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Using empirical orthogonal function analysis, a stationary atmospheric wavenumber-4 (AW4) pattern is identified in the Southern mid-latitudes during austral summer. The generation mechanism and its linkage to the Southern Hemisphere climate are explored using a linear response model and composite analysis. It is found that AW4 pattern is forced by a Rossby wave source in the upstream region of the upper-tropospheric westerly waveguide. The vortex stretching associated with the anomalous convection over the subtropical western Pacific Ocean (near the New Zealand coast) adjacent to the westerly jet triggers the Rossby wave train around mid-November. This disturbance gets trapped in the Southern Hemisphere westerly jet waveguide and circumnavigates the globe. Around 15–25 days later (in early December), a steady AW4 pattern is established in the Southern mid-latitudes. Further, correlation analysis suggests the AW4 pattern is independent of other natural variabilities such as El Nino/Southern Oscillation, Southern Annular Mode, and Indian Ocean Dipole. The AW4 pattern is found to influence the rainfall over different parts of South America and Australia by modulating upper-level divergence.

The life cycle dynamics and intensification processes of three long-duration tropical cyclones (TCs), viz., Fani (2019), Luban (2018), and Ockhi (2017) formed over the North Indian Ocean (NIO) have been investigated by developing a high-resolution (6 km × 6 km) mesoscale analysis using WRF and En3DVAR data assimilation system. The release of CAPE in nearly saturated middle-level relative humidity caused intense diabatic heating, leading to an increase in low-level convergence triggering rapid intensification (RI). The strengthening of the relative vorticity tendency terms was due to vertical stretching (TC Fani) and middle tropospheric advection (TCs Luban and Ockhi). The increase or decrease in upper-tropospheric divergence led to RI through two different mechanisms. The increase in upper divergence strengthens the vortical convection (in TC Luban and Fani) by enhancing the moisture and heat transport, whereas its decrease caused a reduction in the upper-level ventilation flow at 200 hPa followed by moisture accumulation, enhanced diabatic heating, and strengthened the warm core (TC Ockhi). The RI caused the vortex of three cyclones to extend up to the upper troposphere. The well organised wind during RI led the unorganised, weak, discontinuous vertical vortex columns to become organised with intense vertical velocity throughout the column. Spatial distributions of Okubo–Wiess (OW) parameter showed TC core dominated by vorticity than strain, since deep depression (DD) stages.

We consider a family of nonlocal problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish stable self-similar blow-up near a family of known self-similar blow-up solutions.

To better understand the coupled dynamics of turbulence and premixed flames, this study experimentally investigates the effects of turbulence on reacting vorticity dynamics. In this investigation, a bluff-body stabilized, turbulent, premixed flame is analyzed in a high-speed combustor. A custom-designed turbulence generator is used to vary the inflow turbulence conditions and understand the subsequent impacts on the flame-flow field. The turbulent reacting flow-field is measured using simultaneous high-speed particle imaging velocimetry (PIV) and CH* chemiluminescence. A Lagrangian tracking method is implemented to study flame-vortex dynamics. Lagrangian fluid elements are tagged from the experimental data and are tracked as they convect through the flame, from reactants to products. The components of the vorticity transport equation are decomposed along the Lagrangian trajectories to determine their relative balance under various turbulence conditions. The results confirm that altering the turbulence intensity influences flame-vortex interactions and the relative balance of the vorticity components. At high turbulence intensities, the baroclinic torque and dilatation decrease, while the magnitude of viscous diffusion increases, and vortex stretching dominates the reacting flow field. These results suggest that increasing the turbulence intensity alters the dominant physical processes in the reacting domain as the combustion-driven phenomena become less significant.

The turbulent cavitating flow around the propelling pump tip clearance is numerically simulated using the large eddy simulation (LES) method coupled with the Zwart-Gerber-Belamri (ZGB) cavitation model to investigate the cavitation-vortex interaction mechanism. The calculated cavitation structures around the blades are in a remarkable agreement with the experimental results. The distributions of the tip clearance vortex under two cavitation conditions are obtained and compared. The results show that the cavitation development enhances the vorticity generation and the flow unsteadiness around the tip clearance of a propelling pump. Vortices are basically located around the cavitation areas, particularly in the tip clearance region, during the cavitation. The relative vorticity transport equation is applied for the cavitating turbulent flows and it is further indicated that the vortex stretching term makes the main contribution in the vortex production, and the baroclinic torque and dilation terms are important source terms for the vorticity generation in the cavitating flow. In addition, the viscous diffusion term and the Coriolis force term are significant in modifying the vorticity field inside the blade tip clearance.

Inter-blade cavitation vortex is substantially considered as a particular cavitation flowing phenomenon associated with liquid transportation in Francis turbine. It causes several adverse effects on the pressure and velocity fields and cannot be eliminated by hydraulic design or optimization. This paper presents the numerical and experimental investigations on cavitation fluid for a reduced scale model of Francis turbine. The inter-blade cavitation vortex structure predicted by numerical simulation yields a very good validation against the experimental visualization. The vapor volume caused by cavitation flowing oscillates periodically and is accompanied by the precessing frequency of inter-blade vortex that is equivalent to the rotational frequency of the runner. Flow separation induced by negative incident angle at the leading edge of runner is identified as the main reason for the incipient and development of the inter-blade cavitation vortex. Cavitation-vortex interaction analysis in terms of the relative vorticity transport equation evidently shows that the vortex stretching term and Coriolis force term always significantly influence the vorticity production near the suction side of the runner blades while the dilatation term and baroclinic torque term play decisive roles on vorticity development adjacent to the vortex center.

A diagnostic framework is developed to explain the response of tropical cyclones (TCs) to climate in high-resolution global atmospheric models having different complexity of boundary conditions. The framework uses vortex dynamics to identify the large-scale control on the evolution of TC precursors—first non-rotating convective clusters and then weakly rotating seeds. In experiments with perturbed sea surface temperature (SST) and $$\hbox {CO}_2$$ CO 2 concentration from the historical values, the response of TCs follows the response of seeds. The distribution of seeds is explained by the distribution of the non-rotating convective clusters multiplied by a probability that they transition to seeds. The distribution of convective clusters is constrained by the large-scale vertical velocity and is verified in aquaplanet experiments with shifting Inter tropical Convergence Zones. The probability of transition to seeds is constrained by the large-scale vorticity via an analytical function, representing the relative importance between vortex stretching and vorticity advection, and is verified in aquaplanet experiments with uniform SST. The consistency between seed and TC responses breaks down substantially when the realistic SST is perturbed such that the spatial gradient is significantly enhanced or reduced. In such cases, the difference between the responses is explained by a change in the ventilation index, which influences the fraction of seeds that develop into TCs. The proposed TC-climate relationship serves as a framework to explain the diversity of TC projection across models and forcing scenarios.

Author(s): Paloczy, Andre; McClean, Julie L; Gille, Sarah T; Wang, He | Abstract: ABSTRACTThe depth-integrated vorticity budget of a global, eddy-permitting ocean/sea ice simulation over the Antarctic continental margin (ACM) is diagnosed to understand the physical mechanisms implicated in meridional transport. The leading-order balance is between the torques due to lateral friction, nonlinear effects, and bottom vortex stretching, although details vary regionally. Maps of the time-averaged depth-integrated vorticity budget terms and time series of the spatially averaged, depth-integrated vorticity budget terms reveal that the flow in the Amundsen, Bellingshausen, and Weddell Seas and, to a lesser extent, in the western portion of East Antarctica, is closer to an approximate topographic Sverdrup balance (TSB) compared to other segments of the ACM. Correlation and coherence analyses further support these findings, and also show that inclusion of the vorticity tendency term in the response (the planetary vorticity advection and the bottom vortex stretching term) increases the correlation with the forcing (the vertical net stress curl), and also increases the coherence between forcing and response at high frequencies across the ACM, except for the West Antarctic Peninsula. These findings suggest that the surface stress curl, imparted by the wind and the sea ice, has the potential to contribute to the meridional, approximately cross-slope, transport to a greater extent in the Amundsen, Bellingshausen, Weddell, and part of the East Antarctic continental margin than elsewhere in the ACM.

We consider the 3D incompressible Navier–Stokes equations under the following $$2+\frac{1}{2}$$ -dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove enhanced dissipation induced by such vortex-stretching.

Based on fine-resolution simulations, we present a case study of the frontogenetic generation of submesoscale flows associated with a convergence field inside an anticyclonic mesoscale eddy in the Kuroshio Extension. The results reveal that the generation of submesoscale flows on the edge of the eddy is closely related to the convergent zone in the ageostrophic secondary circulation (ASC) that develops from frontal sharpening. Diagnostic analysis of the frontal tendency based on flow decomposition shows that frontal sharpening is initiated by mesoscale strain and accelerated by submesoscale convergence. With convergence on the cold side and divergence on the warm side of fronts, submesoscale divergent fields contribute to the asymmetry of the frontal tendency because the fronts tend to be strengthened by convergent motions and weakened by divergent motions. During frontal sharpening, the cross-front ASCs generate additional positive vorticity in their downwardbranches characterized by convergence via vortex stretching, which involves neighboring submesoscale vortices. Moreover, the enhanced lateral buoyancy gradients and surface buoyancy loss are conducive to triggering symmetric instability (SI) and ageostrophic anticyclonic instability (AAI) on the edge of the eddy. In response to these submesoscale instabilities and the subsequent slumping of fronts, the removal of kinetic energy (KE) associated with shear flows is comparable to the source of submesoscale KE from the eddy, which indicates that mesoscale energy can be drained by submesoscale instabilities during frontal sharpening. This study focuses on and describes the frontogenetic generation of submesoscale flows in mesoscale eddies in the Kuroshio Extension.

In large eddy simulation (LES) of turbulent flows, dynamic subgrid models would account for an average cascade of kinetic energy from the largest to the smallest scales of the flow. Yet, it is unclear which of the most critical dynamical processes can ensure the criterion mentioned above. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study essential statistical characteristics of vortex stretching. Our numerical results demonstrate that vortex stretching rate provides the energy dissipation rate necessary for modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. The individual and the joint probability of vortex stretching and strain amplification show that vortex stretching rate is highly correlated with the energy cascade rate. Sheet-like flow structures are correlated with viscous dissipation, and vortex tubes are more stretched than compressed. The overall results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

When placed in a canonical flow (straining, rotational, and vortex stretching corresponding to the top, middle, and bottom row), finite-density particles can follow various paths. The present article analytically predicts their long-term behavior, namely, whether they will cluster or disperse or whether their trajectories cross.

Convectively coupled equatorial Kelvin waves (CCKWs) are high-impact tropical weather systems that can lead to severe flooding over the Maritime Continent. Here, a vorticity budget for CCKWs over the Indian Ocean is constructed using reanalysis data, to identify the basic mechanisms of eastward propagation and growth. The budget is reasonably well closed, with a small residual/sub-gridscale term. In the lower troposphere, CCKWs behave like strongly modified theoretical equatorial Kelvin waves. Vortex stretching, from the divergence of the Kelvin wave acting on planetary vorticity (the -fD term), is the sole mechanism by which the vorticity structure of a theoretical Kelvin wave propagates eastward. In the lower and middle troposphere, this term is also the key mechanism for the eastward propagation of CCKWs but, due to subtleties in its structure and phasing linked to a combination of modal structures, it also contributes to growth. Unlike in the theoretical Kelvin wave, other vorticity source terms also play a role in the propagation and growth of CCKWs. In particular, vortex stretching from relative vorticity (the -zeta D term) is the largest source term, and this leads strongly to growth, through interactions between the background and perturbation vorticity and divergence. Horizontal vorticity advection by the background flow contributes to propagation, and also acts to retard the growth of the CCKW. The sum of the source terms in this complex vorticity budget leads to eastward propagation and growth of CCKWs. The structure and vorticity budget of CCKWs in the upper troposphere is quite unlike that of a Kelvin wave, and appears to arise as a forced response to the lower tropospheric structure. The implications for numerical weather prediction and climate simulations are discussed.

In order to study the evolution characteristics of suction-side-perpendicular cavitating vortex in an axial-flow pump under low flow conditions, model tests, high-speed imaging, and an SST-CC turbulence model were used to simulate the external characteristics and cavitation morphology of the pump. The evolution law of suction-side-perpendicular cavitating vortex (SSPCV) was revealed by turbulent kinetic energy, liutex vortex identification, and vorticity transport equation. The results show that the evolution of suction-side-perpendicular cavitating vortex at low cavitation number can be divided into three stages: generation, development, and breaking stage. In the generation stage, the turbulent kinetic energy, velocity gradient and vortex kinetic energy continue to increase, reaching the maximum at the early stage of development. Afterwards, due to the viscosity of the water, the vortex slowly dissipates and enters the stage of development. Finally, it is affected by the next blade and enters the breaking stage, which accelerates the dissipation of the vortex. The vortex stretching term and vortex expansion term are the main contributors to the vorticity. During the development of the vortex, the vorticity is mainly caused by the deformation of the fluid micelle. The breaking stage mainly affects the stretching term, and the Coriolis force term cannot be ignored in the rotating coordinates.

Studies of shock-vortex interactions in the past have predominantly been numerical, with a number of idealizations such as assuming an isolated vortex and a plane shock wave. In the present case the vortex is generated from flow separation at a corner. A shear layer results which wraps up into a spiral vortex. The flow is impulsively initiated by the diffraction of a shock wave over the edge. The strength of the shock determines the nature of the flow at the corner and that induced behind the diffracted wave. A wide variety of cases are considered using different experimental arrangements such as having two independent shock waves arriving at the corner at different times, to reflecting the diffracting wave off different surfaces back into the vortex, and to examining the flow around bends where the reflection off the far wall reflects back onto the vortex. The majority of studies have shown that the vortex normally retains its integrity after shock transit. Some studies with curved shock waves and numerous traverses have shown evidence of vortex breakup and the development of turbulent patches in the flow, as well as significant vortex stretching. Depending on the direction of approach of the shock wave it refracts through the shear layer thereby changing the strength and direction of both. Of particular note is that the two diffracted waves which emerge from the vortex as the incident wave passes through interact with each other resulting in a pressure spike of considerable magnitude. An additional spike is also identified.

Significance The entire Sun completes a full rotation in roughly 28 d. Within the outer 30% of the solar interior, turbulent thermal convection powers fluid outward. Rotation deflects the fluid and determines the morphology of eddies and large-scale shear. Such flows are the ultimate agents of astrophysical and planetary magnetic field generation, one of the most important open problems in all of science. Our results make theoretical predictions regarding the Sun’s internal flow structure and rotational constraint. We predict tall and slender vortices persisting throughout much of the convection zone under the sway of strong rotation. We also clarify previous observational discrepancies and explain why such structures have been hard to reproduce in numerical simulations., The observational absence of giant convection cells near the Sun’s outer surface is a long-standing conundrum for solar modelers. We herein propose an explanation. Rotation strongly influences the internal dynamics, leading to suppressed convective velocities, enhanced thermal-transport efficiency, and (most significantly) relatively smaller dominant length scales. We specifically predict a characteristic convection length scale of roughly 30-Mm throughout much of the convection zone, implying weak flow amplitudes at 100- to 200-Mm giant cells scales, representative of the total envelope depth. Our reasoning is such that Coriolis forces primarily balance pressure gradients (geostrophy). Background vortex stretching balances baroclinic torques. Both together balance nonlinear advection. Turbulent fluxes convey the excess part of the solar luminosity that radiative diffusion cannot. We show that these four relations determine estimates for the dominant length scales and dynamical amplitudes strictly in terms of known physical quantities. We predict that the dynamical Rossby number for convection is less than unity below the near-surface shear layer, indicating rotational constraint.

To understand the effect of cavitation on the tip leakage vortex (TLV), turbulent cavitating flows were numerically investigated using the shear-stress transport (SST) k–ω turbulence model and the Zwart–Gerber–Belamri cavitation model. In this work, two computations were performed—one without cavitation and the other with cavitation—by changing the inlet pressure of the pump. The results showed that cavitation had little effect on the pressure difference between the blade surfaces for a certain cavitation number. Instead, it changed the clearance flow and TLV vortex structure. Cavitation caused the TLV core trajectory to be farther from the suction surface and closer to the endwall upstream of the blade. Cavitation also changed the vortex strength distribution, making the vortex more dispersed. The vortex flow velocity and turbulent kinetic energy were lower, and the pressure pulsation was more intense in the cavitating case. The vorticity transport equation was used to further analyze the influence of cavitation on the evolution of vortices. Cavitation could change the vortex stretching term and delay the vortex bending term. In addition, the vortex dilation term was drastically changed at the vapor–liquid interface.

It is well known from modelling studies that surface topography influences the large-scale atmospheric circulation and that several model biases are associated with incorrect representation of topography. The textbook explanation of topographic effects on large-scale circulation appeals to the theoretical relationship between surface forcing and vortex stretching along trajectories in single-layer models. The goal of this study is to design and use a simple diagnostic of the large-scale forcing on the atmosphere when air is passing over topography, directly from atmospheric fields, based on this theoretical relationship. The study examines the interaction of the atmosphere with the North American Cordillera and samples the flow by means of trajectories during Northern Hemisphere winter. We detect a signal of topographic forcing in the atmospheric dataset, which, although much less distinct than in the theoretical relationship, nevertheless exhibits a number of expected properties. Namely, the signal increases with latitude, is usually stronger upslope than downslope, and is enhanced if the flow is more orthogonal to the mountain ridge, for example during periods of positive PNA. Furthermore, a connection is found between an enhanced signal of topographic forcing downslope of the North American Cordillera and periods of more frequent downstream European blocking.

We prove finite-time singularity formation for De Gregorio's model of the three-dimensional vorticity equation in the class of $L^p\cap C^\alpha(\mathbb{R})$ vorticities for some $\alpha>0$ and $p0$., Comment: 48 pages

A thorough understanding of the internal flow dynamics inside a poppet valve makes sense for an improved control performance. Hence, a numerical simulation for the cavitating jet is performed with main concern on the cavitation-vortex interaction. The periodic cavitation structure, along with corresponding variation in vorticity distribution and large scale eddy, is presented for the quasi-steady flow from numerical results. As expected, cavitation inception exhibits great dependence on coherent structure, which is organized as paired vortex rings. Besides, cavitation is persistently located at core of vortex, indicating strong correlation between cavitation and vortex dynamics. The cavitation-vortex correlation is further discussed with analysis of vorticity transport equation, involving vortex stretching, dilatation and baroclinic torque terms. At incepting stage, vortex stretching is the dominant factor, responsible for vortex growth and the elliptical shape of cavitation ring. In comparison, the dilatation term could produce either enhancement or suppression in local vorticity, depending on the volumetric variation induced by cavitation. During the collapse stage, the bubble collapse creates baroclinic vorticity, and contributes to 3-dimensional vorticity. The most significant finding of the present study is the suppression of vorticity during the growing process of cavitation, contributing to an enhanced understanding of the cavitation-vortex interaction.

A three-dimensional transient round liquid jet within a low-speed coaxial outer gas flow is numerically simulated and analysed via vortex dynamics ($\unicode[STIX]{x1D706}_{2}$ analysis). Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem. First, there are those inside the recirculation zone behind the leading cap – directly affecting the cap dynamics and well explained by the local vortices. Second, deformations upstream of the cap are mainly driven by the Kelvin–Helmholtz (KH) instability, unaffected by the vortices in the behind-the-cap region (BCR), and are important in the eventual atomization process. Different atomization mechanisms are identified and are delineated on a gas Weber number ($We_{g}$) versus liquid Reynolds number ($Re_{l}$) map based on the relative gas–liquid velocity. In a frame moving with the liquid velocity, this result is consistent with prior temporal studies. A simpler and clearer portrait of similarity of the atomization domains is shown by using the relative gas–liquid axial velocity, i.e. $We_{r}$ and $Re_{r}$, and avoiding the widely used velocity ratio as a third key parameter. A detailed comparison of vorticity along the axis in an Eulerian frame versus a frame fixed to a surface wave reveals that the vortex development and surface deformations are periodic in the upstream region, but this periodicity is lost closer to the BCR. In the practical range of the density ratio and for early times in the process, axial vorticity is mainly generated by baroclinicity while streamwise vortex stretching becomes more important at later times and only at lower relative velocities when pressure gradients are reduced. The inertia, vortex, pressure, viscous and surface tension forces are analysed to delineate the dominant causes of the three-dimensional instability of the axisymmetric KH structure due to surface acceleration in the axial, radial and azimuthal directions. The inertia force related to the axial gradient of kinetic energy is the main cause of the axial acceleration of the waves, while the azimuthal acceleration is mainly caused by the pressure and viscous forces. The viscous forces are negligible in the radial direction and away from the nozzle exit in the axial direction. It is interesting to note that azimuthal viscous forces are important even at high $Re_{l}$, indicating that inertia is not totally dominant in this instability occurring early in the atomization cascade.

The contributions of vortex stretching, dilatation, baroclinic torque and viscous diffusion to Reynolds-averaged enstrophy transport in turbulent swirl flames were experimentally measured using tomographic particle image velocimetry and$\text{CH}_{2}\text{O}$planar laser induced fluorescence at jet Reynolds numbers of 26 000–51 000. The mean baroclinic torque was determined by subtracting the other terms in the enstrophy transport equation from the mean Lagrangian derivative. Enstrophy production from baroclinic torque was found to be significant relative to the other transport terms across all conditions studies. This result contrasts with direct numerical simulations of flames in homogeneous isotropic turbulence, which show a decreasing relative significance of baroclinic torque with increasing turbulence intensity (e.g. Bobbitt, Lapointe & Blanquart,Phys. Fluids, vol. 28 (1), 2016, 015101). Hence, the significance of baroclinic enstrophy production in flames is not determined entirely by the local turbulence and flame properties, but also depends on the configuration-specific pressure field.

This paper investigates the coupling between the rotational and divergent circulations aiming to explain the observations that show that the tropical eddy momentum flux is due to correlations between divergent eddy meridional velocities and rotational eddy zonal velocities. A simple linear model in which the observed eddy divergence field is used to force the vorticity equation can reproduce quite well the observed tropical eddy momentum flux. The eddy momentum flux in the model shows little sensitivity to the basic-state winds and is mainly determined by the characteristics of the divergent forcing. Vortex stretching and divergent advection of planetary vorticity produce eddy momentum flux contributions with the same sign but the former forcing dominates. It is shown that the main factor affecting the direction of the eddy momentum flux response to both forcings is the meridional tilt of the divergence phase lines, albeit with an opposite sign to the classical relation between rotational momentum flux and streamfunction phase tilt. How this divergent structure is determined remains an open question.

Two and three dimensional large eddy simulations of a spatially developing supersonic mixing layer are performed using an in-house hybrid finite volume code that combines a fourth order non-dissipative MacCormack scheme for capturing turbulence and a second order SLAU2 upwind scheme for capturing shocks and other discontinuities in the flow. Three-dimensional predictions of growth rate and statistical moments in the self similar regime are consistent with past experimental and direct numerical simulation studies. The peak values of the transverse turbulence stresses are over predicted in two dimensional simulations. This may be attributed to the lack of vortex stretching and the lack of significant energy transfer to the smaller scales. This also leads to sustenance, pairing and overall growth of large coherent structures that result in an over-prediction of growth rate by about 20%.

A safe revision of current aircraft separation minima requires detailed knowledge of the vortex decay and its effect on encountering aircraft. The wake vortex system generated by an aircraft rolls ...

Numerical investigations of the supersonic axisymmetric base flow at Mach number 2.46 and Reynolds number 2.858 × 10 6 are carried out using the scale-adaptive simulation (SAS) approach. To achieve SAS computation, three mathematical forms of von Karman length scale are utilized. The first one is calculated from the strain rate tensor and second derivative of the velocity field (this SAS can be marked as “SAS-1”). Computation of the second one is employed using the vorticity and its first derivative (this SAS can be denoted as “SAS-2”). The third one is computed from the vorticity and the second derivative of the velocity field (this SAS can be named as “SAS-3”). Their effects on the quantitative predictions are assessed. Two inflow conditions are also investigated, i.e., inflow condition with/without turbulent-boundary-layer profiles. Results show that the inflow conditions have the significant effects on the base-pressure and streamwise velocity distributions, and the predicted results at the inflow condition with profiles show better agreement with experimental data than that at the inflow condition without profiles. The inflow conditions and von Karman length scales only have the relatively slight effects on the radial velocity distributions. Similarly, at the inflow condition with profiles, the base-pressure distributions are also not sensitive to mathematical forms of von Karman length scale. More comparisons reveal that the best predictions can be obtained by SAS-2 and SAS-3. It may be associated with the vortex stretching effects explicitly considered in the von Karman length scales of SAS-2 and SAS-3. Although the mean flow field predicted by SAS-2 is slightly better than that obtained by SAS-3. However, SAS-3 can give the slightly better predictions for the Reynolds stresses than SAS-2.

This study investigates the vertical structure of the dynamical properties of a warm-core ring in the Gulf of Mexico (Loop Current ring) using glider observations. We introduce a new method to correct the glider’s along-track coordinate which is, in general, biased by the unsteady relative movements of the glider and the eddy, yielding large errors on horizontal derivatives. Here, we take advantage of the synopticity of satellite along-track altimetry to apply corrections on the glider’s position, by matching in situ steric height with satellite-measured sea surface height. This relocation method allows to recover the eddy’s azimuthal symmetry, to precisely estimate the rotation axis position, and to compute reliable horizontal derivatives. It is shown to be particularly appropriate to compute the eddy’s cyclo-geostrophic velocity, relative vorticity, and shear strain, which are otherwise out of reach when using the glider’s raw traveled distance as an horizontal coordinate. The Ertel potential vorticity (PV) structure of the warm core ring is studied in details, and we show that the PV anomaly is entirely controlled by vortex stretching. Sign reversal of the PV gradient across the water column suggests that the ring might be baroclinically unstable. The PV gradient is also largely controlled by gradients of the vortex stretching term. We also show that the ring’s total energy partition is strongly skewed, with available potential energy being 3 times larger than kinetic energy. The possible impact of this energy distribution on the Loop Current rings longevity is also discussed.

We employ reconnection-capable, vortex filament methods and finite-volume, Navier–Stokes flow solvers to investigate the topological and helicity dynamics of vortex links for medium and high Reynolds numbers. Our vortex-dynamical model is based on discretization of vortex tubes into bundles of numerical analogues of vortex lines. Due to their nearly singular nature, the numerical vortex lines have topological writhe but not twist. By means of our reconnecting vortex tube model, it is shown that the helicity of a vortex link is conserved during the unknotting process. The dynamics of linking and writhe topological measures indicate that most of the initial linking becomes writhe during the post-reconnection evolution. The helicity spectra of the vortex link present alternating-sign helicity fluctuations at all (potential flow) scales up to the vortex core. At pre-reconnection times, these fluctuations are damped by Biot–Savart vortex stretching and helicity becomes single signed. The post-reconnection spectra indicate an inverse helicity cascade corresponding to the creation of a homogenized vortex blob, a process reminiscent of coherent structure formation in turbulence. An accompanying Navier–Stokes calculation of vortex link dynamics at Reynolds numbers Re=1500 confirms the post-reconnection transformation of linking into different topological measures, the pre-reconnection damping of helicity spectra fluctuations and the spectral shift to low wavenumbers at post-reconnection times. Due to viscous dissipation action, however, this shift is accompanied by progressive reduction of helicity peak values.

Both simulations and observations have shown that turbulence is a pervasive phenomenon in cosmic scenarios, yet it is particularly difficult to model numerically due to its intrinsically multiscale character which demands high resolutions. Additionally, turbulence is tightly connected to the dynamical state and the formation history of galaxies and galaxy clusters, producing a diverse phenomenlogy which requires large samples of such structures to attain robust conclusions. In this work, we use an adaptive mesh refinement (AMR) cosmological simulation to explore the generation and dissipation of turbulence in galaxy clusters, in connection to its assembly history. We find that major mergers, and more generally accretion of gas, is the main process driving turbulence in the intracluster medium. We have especially focused on solenoidal turbulence, which can be quantified through enstrophy. Our results seem to confirm a scenario for its generation which involves baroclinicity and compression at the external (accretion) and internal (merger) shocks, followed by vortex stretching downstream of them. We have also looked at the infall of mass to the cluster beyond its virial boundary, finding that gas follows trajectories with some degree of helicity, as it has already developed some vorticity in the external shocks., 19 pages, 12 figures; accepted for publication in MNRAS

International audience; We study the three-dimensional structure of turbulent velocity fields around extreme events of local energy transfer in the dissipative range. Velocity fields are measured by tomographic particle velocimetry at the centre of a von Kármán flow with resolution reaching the Kolmogorov scale. The characterization is performed through both direct observation and an analysis of the velocity gradient tensor invariants at the extremes. The conditional average of local energy transfer on the second and third invariants seems to be the largest in the sheet zone, but the most extreme events of local energy transfer mostly correspond to the vortex stretching topology. The direct observation of the velocity fields allows for identification of three different structures: the screw and roll vortices, and the U-turn. They may correspond to a single structure seen at different times or in different frames of reference. The extreme events of local energy transfer come along with large velocity and vorticity norms, and the structure of the vorticity field around these events agrees with previous observations of numerical works at similar Reynolds numbers.

The dynamics of intense vorticity is investigated by means of synchronisation experiments in direct numerical simulations of isotropic turbulence. By imposing similar dynamics above the dissipative range, the same structures of intense vorticity appear in two independent turbulent flows, showing that intense vorticity synchronises to large-scale dynamics. Remarkably, this synchronisation takes place despite the presence of chaos, and affects mostly the intense vorticity, but not so much the weak vorticity background, which remains comparatively asynchronous. These results pinpoint the role of large-scale dynamics in the formation of intense vorticity structures, the so-called ‘worms’, and rule out the possibility that they emerge primarily due to interactions within the dissipative range, and then grow or coalesce into elongated structures. The stretching of the vorticity vector by the large-scale rate-of-strain tensor is identified as the mechanism responsible for the synchronisation of intense vorticity, supporting the extended view of vortex stretching as a fundamental inter-scale mechanism in turbulence.

By analysing a database (Lozano-Duran & Jimenez, Phys. Fluids, vol. 26, 2014, 011702) of fully developed turbulent channel flow at the friction Reynolds number , we investigate the sustaining mechanism of a hierarchy of coherent structures in the turbulence. For this purpose, we decompose the turbulent fields into different scales by band-pass filters and quantify the real-space energy transfer. Visualizations of the hierarchy of vortices and velocity in the filtered fields show that the largest-scale structures at each distance from the wall are composed of quasi-streamwise vortices and low-speed streaks. These are similar to well known coherent structures in the buffer layer and they are maintained by a hierarchical self-sustaining process. Quantitatively, however, the energy production rate of the largest-scale structures is different in the log and buffer layers. This difference explains the change of the scaling of the Reynolds stress as a function of the Reynolds number. In contrast to the largest-scale structures, vortices smaller than the distance from the wall distribute isotropically, and they are generated by an energy cascading process. The energy of these small-scale structures is transferred predominantly from twice-larger-scale structures and reduced by half-scale ones through the vortex stretching and contraction, respectively. Turbulent advection from the wall hardly contributes to the maintenance of small-scale structures in the log layer.

One of the quickest ways to influence both the wall temperature and thermal NOx emissions in rotary kilns is to change the air–fuel ratio (AFR). The normalized counterpart of the AFR, the equivalence ratio, is usually associated with premixed flames and studies of its influence on diffusion flames are inconsistent, depending on the application. In this paper, the influence of the AFR is investigated numerically for rotary kilns by conducting steady-state simulations. We first conduct three-dimensional simulations where we encounter statistically unstable flow at high inflow conditions, which may be caused by vortex stretching. As vortex stretching vanishes in two-dimensional flow, the 2D simulations no longer encounter convergence problems. The impact of this simplification is shown to be acceptable for the thermal behaviour. It is shown that both the wall temperature and thermal NOx emissions peak at the fuel-rich and fuel-lean side of the stoichiometric AFR, respectively. If the AFR continues to increase, the wall temperature decreases significantly and thermal NOx emissions drop dramatically. The NOx validation, however, shows different results and indicates that the simulation model is simplified too much, as the measured NOx formation peaks at significantly fuel-lean conditions.

International audience; We consider three-dimensional turbulence from which vortex stretching is removed. The resulting system conserves enstrophy, but does not conserve kinetic energy. Using spectral closure, it is shown that enstrophy is transferred to small scales by a direct cascade. The inviscid truncated system tends to an equipartition of enstrophy over wave vectors. No inverse cascade is observed once the scales larger than the forcing scale are in equipartition.

Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, . The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.