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Since double-suction centrifugal pumps consume quantities of energy, revealing critical factors for energy dissipation is helpful for energy-saving design. This study aims to investigate the relationship between energy dissipation and vortex based on Rortex method in a double-suction centrifugal pump. Detached eddy simulation was applied to obtain the flow field. Enstrophy was used to present the strength of the local rigid vortex and shear. The results indicate that the local shear dominates energy dissipation in the pump. Owing to jet flows, the energy loss on blade leading edges (LE) and trailing edges (TE) were 10²-10³ times that of the middle region at 0.4Qd and ten times at 1.4Qd. The energy dissipation on pressure sides (PS) was ten times greater than that on suction sides (SS) at the TE, while flow separation at the middle of SS caused by wake flow increased energy dissipation to nearly ten times that of PS. Jet-wake flow near volute inlet was the dominant factor for energy dissipation at part-load, while separation flows in volute discharge was more significant at overload. The induced high local shear strength was responsible for energy dissipation. Therefore, reducing local shear is a potential energy-saving approach in pumps. [ABSTRACT FROM AUTHOR]

Atmospheric blocking is the most common cause of extreme weather conditions. In the present paper, model data are used to investigate the relationship between the Arctic Oscillation index and the characteristics of atmospheric blocking. The dependence of the duration and intensity of blocking on the index (or phase) of the principal mode during its initial period is estimated. A typical blocking episode is considered, and it is shown that increased values of integral regional enstrophy can be an indicator of the change in the dynamic regime. [ABSTRACT FROM AUTHOR]

Rip-currents, commonly observed on natural beaches, are vorticity induced and part of large scale near-shore circulations. The questions arise: how do bathymetric gradients magnitudes relate to rip velocities? how does rip current vorticity scale with wave characteristics and dissipation? What is the dynamics of the large scale 2D vorticity? To address these questions, we utilize a Non Linear Shallow Water model with a shock-capturing scheme. It is validated with preexisting experiments of wave induced rip-currents on uneven bathymetries generated by irregular waves. To do so the enstrophy (spatially averaged square of the vorticity) is shown to be a relevant metric to calibrate the bottom friction coefficient of the model. The numerical study based on a large number of simulations with monochromatic wave forcing shows that the more non-uniform the bathymetry is, the stronger the gradients in wave dissipation are and the stronger the enstrophy is. The rip current velocity is shown to linearly increase with the square root of the local enstrophy. The wave-averaged shallow water vorticity equation terms are evaluated. It is suggested that large scale 2D vorticity dynamics mainly result from an equilibrium between vorticity production, vorticity advection by the circulation and dissipation by bottom friction. [ABSTRACT FROM AUTHOR]

The original UNIFAES, as any exponential-type scheme, applies to the combined advective and diffusive terms of the viscous fluid transport equations. This work generalizes the scheme by making explicit the first and second derivatives of its interpolating curve, so that it can be applied, alongside classic central differencing schemes, to the statistical correlations of the transport equations of fluctuating kinetic energy, helicity and enstrophy. Tests are performed in a perturbed laminar incompressible Couette flow, obtained with a three-dimensional primitive variables solver using the original UNIFAES, the semi-staggered mesh, the Poisson equation for pressure and the forth order Runge-Kutta time-wise integration. Both the asymptotic tendencies of the correlations at low Reynolds number and the numerical stability of the solver for any Reynolds number are demonstrated with modest meshes. [ABSTRACT FROM AUTHOR]

The energy loss inside a centrifugal pump has a significant effect on its performance characteristics. Based on the structural characteristics of the humpback pectoral fin, a new tongue was designed to improve the performance of the centrifugal pump. The influence of three sinusoidal tubercle volute tongues (STVT) and one original volute tongue (OVT) on energy dissipation using the enstrophy analysis method was investigated. To accomplish this, the pressure fluctuations and performances of four centrifugal pumps were analyzed. The results indicate that enstrophy is primarily distributed at the impeller outlet and near the tongue. The total enstrophy of the profiles of STVT was smaller than that of the profiles of OVT. This difference was more obvious near the tongue. The reductions in the total enstrophy of the pumps were 8% (STVT−1), 8.2% (STVT−2), and 9% (STVT−3). The pressure fluctuations of the STVT profiles also decreased to different degrees. The average pressure fluctuations at the monitoring points decreased by 20.6% (STVT−1), 21.7% (STVT−2), and 23.3% (STVT−3). The performances of the bionic retrofit pumps increased by 1.5% (STVT−1), 2% (STVT−2), and 2.45% (STVT−3) under the design flow rate. This study guides the structural optimization of pumps. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the paper is to disclose the effect of the relative position (d) between the impeller and non-vane cavity on the hydraulic performance and unsteady characteristics of vortex pump. Design/methodology/approach: Three groups of vortex pump models with different impeller installation positions were analyzed and studied by combining experimental and CFD (Computational Fluid Dynamics) numerical calculations. Findings: The steady numerical results show that as the width (d) of the impeller moves into the non-vane cavity increases, the proportion of circulation flow in the non-vane cavity is reduced and both the pump head and efficiency are on the rise. The unsteady numerical results and the Enstrophy analysis show that the dynamic and static interference between the circulation flow and the volute tongue is the main reason for the pressure pulsation with a frequency of 2fn in the vortex pump. With the increase of the d value, the dynamic and static interference between the circulation flow and the volute tongue is enhanced. The pulsation amplitude at the volute tongue of the d = 16.5 mm model increases about six times compared with the d = 0 mm model; the distribution of the vortex core in the non-vane cavity is closely related to the position of the impeller, and the peak of the Enstrophy of the circulation flow vortex belt always appears at the top of the impeller. Originality/value: The research results provide a theoretical foundation for the optimization and improvement of the vortex pump. [ABSTRACT FROM AUTHOR]

The dynamics of cocurrent liquid–gas flow control the flow patterns and phase distribution inside the submerged entry nozzle (SEN) in the continuous casting. This regime transition from bubbly flow to annular flow is usually associated with a hysteresis effect that is not fully understood yet. Herein, the regime transition in an analogous liquid–gas flow is investigated using the volume of fluid (VOF) method. A downward turbulent water flow in a vertical pipe is considered as the computational domain at the top of which the gas is injected as a volumetric source in the VOF equation. By temporal variation of the gas volume rate following a linear ramp‐up and then ramp‐down, a transition from bubbly to annular flow and vice versa is observed. However, the transition occurs at different operation points and the numerical simulation pictures this hysteresis phenomenon. The regime transition is connected to the evolution of interfacial turbulence in each phase represented by the amount of vortical energy, that is, enstrophy. In addition, the temporal variation of different enstrophy generation/destruction mechanisms is evaluated. The hysteresis phenomenon is explained by the differences in the history of these mechanisms and the difference in the enstrophy generation level upon transition. [ABSTRACT FROM AUTHOR]

Flow past a circular cylinder is a widely studied phenomenon which finds application in a wide array of real life scenarios, like flow past cables, poles, building protrusions, automobile parts etc. The present study aims at analysing the vortex shedding phenomenon occurring in the wake of a circular cylinder and observing the effect of a splitter plate, attached to the rear stagnation point, on this flow. Finite volume method has been utilized via commercial CFD software, ANSYS Fluent, to solve transient, laminar, incompressible, isothermal flow. The study has been carried out in the low Reynolds number regime with Re = 100, 125 and 150, where the flow remains two-dimensional. The effect of splitter plate on the flow properties, such as coefficient of lift and drag, have been studied. Validation shows that the present numerical model is in good agreement with available literature. Proper Orthogonal Decomposition (POD) technique has been employed on vorticity field in order to study the dominant modes and their corresponding enstrophies along with the time coefficients. It is found that the first six modes contribute more than 95% of the total enstrophy in all the cases studied. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of the convergence of an Oseen type of problem for a uid model known as Time Relaxation Model, TRM. Furthermore conservation of energy and enstrophy of TRM are presented along with a dimensional analysis study of these properties. The paper contains two types of numerical experiments, one of which is based on finite element discretization that employs the Oseen type of problem for dealing with the nonlinearity of the TRM. The second type is the spectral related tests for the study of TRM dimensional analysis. Our numerical experiments confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

We derive a model for Bingham fluid flows down an inclined plane with a consistent asymptotic method in the shallow-flow approximation. The variables are expanded up to the first order of accuracy both in the sheared and pseudo-plug layers. The divergence of the strain rate, which is obtained in classical approaches, is here avoided by a specific regularization of the rheology allowing to implement a regular perturbation method in the whole fluid domain. Unlike classical regularization methods, the material is here characterized by a true yield stress. Below the yield point, the behavior is perfectly rigid. An alternative tensor expression of the constitutive law is proposed. In particular, the assumption of an alignment between the yield-stress tensor and the strain-rate tensor is removed. The model is derived by averaging the mass, momentum and energy balance equations over the depth. This yields a hyperbolic model of three equations for the fluid depth, the average velocity and a third variable, called enstrophy, related to the variance of the velocity. The model features new relaxation source terms and admits an exact balance energy equation. The velocity field in the depth is consistently reconstructed using only the variables of the depth-averaged model without any derivative. The physical relevance of the enstrophy is related to the shape of the velocity profile. The linear stability of a uniform solution is investigated for this model, showing a stabilizing effect of the plasticity. Roll waves are simulated numerically using a classical Godunov's scheme. The model for a Newtonian fluid is presented as a particular case. • A consistent three-equation shallow-flow model for Bingham fluids is derived. • Smooth asymptotic velocity profiles can be reconstructed from the model. • An alternative tensorial extension of the Bingham constitutive law is proposed. • Roll waves in viscoplastic fluid are computed. [ABSTRACT FROM AUTHOR]

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF 6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: M s = 1. 12 , 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated. • Shock Mach number effects on RM instability in heavy square bubble are investigated. • Flow morphology of bubble is significantly altered with increasing shock Mach number. • Detailed mechanism of vorticity generation and its production terms are discussed. • Kinetic energy and vorticity are enhanced when shock Mach number is raised. [ABSTRACT FROM AUTHOR]

This study aims to investigate the evolution of transient force and energy features in a thermo-sensitive cavitating flow around a hydrofoil. A cavitation model is extended to investigate the thermal effect, and a shear stress transfer — partially averaged Navier–Stokes turbulence model is adopted to simulate the cavitating turbulent flow. The distribution of changed cavitation number is consistent with the cavity shape. The evident temperature gradient exists in the vicinity of the closure line, which leads the temperature drop to increasing gradually from the closure line to the centre of the cavity. The changed cavitation number also increases according to this rule. The force element analysis reveals that vortex structures induced by cavity evolution make the lift and drag forces fluctuation. Lift and drag forces increase approximately linearly with the development of sheet cavity. When the large attached sheet cavity separates from the suction surface, the lift and drag forces increase substantially. Conversely, the collapse of cloud cavity causes a sudden reduction of lift and drag forces. About the detailed evolution mechanisms of lift and drag forces, this work also expounds. Moreover, the terms in the kinetic energy transport equation are applied to depict the dissipation and transitivity of energy. The attached sheet cavity suppresses energy dissipation because of the stable flow field. The separation of sheet cavity and the shedding of cloud cavity induce the generation of multiscale vortex structures, and causes the energy loss to increase obviously. Combined with the analysis of the lift and drag forces, the evolution of fluid forces on the hydrofoil is also related to the energy loss. • The temperature transport equation is used to analyse the temperature drop. • Effects of vortices on forces of the hydrofoil are explained by Force Element Method. • The energy conversion and dissipation in the cavitating flow are studied in detail. • The relevance between energy conversion and lift, drag forces are analysed. [ABSTRACT FROM AUTHOR]

The problem of the propagation of linear Rossby waves in horizontally inhomogeneous non-zonal flows is studied. The explicit solution within the geometric optics (WKBJ) approximation is found to be identical to the exact Cauchy problem solution for the case of a constant horizontal velocity shear.The effect of the short-wave transformation of Rossby waves near the so-called critical layer is detailed for the arbitrary direction of non-zonal flow. In the general case, this transformation can occur in two ways: (1) as an adhering, a monotonic approaching of wave packets to the critical layer for an infinitely long time. The sign of the intrinsic frequency of the packet remains the same all the time; (2) as an adhering with overshooting when the wave packet, first, crosses its critical layer at finite wavenumber. The wave changes the sign of the intrinsic frequency when overshooting the critical layer and then keeps the sign when it is adhering to this layer asymptotically similarly to the previous scenario. The latter regime does not exist for zonal flows, that degenerates the short-wave dynamics of Rossby waves in this special case. On the contrary, the anisotropy of the dispersion relation permits both positive and negative frequencies in a non-zonal flow. It allows for the effective use of the concept of waves of negative energy for the analysis of the stability of large-scale currents. [ABSTRACT FROM AUTHOR]

A framework of variational principles for stochastic fluid dynamics was presented by Holm, and these stochastic equations were also derived by Cotter, Gottwald and Holm. We present a conforming finite element discretisation for the stochastic quasi-geostrophic equation that was derived from this framework. The discretisation preserves the first two moments of potential vorticity, i.e. the mean potential vorticity and the enstrophy. Following the work of Dubinkina and Frank, who investigated the statistical mechanics of discretisations of the deterministic quasi-geostrophic equation, we investigate the statistical mechanics of our discretisation of the stochastic quasi-geostrophic equation. We compare the statistical properties of our discretisation with the Gibbs distribution under assumption of these conserved quantities, finding that there is an agreement between the statistics under a wide range of set-ups. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in studying the existence of the nonstationary solutions in the global attractor of the 2D Navier–Stokes equations with constant energy and enstrophy. We particularly focus on a subclass of these solutions that the geometric structures have a supplementary stability property which were called "chained ghost solutions" in Tian and Zhang (Indiana Univ Math J 64:1925–1958, 2015). By solving a Galerkin system of a particular form, we show the nonexistence of the chained ghost solutions for certain cases. [ABSTRACT FROM AUTHOR]

Highlights • An term-by-term estimation was made of the key terms in the kinetic energy equation using detailed experimental data. • An term-by-term estimation was made of the key terms in the enstrophy equation equation using detailed experimental data. • Role of secondary flow in the transport and dissipation of kinetic energy. Abstract In sharp open-channel bends, there exists nonlinear interactions between streamwise and cross-stream velocities, which leads to the adjustment of flow energy transport, increases the energy dissipation and eventually influences the development of river bends. However, previous studies have not yet fully understood the mechanisms underlying the transport and dissipation of energy in open-channel bends. In addition, energy dissipation is directly related to the evolution of enstrophy Ω · Ω / 2. However, it has not yet received much attention in the study of the resistance in meandering rivers. To gain an insight into these mechanisms, with the aid of detailed experimental data collected in a sharp open-channel bend, this study quantified the impacts of the key terms in the kinetic energy equation and the enstrophy equation. Results show that the term related to the transport of kinetic energy by cross-stream circulation is at least an order of magnitude larger than the other terms in the kinetic energy equation, which contributes significantly to the redistribution of kinetic energy over the cross section. The term related to the production of turbulent kinetic energy in the kinetic energy equation shows the smallest order of magnitude and thus is almost negligible for the time-averaged flow field. Furthermore, over most of the measured area, the term related to the centrifugal force shows values of at least an order of magnitude larger than the other terms in the enstrophy equation, which means that this term exerts the dominant influence on the energy dissipation. The results also revealed that the transformation process is insensitive to the variations in Froude number. These results are expected to improve the understanding of the complete process of energy transformation, especially the resistance caused by secondary flow in meandering rivers. [ABSTRACT FROM AUTHOR]

In the present study, flow field around rigid flat plate wings executing main flapping motion has been studied using phaselocked two-dimensional particle image velocimetry measurements. Experiments have been conducted in water as a fluid medium for an asymmetric upper-lower stroke single degree of freedom main flapping motion. Two different aspect ratio (1.5 and 1.0) rectangular wings at 1.5 and 2.0 Hz flapping frequency in hovering flight mode (advance ratio, J=0), zero wing pitch angle, and chord-based Reynolds number of the order of 104 have been studied. Velocity field and vorticity field with λ2 criterion information have been obtained for the complete stroke in great detail to reveal the minute aspects of flow dynamics. The flow features during the downstroke and upstroke have been observed to be consistent for all four cases investigated. The predominant characteristic of the flow during downstroke and upstroke has been referred to as vortex filamentation and fragmentation phenomena. Quantities such as circulation, rate of strain, rate of rotation, and enstrophy have been studied to identity the effect of minor change in aspect ratio and flapping frequency. It is found that for higher aspect ratio wing hyperbolic behavior is predominant except for end of downstroke and beginning of upstroke where elliptic behavior is observed. For lower aspect ratio, wing elliptic behavior is predominant except for end of upstroke and beginning of downstroke where hyperbolic behavior is seen. The hyperbolic behavior became stronger at higher frequency. From enstrophy distribution it is evident that higher frequencies play a more dominant role than aspect ratio in determining the budget. [ABSTRACT FROM AUTHOR]

Abstract: Possible consequences of the application of the Kolmogorov theory of local isotropy to two-dimensional turbulence are discussed. In this regard, the cases of both freely decaying and stationary turbulence are considered. Formulae for the third-order structure functions in the inertial interval are obtained as the solutions of the Karman—Howarth equation with the use of the well-known relation between the velocity and vorticity correlators. These formulae differ from those given by other authors; that is, the variable term linear in space turns out to be negative in the corresponding formula, as in the three-dimensional case. The possible relation of the results to the form of the energy spectrum is briefly mentioned. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by large-scale and/or laminar vortical motion. The proposed coherent-vorticity preserving (CvP) LES methodology is based on the evaluation of the ratio of the test-filtered to resolved (or grid-filtered) enstrophy, σ . Values of σ close to 1 indicate low sub-test-filter turbulent activity, justifying local deactivation of the SGS dissipation. The intensity of the SGS dissipation is progressively increased for σ < 1 which corresponds to a small-scale spectral broadening. The SGS dissipation is then fully activated in developed turbulence characterized by σ ≤ σ e q , where the value σ e q is derived assuming a Kolmogorov spectrum. The proposed approach can be applied to any eddy-viscosity model, is algorithmically simple and computationally inexpensive. LES of Taylor–Green vortex breakdown demonstrates that the CvP methodology improves the performance of traditional, non-dynamic dissipative SGS models, capturing the peak of total turbulent kinetic energy dissipation during transition. Similar accuracy is obtained by adopting Germano's dynamic procedure albeit at more than twice the computational overhead. A CvP-LES of a pair of unstable periodic helical vortices is shown to predict accurately the experimentally observed growth rate using coarse resolutions. The ability of the CvP methodology to dynamically sort the coherent, large-scale motion from the smaller, broadband scales during transition is demonstrated via flow visualizations. LES of compressible channel are carried out and show a good match with a reference DNS. [ABSTRACT FROM AUTHOR]

This study revisits bounds on the projection of the global attractor in the energy–enstrophy plane for 2D incompressible turbulence [Dascaliuc, Foias, and Jolly, 2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in particular often use a stochastic white-noise forcing to achieve a prescribed mean energy injection rate. The analytical bounds are demonstrated numerically for the case of white-noise forcing. [ABSTRACT FROM AUTHOR]

The dynamic character of an enstrophy-based diagnostic, previously used in the study of atmospheric blocking, is examined here, in near-term future simulations from the Institut Pierre Simon Laplace Climate Model version 4 (IPSL-CM4) and version 5 (IPSL-CM5) climate models of the Northern Hemisphere flow for moderate climate change scenarios. Previous research has shown that integrated regional enstrophy (IE) increases during blocking onset and decay, which is a reflection of planetary-scale instability. In addition, IE has been shown previously to increase during flow regime transitions in general, even those not associated with blocking events. Here, a 31-year IE diagnostic time series is examined for changes in short term (5-40 days) planetary-scale variability that may correspond flow regime changes in an increased carbon dioxide environment. The time-series analysis herein indicates that the IE diagnostic provides evidence for approximately 30-35 atmospheric flow regime transitions per year in a warmer climate, which is similar to that of the control run and the latest 30-year observed climate, as derived from re-analyses. This result has implications regarding the predictability of weather in a warmer world. [ABSTRACT FROM AUTHOR]

Enstrophy in a fluid relates to the dissipation tendency in a fluid that has use in studying turbulent flows. It also corresponds to vorticity as kinetic energy does to velocity. Earlier work showed that the integrated regional enstrophy (IRE) was related to the sum of the positive Lyapunov exponents. Lyapunov exponents are the characteristic exponent(s) of a dynamic system or a measure of the divergence or convergence of system trajectories that are initially close together. Relatively high values of IRE derived from an atmospheric flow field in the study of atmospheric blocking was identified with the onset or demise of blocking events, but also transitions of the large-scale flow in general. Kolmogorv-Sinai Entropy (KSE), also known as metric entropy, is related to the sum of the positive Lyapunov exponents as well. This quantity can be thought of as a measure of predictability (higher values, less predictability) and will be non-zero for a chaotic system. Thus, the measure of IRE is related to KSE as well. This study will show that relatively low (high) values of IRE derived from atmospheric flows correspond to a more stable (transitioning) large-scale flow with a greater (lesser) degree of predictability and KSE. The transition is least predictable and should be associated with higher IRE and KSE. [ABSTRACT FROM AUTHOR]

For numerical discretization schemes, the violation of enstrophy conservation causes a systematic and unrealistic energy cascade towards high wave numbers. The same occurs in data assimilation schemes, where the total energy, enstrophy and divergence could be strongly affected. In this article, we construct an ensemble data assimilation algorithm that conserves mass, total energy and enstrophy. The algorithm uses B-spline functions for localization and sequential quadratic programming to solve nonlinear constrained minimization problem. Idealized experiments are performed using a 2D shallow-water model, with selected contraints derived from the nature run. It is found that all experiments exhibit comparable root-mean-square errors, with a slight advantage for those that include the conservation constraint on the globally integrated enstrophy. However, the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of the rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14 day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts. [ABSTRACT FROM AUTHOR]

The transport of vorticity and enstrophy in the near-wall region for head-on quenching of turbulent combustion by an isothermal inert wall has been analysed using three-dimensional Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames characterised by various global Lewis numbers L e (ranging from 0.8 to 1.2) and turbulence intensities. In all cases the vorticity magnitude shows its maximum value at the wall and the vorticity magnitude drops significantly from the unburned to the burned gas side of the flame-brush. Moreover, the vorticity magnitude shows an increasing trend with decreasing L e , and increasing turbulence intensity. A significant amount of anisotropy has been observed between the vorticity components within the flame-brush and this anisotropy increases as the wall is approached. The baroclinic torque term has been found to be principally responsible for this anisotropic behaviour. The vortex-stretching and viscous dissipation terms remain the leading order contributors to the vorticity and enstrophy transport for all cases when the flame is away from the wall, but as flame approach the wall, the baroclinic torque begins to play an increasingly important role. The combined molecular diffusion and dissipation contribution to the enstrophy transport remains negative away from the wall but it changes its sign near the wall due to the torque arising from dilatation rate gradient. Detailed physical explanations have been provided for the observed influences of flame and wall on the statistical behaviours of vorticity and enstrophy and the various terms of their transport equations. [ABSTRACT FROM AUTHOR]

The local and non-local statistics of vorticity ... (i.e. curl of velocity vector ...) and pseudo-vorticity ... (i.e. curl of density-weighted velocity vector ...) have been investigated in detail based on a direct numerical simulation (DNS) database of freely propagating statistically planar flames in different regimes of premixed turbulent combustion. It has been found that the relative orientation of ... can be significantly different to that of ... for small values of the Karlovitz number and large values of the Reynolds number. The vorticity ... shows, depending on the case, considerable alignment with either the most extensive or compressive principal strain rate. In contrast, ... has been found to align with the intermediate principal strain rate for all cases. The transport statistics of Reynolds averaged enstrophy (i.e. ...) and pseudo-enstrophy (i.e. ...) have been investigated in detail. The non-local vorticity statistics in turbulent premixed combustion have been investigated based on the vorticity line segment (VLS) structure, which is defined with respect to each grid point as the part of the (pseudo) vorticity line bounded by the two adjacent extremal points of the (pseudo) vorticitymagnitude. VLS can be characterised by the segment length and the (pseudo) vorticity magnitude difference across the segment, i.e. (Δω*) Δω. Strong dilatation effects tend to increase VLS length, whereas turbulent convection disturbs the flow field resulting in shorter VLS. The joint PDFs between the segment length and (Δω) Δω* are found to be symmetric, whereas the joint PDFs between the segment length and the pseudo-vorticity magnitude difference across the VLS in the flame normal direction show significant asymmetry, which is primarily determined by density variation across the flame front and turbulence intensity. [ABSTRACT FROM AUTHOR]

The interaction between locally monochromatic finite-amplitude mesoscale waves, their nonlinearly induced higher harmonics, and a synoptic-scale flow is reconsidered, both in the tropospheric regime of weak stratification and in the stratospheric regime of moderately strong stratification. A review of the basic assumptions of quasi-geostrophic theory on an f-plane yields all synoptic scales in terms of a minimal number of natural variables, i.e. two out of the speed of sound, gravitational acceleration and Coriolis parameter. The wave scaling is defined so that all spatial and temporal scales are shorter by one order in the Rossby number, and by assuming their buoyancy field to be close to static instability. WKB theory is applied, with the Rossby number as scale separation parameter, combined with a systematic Rossby-number expansion of all fields. Classic results for synoptic-scale-flow balances and inertia-gravity-wave (IGW) dynamics are recovered. These are supplemented by explicit expressions for the interaction between mesoscale geostrophic modes (GMs), a possibly somewhat overlooked agent of horizontal coupling in the atmosphere, and the synoptic-scale flow. It is shown that IGW higher harmonics are slaved to the basic IGW, and that their amplitude is one order of magnitude smaller than the basic-wave amplitude. GM higher harmonics are not that weak and they are in intense nonlinear interaction between themselves and the basic GM. Compressible dynamics plays a significant role in the stratospheric stratification regime, where anelastic theory would yield insufficient results. Supplementing classic derivations, it is moreover shown that, in the absence of mesoscale waves, quasi-geostrophic theory holds also in the stratospheric stratification regime. [ABSTRACT FROM AUTHOR]

Numerical discretization schemes have a long history of incorporating the most important conservation properties of the continuous system in order to improve the prediction of the nonlinear flow. The question arises whether data assimilation algorithms should follow a similar approach. To address this issue, we explore the conservation properties during data assimilation using perfect model experiments with a 2D shallow-water model preserving important properties of the true nonlinear flow. The data assimilation scheme used here is the Local Ensemble Transform Kalman Filter with varying observed variables, inflation, localization radius and thinning interval. It is found that, during the assimilation, the total energy of the analysis ensemble mean converges with time towards the nature run value. However, enstrophy, divergence and the energy spectra are strongly affected by the data assimilation settings. Having in mind that the conservation of both the kinetic energy and enstrophy by the momentum advection schemes in the case of non-divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we test the effects on the prediction depending on the type of error in the initial condition. During the assimilation, we assess the downward nonlinear energy cascade through a scalar, domain-averaged noise measure. We show that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction. [ABSTRACT FROM AUTHOR]

This study is motivated by the question of how singularity formation and other forms of extreme behavior in nonlinear dissipative partial differential equations are affected by stochastic excitations. To address this question we consider the 1D fractional Burgers equation with additive colored noise as a model problem. This system is interesting, because in the deterministic setting it exhibits finite-time blow-up or a globally well-posed behavior depending on the value of the fractional dissipation exponent. The problem is studied by performing a series of accurate numerical computations combining spectrally-accurate spatial discretization with a Monte-Carlo approach. First, we carefully document the singularity formation in the deterministic system in the supercritical regime where the blow-up time is shown to be a decreasing function of the fractional dissipation exponent. Our main result for the stochastic problem is that there is no evidence for additive noise to regularize the evolution by suppressing singularities in the supercritical regime, or for the noise to trigger singularities in the subcritical regime. However, as the noise amplitude becomes large, the maximum existence time of the solution in the supercritical regime is shown to exhibit an increasingly non-Gaussian behavior. Analogous observations are also made for the maximum attained values of the enstrophy and the times when the maxima occur in the subcritical regime. • Computational investigation of singularity formation in 1D fractional Burgers equation in the super critical regime. • Monte-Carlo analysis of the effect of noise on extreme and singular behavior in 1D fractional Burgers flows. • No evidence for noise to regularize the evolution by suppressing blow-up in the supercritical regime. • No evidence for noise to trigger blow-up in the subcritical regime. [ABSTRACT FROM AUTHOR]

In this work we present Lattice Boltzmann simulations of a decaying vortex array in a 2D rectangular domain, which is bounded by a random rough wall from one side. In order to separate the effects of the collisions with the rough wall, the opposite (smooth) rigid wall is placed at a larger distance from the center of the vortex array. Periodic boundary condition is imposed in the perpendicular direction. Well defined random roughness is generated by the widely studied Wolf-Villain surface growth algorithm. The main finding is that collisions with a rough wall generate excess vorticity compared with a smooth boundary, while the kinetic energy decreases monotonously. A proper measure is the integrated excess enstrophy, which exhibits an apparent maximum at an 'optimal' roughness range. Numerical values of the excess enstrophy are very sensitive to a particular configuration (wall shape and vortex lattice randomization), however the 'optimal' roughness exhibits surface features of similar characteristic sizes than that of the decaying vortices. [ABSTRACT FROM AUTHOR]

For the past few years, heave plates have been used in the offshore industry due to their favorable hydrodynamic characteristics in oscillating flows, i.e., increased added mass and damping. The hydrodynamic coefficients of heave plates are strongly influenced by the proximity of solid boundaries. Assessing how this variation depends on the proximity to the seabed and on the amplitude of the oscillation is the main aim of this paper. In this process, a new model describing the work done by damping in terms of the flow enstrophy is described herein. This new approach is able to provide a direct correlation between the vortex shedding processes and the linear damping coefficient. Numerical simulations have been performed using the finite volume open source solver OpenFOAM. Simulations have been conducted on a solid circular disc oscillating axially in water at various elevations above an impermeable seabed boundary. Results for hydrodynamic coefficients are validated against previously published experimental data. At low KC numbers, a systematic increase in added mass and damping, corresponding to an increase in the seabed proximity, is observed. As seen in experiments, a critical KC where the monotonic trend of the hydrodynamic coefficients with KC is disrupted and that depends on the seabed distance exists. The physical behavior of the flow around the critical KC is explained through an analysis of the flow enstrophy. [ABSTRACT FROM AUTHOR]

Molten salt pump (MSP) used in concentrating solar power (CSP) system to circulate the molten salt. The operation of MSP needs to understand the energy conversion characteristics in the flow field. In this study, the energy conversion characteristics of MSP were investigated based on energy transport theory. A significant portion of power is consumed in the propulsion of pressure between the inlet throat to the outlet throat of the impeller passage. The increase in the energy of medium by the Lamb vector divergence mainly occurs on the rear of the impeller passage. Whereas the enstrophy dissipation area is primarily located in the suction surface area at the impeller outlet. In addition, the pressure propulsion power is critical for energy transfer in the impeller, while the contribution of Lamb vector divergence and enstrophy dissipation is limited. It was observed that the distribution of the three energy transport dynamic parameters have a high degree of coincidence irrespective of the medium density, which indicates that the density of the medium does not have a significant impact on the law of energy conversion. Therefore, when the geometrical characteristics of the impeller are determined, the energy conversion characteristics of different medium do not change significantly. • Energy conversion characteristics in MSP are analyzed by using energy transport theory. • Medium physical properties effect on energy conversion characteristics are analyzed in detail. • The composition of energy transport is analyzed. • The contribution of different energy transport components are analyzed. [ABSTRACT FROM AUTHOR]

Strong nonlinear or very fast phenomena such as mixing, coalescence and breakup in chemical engineering processes, are not correctly described using average turbulence properties. Since these phenomena are modeled by the interaction of fluid particles with single or paired vortices, distribution of the properties of individual turbulent vortices should be studied and understood. In this paper, statistical analysis of turbulent vortices was performed using a novel vortex tracking algorithm. The vortices were identified using the normalized Q-criterion with extended volumes calculated using the Biot-Savart law in order to capture most of the coherent structure related to each vortex. This new and fast algorithm makes it possible to estimate the volume of all resolved vortices. Turbulence was modeled using large-eddy simulation with the dynamic Smagorinsky-Lilly subgrid scale model for different Reynolds numbers. Number density of turbulent vortices were quantified and compared with different models. It is concluded that the calculated number densities for vortices in the inertial subrange and also for the larger scales are in very good agreement with the models proposed by Batchelor and Martinez-Bazán. Moreover, the associated enstrophy within the same size of coherent structures is quantified and its distribution is compared to models for distribution of turbulent kinetic energy. The associated enstrophy within the same size of coherent structures has a wide distribution that is normal distributed in the logarithmic scale. [ABSTRACT FROM AUTHOR]

In the near future we expect the resolution of many IPCC-class ocean models to enter the "eddy-permitting" regime. At this resolution models can produce reasonable eddy-like disturbances, but can still not properly resolve geostrophic eddies at all relevant scales. Adequate parameterizations representing sub-grid eddy effects are thus necessary. Most eddy-permitting models presently employ some kind of hyper-viscosity, which is shown to cause a significant amount of energy dissipation. However, comparison to higher resolution simulations shows that only enstrophy, but almost no energy, should be dissipated below the grid-scale. As a result of the artificial energy sink associated with viscous parameterizations, the eddy fields in eddy permitting models are generally not energetic enough. To overcome this problem, we propose a class of sub-grid parameterizations which dissipate enstrophy but little or no energy. The idea is to combine a standard hyperviscous closure with some mechanism to return dissipated energy to the resolved flow. Enstrophy dissipation remains ensured because the energy is returned at larger scales. Two simple ways to return the energy are proposed: one using a stochastic excitation and one using a negative Laplacian viscosity. Both approaches are tested in an idealized two-layer quasi-geostrophic model. Either approach is shown to greatly improve the solutions in simulations with typical eddy-permitting resolutions. The adaptation of the proposed parameterization for use in realistic ocean models is discussed. [ABSTRACT FROM AUTHOR]

This article proposes a method to identify blocking onset and decay by means of two stability indicators: enstrophy advection and its integral. The key to this technique is the use of local Lyapunov exponents for the barotropic vorticity equation, which can be approximated by the integral of enstrophy (IRE) over a fixed, finite region. The IRE can then be viewed as a measure of stability. However, by differentiating the IRE with respect to time, two measures of stability can be derived to assess blocking onset and decay: (i) the integral of enstrophy advection (DIRE), for which a time series is used to assess stability, and (ii) enstrophy advection, for which contours are plotted in conjunction with 500 hPa heights to locate blocking. One year's worth of Northern Hemisphere blocking events from July 2011-July 2012 are studied to demonstrate that the integral of enstrophy advection is a useful diagnostic. In particular, time series of IRE and DIRE for four of the blocking cases are presented, while contour plots of enstrophy advection for one case are presented. In all cases studied, the diagnostics were seen to detect the instability in an incipient blocking event and in its decay. [ABSTRACT FROM AUTHOR]

Highlights: [•] New equations for enstrophy and enstrophy advection are derived. [•] Enstrophy has geopotential, vorticity, zonal wind, and deformation terms. [•] Enstrophy advection has ageostrophic relative vorticity and deformation terms. [•] A blocking event is examined using the enstrophy equation. [ABSTRACT FROM AUTHOR]

The evolution of low-speed streaks in the turbulent boundary layer of the minimum channel flow unit at a low Reynolds number is simulated by the direct numerical simulation (DNS) based on the standard Fourier-Chebyshev spectral method. The subharmonic sinuous (SS) mode for two spanwise-aligned low-speed streaks is excited by imposing the initial perturbations. The possibilities and the physical realities of the turbulent sustaining in the minimal channel unit are examined. Based on such a flow field environment, the evolution of the low-speed streaks during a cycle of turbulent sustaining, including lift-up, oscillation, and breakdown, is investigated. The development of streamwise vortices and the dynamics of vortex structures are examined. The results show that the vortices generated from the same streak are staggered along the streamwise direction, while the vortices induced by different streaks tilt toward the normal direction due to the mutual induction effect. It is the spatial variations of the streamwise vortices that cause the lift-up of the streaks. By resolving the transport dynamics of enstrophy, the strength of the vortices is found to continuously grow in the logarithmic layer through the vortex stretching mechanism during the evolution of streaks. The enhancement of the vortices contributes to the spanwise oscillation and the following breakdown of the low-speed streaks. [ABSTRACT FROM AUTHOR]

We examine how the global attractor of the 2D periodic Navier- Stokes equations projects in the energy-enstrophy-plane when the force is an eigenvector of the Stokes operator. We find sharper bounds than in Dascaliuc et al. (J Dyn Diff Equat 17:643-736, ) for a general force. We also find regions of the plane in which the energy and enstrophy must decrease, and calculate the curvature of the projected solution at certain initial data. Finally, we obtain restrictions on solutions that project onto a single point in the plane. [ABSTRACT FROM AUTHOR]

Abstract: We present a methodology to determine the best turbulence closure for an eddy-permitting ocean model through measurement of the error-landscape of the closure’s subgrid spectral transfers and flux. We apply this method to 6 different closures for forced-dissipative simulations of the barotropic vorticity equation on an f-plane (2D Navier–Stokes equation). Using a high-resolution benchmark, we compare each closure’s model of energy and enstrophy transfer to the actual transfer observed in the benchmark run. The error-landscape norm enables us to both make objective comparisons between the closures and to optimize each closure’s free parameter for a fair comparison. The hyper-viscous closure most closely reproduces the enstrophy cascade, especially at larger scales due to the concentration of its dissipative effects to the very smallest scales. The viscous and Leith closures perform nearly as well, especially at smaller scales where all three models were dissipative. The Smagorinsky closure dissipates enstrophy at the wrong scales. The anticipated potential vorticity closure was the only model to reproduce the upscale transfer of kinetic energy from the unresolved scales, but would require high-order Laplacian corrections in order to concentrate dissipation at the smallest scales. The Lagrangian-averaged α-model closure did not perform successfully for forced 2D isotropic Navier–Stokes: small-scale filamentation is only slightly reduced by the model while small-scale roll-up is prevented. Together, this reduces the effects of diffusion. [Copyright &y& Elsevier]

Abstract: I will prove a recurrence theorem which says that any () solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small neighborhood. The periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of Li [Y. Li, A recurrence theorem on the solutions to the 2D Euler equation, Asian J. Math. 13 (1) (2009) 1–6] on the 2D Euler equation under periodic boundary conditions along both directions. [Copyright &y& Elsevier]

Abstract: Using high-resolution direct numerical simulations, the height and Reynolds number dependence of high-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers and . The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy show relatively small variations for . [Copyright &y& Elsevier]

Viscous incompressible fluid flow along the clearance between two parallel eccentric circular cylinders is studied numerically. The geometric parameters and the Reynolds number are taken so that the turbulent flow regime takes place in a part of flow, namely, in the zone where the clearance is wide, while the low is laminar in the narrow clearance zone. Criteria using which these zones can be distinguished are discussed. [ABSTRACT FROM AUTHOR]

This article employs LES to simulate temporal mixing layers with Mach numbers ranging from M = 0.3 to M = 1.2. A form of approximate deconvolution together with a dynamic Smagorinsky subgrid model are employed as subgrid models. A large computational domain is used along with relatively good resolution. The LES results regarding growth rate, turbulence levels, turbulence anisotropy, and pressure-strain correlation show excellent agreement with those available from previous experimental and DNS results of the same flow configuration, underlining the effectiveness and accuracy of properly conducted LES. Coherent structures during the transitional stage change from spanwise aligned rollers to streamwise-aligned thinner vortices at high Mach number. In the quasi-self-similar turbulent stage, the resolved-scale vorticity is more isotropic at higher M, and its vertical correlation length scale is smaller. The ratio of the vertical integral length scale of streamwise velocity fluctuation to a characteristic isotropic estimate is found to decrease with increasing M. Thus, compressibility leads to increased spatial decorrelation of turbulence which is one reason for the reduction in pressure-strain correlation with increasing M. The balance of the resolved-scale fluctuating vorticity is examined, and it is observed that the linear production by mean shear becomes less important compared to nonlinear vortex stretching at high M. A spectral decomposition of the pressure fluctuations into low- and intermediate-to-high-wave numbers is performed. The low-wave number part of the pressure field is found not to correlate with the strain field, although it does have a significant contribution to the r.m.s of the fluctuating pressure. As a consequence, the pressure-strain correlation can be analyzed using a simplified Green's function for the Poisson equation as is demonstrated here using the LES data. [ABSTRACT FROM AUTHOR]

Abstract: A previously attempted data reduction in turbulent viscoelastic channel flow [J. Non-Newton. Fluid Mech., 160 (2009) 55–63] used projections of the numerical velocity fields onto the most energetic, large scale, Karhunen–Loeve (K–L) modes of the fluctuating kinetic energy. However, the conformation field could not be adequately reproduced from the reduced velocity data when those were used in integrating the constitutive model (Giesekus) in a post-processing step. Here we investigate three different data reduction approaches in order to introduce small-scale information. Simultaneously, we also develop a novel formulation, which extends the K–L decomposition to more general objective functions. First, we use as a new objective function a weighted average of the pseudodissipation and the fluctuating kinetic energy. Second, we use the enstrophy. Third, we use the standard K–L approach, but this time in the reconstruction stage of the conformation tensor, we compensate for the loss of information of the flow deformation by suitably rescaling the Weissenberg number. It is shown that, whereas the first two methods fail to give any improvement over the classical K–L approach, the conformation field can be reconstructed fairly accurately using the third. [ABSTRACT FROM AUTHOR]

Abstract: The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy and the energy dissipation rate with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region. [Copyright &y& Elsevier]

Abstract: A nonlinear adjoint-based optimal control approach of cylinder wake flow by using electro-magnetic forcing has been proposed and investigated numerically in the paper. A cost functional representing the balance between the enstrophy Ω 2 and the interaction parameter N has been developed, and its corresponding adjoint equations have been derived. The sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. Under the action of optimal force, N(t), the flow separation is suppressed successfully, the oscillations of drag and lift disappear and the total drag coefficient decreases dramatically. Furthermore, the global enstrophy is proved to be equal to the total squared strain during the control, which validates the conservation rule of Okubo-Weiss function. [Copyright &y& Elsevier]

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder controlled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed. [ABSTRACT FROM AUTHOR]

• Vortex-bubble interaction process. • Turbulent breakup of bubbles. • Vortex destabilization by the vorticity entrained from the bubble's wake. • The vortex enstrophy increases due to vorticity generation when it interacts with a bubble. The turbulent breakup of bubbles is a complex phenomenon present in a large number of engineering applications and natural processes. Simplified models are essential to better understand the interaction between turbulent eddies and bubbles. Probably the simplest one is that given by a vortex ring colliding with a single bubble. With this motivation, in the present work we perform three-dimensional numerical simulations of a single vortex ring of initial circulation Γ 0 , radius R 0 and Reynolds number R e = Γ 0 / ν l = 15 , 000 , interacting with a bubble of radius R b immersed in a liquid of kinematic viscosity ν l. The temporal evolution of the vortex ring is compared with analytical models for the size of the vortex core, a (t) , the kinetic energy, E k (t) , and the enstrophy Ω (t) , looking for a concurrence of this magnitude with the rate of dissipation of E k. The dynamics of the bubble-vortex interaction process is described varying the vortex-to-bubble size ratio, R 0 / R b , and the Weber number, W e = ρ l (Γ 0 / 2 π R 0) 2 / (σ / R b). With respect to the bubble, the simulations show that vortices smaller or of the same size as the bubble are not able to break it up. However, vortices slightly larger, although of comparable sizes, can efficiently break the bubble after trapping it inside the vortex core. In these cases, if the Weber number is sufficiently large, the bubble migrates to the vortex core, where the strain is maximum, and elongates along the azimuthal direction to eventually break by a Rayleigh-Plateau mechanism. In fact, we observe that the bubbles always break if W e ⪆ 1 when R 0 / R b > 1. The numerical results are corroborated experimentally for vortex-to-bubble diameter ratios in the range 2.28 ≤ R 0 / R b ≤ 7.5. Regarding the vortex ring, it is observed that when the vortex decelerates the bubble while they interact, the vorticity contained in the bubble boundary layer is engulfed by the vortex core, destabilizing the vortex ring. This makes the total enstrophy to suddenly increase due to the vorticity generation by the vortex stretching mechanism that follows the lost of axial symmetry. This increase in enstrophy is associated to a rapid decrease of kinetic energy, especially at low Weber numbers. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor and negative subgrid-scale stress tensor , enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of , and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of and are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of . [Copyright &y& Elsevier]

Abstract: The evolution of decaying two-dimensional turbulent flows in a bounded domain is considered. It is shown that the global enstrophy is always equal to the total squared strain field, when integrated over a domain with no-slip boundaries, despite the complex evolution of the flow and strong vortex-wall interactions. This property is also valid for a square domain with stress-free walls, and in general for any polygonal boundary. In contrast, the enstrophy is always greater than the squared strain field in a stress-free circular domain, and in general for any closed domain with negatively-signed curvature at all points of the boundary. [Copyright &y& Elsevier]