velocity profiles and high fluctuation intensities. The velocity spectra evaluated just downstream of the nozzle exit are re-examined here with respect to literature data. They agree qualitatively very well with spectra obtained in a fully turbulent pipe flow using direct numerical simulation. The wave numbers dominating in the azimuthal direction are also consistent with measurements of spanwise energy distribution in fully turbulent boundary layers. The initial turbulent structures in the jets, therefore, appear to be organized similarly to those in fully developed wall-bounded flows. [ABSTRACT FROM AUTHOR]

We consider high Reynolds number, freely-decaying, isotropic turbulence in which the large scales evolve in a self-similar manner when normalized by the integral scales, u and ℓ. As it is well known, a range of possible behaviors may be observed depending on the form of the longitudinal velocity correlation at large separation, u2f∞=u2f(r→∞). We consider the cases u2f∞=cmr-m,2≤m≤6, whose spectral counterpart is E(k→0)~cmkm-1 for m<6, with or without a lnk correction, and E(k→0)~Ik4 for m=6. (I is Loitsyansky's integral.) It has long been known that the cm are invariants for m<6, which demands u2ℓm=constant during the decay. This, in turn, sets the energy decay rate as u2~t-(1-p)2m/(m+2), where p is the power-law exponent for the normalized dissipation rate, &eh;ℓ/&eh;ℓu3u3~t-p, observed empirically to be a small positive number in grid turbulence. We systematically explore the properties of these different classes of turbulence and arrive at the following conclusions. (i) The invariance of cm is a direct consequence of linear momentum conservation for m≤4, and angular momentum conservation for m=5. (ii) The classical spectra of Saffman, E(k→0)~c3k2, and Batchelor, E(k→0)~Ik4, are robust in the sense that they emerge from a broad class of initial conditions. In particular, it is necessary only that <ωiω'j>∞≤O(r-8) at t=0. The non-classical spectra (m=2,4,5), on the other hand, require very specific initial conditions in order to be realized, of the form <ωiω'j>∞=O(r-(m+2)). (Note the equality rather than the inequality here.) This makes the non-classical spectra less likely to be observed in practice. (iii) The case of m=2, which is usually associated with the u2~t-1 decay law, is pathological in a number of respects. For example, its spectral tensor diverges as k→0, and the long-range correlations ∞=O(r-2) are too strong to be a consequence of the Biot-Savart law. (It is the Biot-Savart law that lies behind the long-range correlations in the classical spectra.) This suggests that m=2 spectra are unlikely to manifest themselves in grid turbulence. A detailed review of the available experimental data is consistent with this assertion. We conclude, therefore, that the minimum energy decay rate in homogeneous grid turbulence is most probably that of Saffman turbulence. [ABSTRACT FROM AUTHOR]

The length scales of the spectra and correlation functions of the velocity fluctuations in the overlap region of turbulent wall-bounded flows are analyzed. It is found that a mixing length based on the mean local shear works better as a normalization than the distance to the wall. To define an overlap range sufficiently long and independent of the Reynolds number to allow the two scalings to be tested, the classical asymptotic expansion of the mean shear is extended to include a near-wall virtual origin and a wake component. The result represents well the velocity profile in y+ > 70 and y/δ < 0.3 - 0.5 for Reτ≿2000, and the spectral scales for Reτ≿500. It is suggested that the scaling with a local mixing length could be interpreted as an indication that the size of the eddies is more related to the local shear time scale than to the interaction with the wall. It is also noted that the linearity of the mixing length is a more robust indicator of a logarithmic regime than those that rely on a zero virtual origin. [ABSTRACT FROM AUTHOR]

The stretched spiral vortex [T. S. Lundgren, 'Strained spiral vortex model for turbulent structures,' Phys. Fluids 25, 2193 (1982)] is identified in turbulence in homogeneous shear flow and the spectral properties of this flow are studied using direct-numerical simulation data. The effects of mean shear on the genesis, growth, and annihilation processes of the spiral vortex are elucidated, and the role of the spiral vortex in the generation of turbulence is shown. As in homogeneous isotropic turbulence [K. Horiuti and T. Fujisawa, 'The multi mode stretched spiral vortex in homogeneous isotropic turbulence,' J. Fluid Mech. 595, 341 (2008)], multimodes of the spiral vortex are extracted. Two symmetric modes of configurations with regard to the vorticity alignment along the vortex tube in the core region and dual vortex sheets spiraling around the tube are often educed. One of the two symmetric modes is created by a conventional rolling-up of a single spanwise shear layer. Another one is created by the convergence of the recirculating flow or streamwise roll [F. Waleffe, 'Homotopy of exact coherent structures in plane shear flows,' Phys. Fluids 15, 1517 (2003)] caused by the upward and downward motions associated with the streaks. The vortex tube is formed by axial straining and lowering of pressure in the recirculating region. The spanwise shear layers are entrained by the tube and they form spiral turns. The latter symmetric mode tends to be transformed into the former mode with lapse of time due to the action of the pressure Hessian term. The power law in the inertial subrange energy spectrum is studied. The base steady spectrum fits the equilibrium Kolmogorov -5/3 spectrum, to which a nonequilibrium component induced by the fluctuation of the dissipation rate [variant_greek_epsilon] is added. This component is extracted using the conditional sampling on [variant_greek_epsilon], and it is shown that it fits the -7/3 power in accordance with the statistical theory. The correlation between these spectra and the appearance and diminution of the streaks and the two modes of the spiral vortex is discussed. The temporal variations of the spectrum are divided into two regimes, Phases 1 and 2. Large energy contained in the low-wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of -7/3 power component. [ABSTRACT FROM AUTHOR]

Using spectrally accurate, direct numerical simulations, we show that vortices with axial flows (without an imposed strain) generate small scales, i.e., breakdown, when they are randomly perturbed. We show that the breakdown that occurs without the necessity of a stagnation point in the flow is nonlinear and that energy spectra of the breakdown present a range of a k-5/3 scaling (k being a wavenumber). These features are the same for centrifugally stable and unstable azimuthal velocities. However, centrifugally unstable azimuthal velocities promote mixing in vortices with an axial flow. We also find that vortex breakdown could be a physical mechanism against a finite time singularity in Navier-Stokes equations. Contrarily, we do not observe a breakdown using spectrally truncated Euler equations. For these equations we find a scaling of the energy spectra compatible with the existence of a finite time singularity. [ABSTRACT FROM AUTHOR]

The spectrum of a signal consisting of a sum of localized random bursts can exhibit, under certain conditions, an intermediate subrange evolving as the power -3 of the wavenumber k. These bursts should have a smooth and regular pattern, their strength and size should be statistically independent, and their size should be uniformly distributed between two finite wavelengths. This is probably the explanation for the k-3 subrange that is commonly observed in the velocity spectra of bubble-induced turbulence, which results from the interaction of the localized velocity disturbances caused by the bubbles. [ABSTRACT FROM AUTHOR]

The refraction of a spectrum of short internal waves by a packet of inertia waves is considered. It is found that a short inertia-wave packet produces a larger net change in a spectrum of short waves than a long inertia-wave packet, provided the short waves are trapped at some time during the interaction. Specifically, an incident narrow-banded short-wave spectrum broadens more quickly and more fully when refracted by the short inertia-wave packet. The results are explained in terms of a frequency conservation law, which constrains short-wave change in the limit of a long inertia-wave packet. [ABSTRACT FROM AUTHOR]

In this paper, direct numerical simulation of fully developed turbulent pipe flow is carried out at Reτ≈170 and 500 to investigate the effect of the streamwise periodic length on the convergence of turbulence statistics. Mean flow, turbulence intensities, correlations, and energy spectra were computed. The findings show that in the near-wall region (below the buffer region, r+≤30), the required pipe length for all turbulence statistics to converge needs to be at least a viscous length of O(6300) wall units and should not be scaled with the pipe radius (δ). It was also found for convergence of turbulence statistics at the outer region that the pipe length has to be scaled with pipe radius and a proposed pipe length of 8πδ seems sufficient for the Reynolds numbers considered in this study. [ABSTRACT FROM AUTHOR]

Linear forcing has been proposed as a useful method for forced isotropic turbulence simulations because it is a physically realistic forcing method with a straightforward implementation in physical-space numerical codes [T. S. Lundgren, 'Linearly forced isotropic turbulence,' Annual Research Briefs (Center for Turbulence Research, Stanford, CA, 2003), p. 461; C. Rosales and C. Meneveau, 'Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,' Phys. Fluids 17, 095106 (2005)]. Here, extensions to the compressible case are discussed. It is shown that, unlike the incompressible case, separate solenoidal and dilatational parts for the forcing term are necessary for controlling the stationary state of the compressible case. In addition, the forcing coefficients can be cast in a form that allows the control of the stationary state values of the total dissipation (and thus the Kolmogorov microscale) and the ratio of dilatational to solenoidal dissipation. Linear full spectrum forcing is also compared to its low wavenumber restriction. Low wavenumber forcing achieves much larger Taylor Reynolds number at the same resolution. Thus, high Reynolds number asymptotics can be more readily probed with low wavenumber forced simulations. Since, in both cases, a solenoidal/dilatational decomposition of the velocity field is required, the simplicity of the full spectrum linear forcing implementation in physical-space numerical codes is lost. Nevertheless, low wavenumber forcing can be implemented without using a full Fourier transform, and so is computationally less demanding. [ABSTRACT FROM AUTHOR]

We investigate, through both asymptotic and numerical analysis, precessionally driven flows of a homogeneous fluid confined in a spherical container that rotates rapidly with angular velocity Ω and precesses slowly with angular velocity Ωp about an axis that is fixed in space. The precessionally driven flows are primarily characterized by two dimensionless parameters: the Ekman number E providing the measure of relative importance between the viscous force and the Coriolis force, and the Poincaré number Po quantifying the strength of the Poincaré forcing. When E is small but fixed and |Po| is sufficiently small, we derive a time-dependent asymptotic solution for the weakly precessing flow that satisfies the nonslip boundary condition in the mantle frame of reference. No prior assumption about the spatial-temporal structure of the precessing flow is made in the asymptotic analysis. A solvability condition is derived to determine the spatial structure of the precessing flow, via a selection from a complete spectrum of spherical inertial modes in the mantle frame. The weakly precessing flow within the bulk of the fluid is characterized by an inertial wave moving retrogradely. Direct numerical simulation of the same problem in the same frame of reference shows a satisfactory agreement between the time-dependent asymptotic solution and the nonlinear numerical simulation for sufficiently small Poincaré numbers. [ABSTRACT FROM AUTHOR]

The present work examines the combined influence of orientation and buoyancy on vortex shedding from a heated square cylinder with the main flow in the vertically upward direction in the aiding buoyancy configuration. The wake of the cylinder is imaged by a schlieren technique. The study investigates the effect of buoyancy, Reynolds number, and angle of incidence of square cylinder with respect to the incoming flow. The Reynolds numbers based on the cylinder edge have been set equal to 56, 87, and 100. Eight different orientations (θ=0°, 5°, 10°, 15°, 20°, 30°, 40°, and 45°) and a Richardson number range of 0.031–0.291 have been considered. Instantaneous as well as time-averaged schlieren images, velocity profiles, vortex formation length, Strouhal number, and power spectra are reported. Results show that there is no vortex shedding at Re=56 for the zero angle of incidence. Vortex shedding is initiated at this Reynolds number for a higher angle of incidence, indicating that cylinder orientation plays a favoring role in destabilizing the wake. For orientations other than 0° and 45°, the time-averaged wake is asymmetric. With an increase in the angle of incidence, the shear layers roll up over a shorter distance. With heating, the fluid particles in the shear layer are further accelerated and a marginal increase in Strouhal number with Richardson number is observed. As the heating level increases to a higher value, buoyancy delivers sufficient momentum into the wake, diminishes the velocity deficit, and completely eliminates vortex shedding. Suppression of vortex shedding is observed at a certain critical Richardson number that depends on Reynolds number and the angle of incidence. The approach toward complete suppression and the corresponding wake structures are of interest. The present study demonstrates that the properties of the cylinder wake are intricately related to both the heating level and its orientation relative to the incoming flow. [ABSTRACT FROM AUTHOR]

Traveling-wave solutions of the inviscid Burgers equation having smooth initial wave profiles of suitable shapes are known to develop shocks (infinite gradients) in finite times. Such singular solutions are characterized by energy spectra that scale with the wave number k as k-2. In the presence of viscosity ν>0, no shocks can develop, and smooth solutions remain so for all times t>0, eventually decaying to zero as t→∞. At peak energy dissipation, say t=t*, the spectrum of such a smooth solution extends to a finite dissipation wave number kν and falls off more rapidly, presumably exponentially, for k>kν. The number N of Fourier modes within the so-called inertial range is proportional to kν. This represents the number of modes necessary to resolve the dissipation scale and can be thought of as the system’s number of degrees of freedom. The peak energy dissipation rate ε remains positive and becomes independent of ν in the inviscid limit. In this study, we carry out an analysis which verifies the dynamical features described above and derive upper bounds for ε and N. It is found that ε satisfies ε≤ν2α-1|u*|∞2(1-α)|(-Δ)α/2u*|2, where α<1 and u*=u(x,t*) is the velocity field at t=t*. Given ε>0 in the limit ν→0, this implies that the energy spectrum remains no steeper than k-2 in that limit. For the critical k-2 scaling, the bound for ε reduces to ε≤3k0|u0|∞|u0|2, where k0 marks the lower end of the inertial range and u0=u(x,0). This implies N≤3L|u0|∞/ν, where L is the domain size, which is shown to coincide with a rigorous estimate for the number of degrees of freedom defined in terms of local Lyapunov exponents. We demonstrate both analytically and numerically an instance, where the k-2 scaling is uniquely realizable. The numerics also return ε and t*, consistent with analytic values derived from the corresponding limiting weak solution. [ABSTRACT FROM AUTHOR]

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899 (2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20°≤θ≤30° (θ=0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20°≤θ≤30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough. [ABSTRACT FROM AUTHOR]

Combined experimental and numerical study of spatial evolution of unidirectional random water-waves is performed. Numerous realizations of wave fields all having identical initial narrow-banded Gaussian power spectrum but random phases for each harmonic were generated by a wavemaker in a 300 m long wave tank. The measured in the vicinity of the wavemaker temporal variation of the surface elevation was used to determine the initial conditions in the numerical simulations. The cubic Schrödinger equation (CSE) and the modified nonlinear Schrödinger (MNLS) set of equations due to Dysthe were used as the theoretical models. The detailed comparison of the evolution of the wave field along the tank in individual realizations, measured by wave gauges at different distances from the wavemaker and computed using the two theoretical models, was performed. Numerous statistical wave parameters were calculated based on the whole ensemble of realizations. Comparison of the spatial variation of the computed statistical characteristics of the random wave field with laboratory measurements indicates that contrary to the deterministic case, ensemble averaged statistical parameters derived from the CSE simulations compare reasonably well with the experiments and with the results derived from the MNLS model simulations. In particular, simulations based on both models indicate that the statistical characteristics of the random wave field depend on the local width of frequency spectrum and deviate from the Gaussian statistics: the probability of extremely large (the so-called freak) waves is highest when the local spectral width attains maximum. In view of the satisfactory agreement of the numerical results with the laboratory experiments, the computational domain was extended to distances exceeding twice the actual length of the tank and long-scale (at distances approaching 200 dominant wavelengths) variation of the statistical parameters is studied. [ABSTRACT FROM AUTHOR]

Stationary and flying single hot-wire measurements were made to investigate the near to intermediate field in a round free turbulent jet. Measurements were carried out at Reynolds numbers ReD based on the jet exit mean velocity and the nozzle diameter, between 6000 and 100 000. The objective of this study was to investigate the concept of a mixing transition proposed by Dimotakis [“The mixing transition in turbulent flows,” J. Fluid Mech. 409, 69 (2000)]. This was done through the measurement of the velocity spectra and the calculation of Kolmogorov λK, Taylor microscale λT, the Liepmann–Taylor microscale λL, and the viscous length scale λν at different positions in the near to intermediate regions of a round free jet. The present results demonstrate the local nature of mixing transition. It is found that the Kolmogorov, Taylor, and viscous length scales all decrease in magnitude with the local Reynolds number Reδ based on the local center line mean velocity and the local time-averaged diameter of the jet and appear to be only weakly dependent on the radial position, although the ratio ReT/Reδ1/2 varies nonlinearly across the jet radius. The ratio of the laminar to viscous length scale exceeds unity beyond the potential core of the jet. Moreover, the skewness of the axial velocity is approximately -0.4 over 30

For moderate Reynolds numbers, the spectral scaling exponents of both velocity [E(k)∝k-mu] and the transported passive scalar [Eθ(k)∝k-mθ] fields exhibit departures from the asymptotic prediction mu=mθ=5/3. However, at the same Reynolds number, the passive scalar spectrum for homogeneous isotropic turbulence is closer to the universal asymptotic state than the dynamic velocity field that transports it. This paper provides a possible explanation for this behavior, in the case of a gaseous mixing with Prandtl (or Schmidt) number Pr≃1. A scenario of the scalar energy transfer toward higher wavenumbers is proposed and validated using experimental data, in which the velocity field itself is actively involved via its characteristic time. A direct relationship between velocity and scalar spectra and therefore between mu and mθ is thus established. [ABSTRACT FROM AUTHOR]

Continuous spectrum amplitude distributions are calculated for transiently growing roughness-induced perturbations in a flat-plate boundary layer. A direct method is employed when the complete flow is known via direct numerical simulation. A new method using regularizing functionals is developed for calculating the distributions when only partial experimental data are available. These amplitude distributions provide a way of rigorously characterizing the boundary layer receptivity to surface roughness. Contrasting the present results to optimal theory results conclusively demonstrates that roughness-induced disturbances cannot be described by optimal disturbance calculations. The continuous spectrum analysis demonstrates the linearity of the perturbations by correctly reproducing the flow evolution over the measurement domain. Extracting the continuous spectrum amplitudes using the partial data technique reveals the underlying vortex behavior that creates transient growth. The method described is amenable to future work with realistic distributed roughness and complex surface geometries. [ABSTRACT FROM AUTHOR]