Turbulent Enstrophy Research Articles

Development of a coupled wave-flow-vegetation interaction model

Emergent and submerged vegetation can significantly affect coastal hydrodynamics. However, most deterministic numerical models do not take into account their influence on currents, waves, and turbulence. In this paper, we describe the implementation of a wave-flow-vegetation module into a Coupled-Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system that includes a flow model (ROMS) and a wave model (SWAN), and illustrate various interacting processes using an idealized shallow basin application. The flow model has been modified to include plant posture-dependent three-dimensional drag, in-canopy wave-induced streaming, and production of turbulent kinetic energy and enstrophy to parameterize vertical mixing. The coupling framework has been updated to exchange vegetation-related variables between the flow model and the wave model to account for wave energy dissipation due to vegetation. This study i) demonstrates the validity of the plant posture-dependent drag parameterization against field measurements, ii) shows that the model is capable of reproducing the mean and turbulent flow field in the presence of vegetation as compared to various laboratory experiments, iii) provides insight into the flow-vegetation interaction through an analysis of the terms in the momentum balance, iv) describes the influence of a submerged vegetation patch on tidal currents and waves separately and combined, and v) proposes future directions for research and development.

How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence.

This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale "jumps" and "steps," which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

Assessment of subgrid-scale stress statistics in non-premixed turbulent wall-jet flames

ABSTRACTWe investigate the heat-release effects on the characteristics of the subgrid-scale (SGS) stress tensor and SGS dissipation of kinetic energy and enstrophy. Direct numerical simulation data of a non-premixed reacting turbulent wall-jet flow with and without substantial heat release is employed for the analysis. This study comprises, among others, an analysis of the eigenvalues of the resolved strain rate and SGS stress tensors, to identify the heat-release effects on their topology. An assessment of the alignment between the eigenvectors corresponding to the largest eigenvalues of these two tensors is also given to provide further information for modelling of the SGS stress tensor. To find out the heat-release effects on the dynamics of the turbulent kinetic energy and enstrophy dissipation, probability density functions (PDFs) and mean values are analysed. The mean SGS shear stress and turbulent kinetic energy both slightly increase in the buffer layer and substantially decrease further away from the wall, due to the heat-release effects. Contrary to the kinetic energy, heat release decreases the mean SGS dissipation of enstrophy in the near-wall region. Moreover, differences in the shapes of the PDFs between the isothermal and exothermic cases indicate changes in the intermittency level of both SGS dissipations. Heat release also increases the SGS stress anisotropy in the near-wall region. Although, the structure of the mean resolved strain-rate tensor only marginally differs between the isothermal and exothermic cases in the near-wall region, substantial differences are observed in the jet area, where compressibility effects are important and heat-release effects are found to promote compression states. The differences in the relative alignment between the SGS stress and resolved strain-rate tensors in the isothermal and exothermic cases are discussed in connection with the differences in the SGS dissipation of kinetic energy.

Vortex dynamics of a sphere wake in proximity to a wall

Toward getting the vortex dynamics characteristics and wake structure of a sphere in proximity to a wall, the effect of a proximal flat plate on the wake of a stationary sphere is investigated via direct numerical simulation. The vortex shedding process and the significant variation of the wake structure are described in detail. The drag coefficient reduces and the wake structure of the sphere becomes complex due to the combined effect of the wake flow and the wall. A jet flow forms between the sphere and the flat plate, which suppresses the vortex separation on the bottom of the sphere. The asymmetric distributions of the coherent structures and the recirculation region behind the sphere are discussed. Besides vortex shedding patterns, the time-averaged velocity distribution, vortex dynamics, distribution regularities of turbulent kinetic energy and enstrophy are investigated.

Large-eddy simulation of the Richtmyer–Meshkov instability

The subgrid-scale (SGS) terms of turbulence transport are modelled by the stretched-vortex SGS stress model, and a large-eddy simulation code multi-viscous fluid and turbulence (MVFT) is developed to investigate the MVFT problems. Then one AWE shock tube experiment of interface instability is simulated numerically by MVFT code, which reproduces the development process of the interface. The obtained numerical images of interface evolution and wave structures in flow field are consistent with the experimental results. The evolution of perturbed interface and propagation of shock waves in flow field and their interactions are analyzed in detail. The statistics features of turbulence mixing in the form of finer quantities, such as the turbulent kinetic energy, enstrophy, density variance, and turbulent mass flux are investigated, which also proves that the SGS model has a key role in large-eddy simulation. The turbulent kinetic energy and enstrophy decay with time as a power law.

On the stability and diffusive characteristics of Roe-MUSCL and Runge–Kutta schemes for inviscid Taylor–Green vortex

In this study, the stability and diffusive characteristics of second-order Roe-MUSCL in conjunction with three Runge–Kutta-based temporal schemes are investigated for implicit large-eddy simulation (ILES) of the Taylor–Green vortex transitional flow. The excessive dissipation inherent to Roe-MUSCL is mitigated using the Thornber et al. [12] and Bidadi–Rani [8] approaches, referred to as the low-Mach-number and current modifications LM [12] and CM, respectively. The temporal schemes investigated are those of Jameson et al. [3], Shu and Osher [15], and Spiteri and Ruuth [16]. The time evolution of statistics such as turbulent kinetic energy (TKE) and enstrophy are shown for various combinations of modified Roe-MUSCL and temporal schemes at 643 and 1283 grid resolutions. Also, the spectra of TKE, and of the numerical viscosity and dissipation-rate inherent to the modified schemes are presented. In general, it is observed that Shu–Osher method is the most stable among the three time schemes. For the 643 grid case, LM [12] resulted in a stable solution when combined with all three time schemes, whereas CM maintained stability only with Shu–Osher. The dissipation rate spectra reveal that the instability arises due to the insufficient rate of energy transfer from the energy-containing to the inertial-range scales. The instability of Jameson et al. and Spiteri–Ruuth schemes (with CM) is manifested as the larger magnitude of the slope of dissipation rate spectrum at low wavenumbers. For the 1283 grid simulations, temporal evolution of TKE showed that only Shu–Osher with LM remained stable. For the cases where both LM and CM are stable, the former exhibited better accuracy in capturing transition and the subsequent decaying turbulent flow. Estimates of effective Reynolds number from current ILES simulations show good agreement with actual Reynolds numbers in prior direct numerical simulations.

Numerical investigations of shock wave interactions with a supersonic turbulent boundary layer

Direct numerical simulations (DNS) are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. The accuracies of DNS calculations are established by checking the convergence of flow statistics for various grids, by comparing the generated results with those in the literature and also by the balance of contributing terms in the turbulent kinetic energy equation. Instantaneous flow visualizations show the significant effect of shock on turbulence structure in the shock-boundary layer interaction zone and also in the flow downstream of the interaction region. The separation bubbles exhibit highly unsteady and three-dimensional behavior and are larger for stronger shocks but the maximum probability of flow separation is found to be independent of the shock strength. The differences between Reynolds- and Favre-averaged quantities are also observed to be small and largely independent of the shock intensity. The turbulent kinetic energy is amplified across the shock, mainly by the production term in the turbulent kinetic energy equation. The amplification of enstrophy across the shock zone is found to be due to the vortex stretching term in the enstrophy transport equation. A detailed examination of the terms in the turbulent kinetic equation shows a strong coupling between the mean and turbulent fields in the interaction region with energy being continuously exchanged from one field to another. However, the compressibility-related terms in the transport equations for turbulent kinetic energy and enstrophy are found to be small for the simulated flows.

Transient response of enstrophy transport to opposition control in turbulent channel flow

The transient response of the turbulent enstrophy transport to opposition control in the turbulent channel flow is studied with the aid of direct numerical simulation. It is found that the streamwise enstrophy and the spanwise enstrophy are suppressed by the attenuation of the stretching terms at first, while the vertical enstrophy is reduced by inhibiting the tilt of the mean shear. In the initial period of the control, the streamwise enstrophy evolves much slower than the other two components. The vertical vorticity component exhibits a rapid monotonic decrease and also plays an important role in the attenuation of the other two components.

Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations

Direct numerical simulations (DNS) were performed for the forced homogeneous isotropic turbulence (FHIT) with/without polymer additives in order to elaborate the characteristics of the turbulent energy cascading influenced by drag-reducing effects. The finite elastic non-linear extensibility-Peterlin model (FENE-P) was used as the conformation tensor equation for the viscoelastic polymer solution. Detailed analyses of DNS data were carried out in this paper for the turbulence scaling law and the topological dynamics of FHIT as well as the important turbulent parameters, including turbulent kinetic energy spectra, enstrophy and strain, velocity structure function, small-scale intermittency, etc. A natural and straightforward definition for the drag reduction rate was also proposed for the drag-reducing FHIT based on the decrease degree of the turbulent kinetic energy. It was found that the turbulent energy cascading in the FHIT was greatly modified by the drag-reducing polymer additives. The enstrophy and the strain fields in the FHIT of the polymer solution were remarkably weakened as compared with their Newtonian counterparts. The small-scale vortices and the small-scale intermittency were all inhibited by the viscoelastic effects in the FHIT of the polymer solution. However, the scaling law in a fashion of extended self-similarity for the FHIT of the polymer solution, within the presently simulated range of Weissenberg numbers, had no distinct differences compared with that of the Newtonian fluid case.

Changes in turbulent dissipation in a channel flow with oscillating walls

AbstractHarmonic oscillations of the walls of a turbulent plane channel flow are studied by direct numerical simulations to improve our understanding of the physical mechanism for skin-friction drag reduction. The simulations are carried out at constant pressure gradient in order to define an unambiguous inner scaling: in this case, drag reduction manifests itself as an increase of mass flow rate. Energy and enstrophy balances, carried out to emphasize the role of the oscillating spanwise shear layer, show that the viscous dissipation of the mean flow and of the turbulent fluctuations increase with the mass flow rate, and the relative importance of the latter decreases. We then focus on the turbulent enstrophy: through an analysis of the temporal evolution from the beginning of the wall motion, the dominant, oscillation-related term in the turbulent enstrophy is shown to cause the turbulent dissipation to be enhanced in absolute terms, before the slow drift towards the new quasi-equilibrium condition. This mechanism is found to be responsible for the increase in mass flow rate. We finally show that the time-average volume integral of the dominant term is linearly related to the drag reduction.

Decaying versus stationary turbulence in particle-laden isotropic turbulence: Turbulence modulation mechanism

The objective of the current paper is to clarify the physical distinction between turbulence modulations by laden particles in decaying isotropic turbulence and stationary isotropic turbulence. Direct numerical simulations of stationary and decaying isotropic turbulence were carried out using 1283 grid points at a Taylor micro-scale Reynolds number of Rλ ∼ 70. The effect of O(106) solid particles with a different Stokes number (St) was implemented as a point-force approximation in the Navier-Stokes equation. Turbulent kinetic energy, acceleration, enstrophy, strain rate, and various spectra were examined to determine the distinctions. Turbulence modulation in decaying turbulence is qualitatively and quantitatively inconsistent compared to that in stationary turbulence, particularly when the particles have St ≤ 1, mainly due to the artificial forcing necessary for stationary status. For the particles with St > 1, however, decaying and stationary turbulence are qualitatively similar. A simple analysis confirms that stationary turbulence is not appropriate for the study of turbulence modulation by particles with St ≤ 1. Furthermore, the injection perturbation of particles has a significant effect on turbulence modulation in decaying turbulence. An investigation of the correlation between turbulence field zones and the two-way interaction energy was conducted to gain a better understanding of the modulation mechanism.

On the dynamical relevance of coherent vortical structures in turbulent boundary layers

The dynamical relevance of vortex tubes and vortex sheets in a wall-bounded supersonic turbulent flow at Mach numberM= 2 and Reynolds numberReθ≈ 1350 is quantitatively analysed. The flow in the viscous sublayer and in the buffer region is characterized by intense, elongated vorticity tongues forming a shallow angle with respect to the wall, whose characteristic length isO(200) wall units and whose size in the cross-stream direction isO(50) wall units. The formation of vortex tubes takes place starting fromy+≈ 10, and it is mainly associated with the roll-up and the interaction of vortex sheets. The analysis of the non-local dynamical effect of tubes and sheets suggests that the latter have a more important collective effect, being closely associated with low-speed streaks, and being responsible for a substantial contribution to the mean momentum balance and to the production of turbulence kinetic energy and enstrophy.

High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

The dynamics of the reshocked multi-mode Richtmyer–Meshkov instability is investigated using 513 × 2572 three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1:5 air/SF6 Vetter–Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed ow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

Momentum and scalar transport at the turbulent/non-turbulent interface of a jet

Conditionally sampled measurements withparticle image velocimetry(PIV) of a turbulent round submerged liquid jet in a laboratory have been taken atRe= 2 × 103between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planarlaser-induced fluorescence(LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (inProc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.

Vorticity and Turbulence in the Wake of a Bridge Pier

Dissipation rates of turbulence kinetic energy (TKE) epsiv and enstrophy zeta2 are reported in a high Reynolds number turbulent wake. Previous turbulent wake observations have been made in laboratory experiments with relatively low Reynolds number flows O (103). Results presented here are from a set of rare field observations of vorticity and turbulence in a turbulent wake with a high Reynolds number O (107). The turbulent wake was formed by an unsteady strong tidal current interacting with a bridge pier. Measurements were taken mostly in the intermediate wake, i.e., 10 les x/d les 60, where x is the downstream distance and d is the width of the bridge pier. Both epsiv and zeta2 show a similar downstream decay rate that is faster than that predicted by the self-preservation similarity in the far wake. The theoretical relation epsiv = nuzeta2 for high Reynolds number flow is confirmed by field observations. The magnitudes of the vertical and horizontal components of enstrophy do not differ significantly. The turbulence internal intermittency is ~ 0.2, estimated from autocorrelation coefficients of enstrophy; this value is close to that reported previously in turbulent wakes and jets.

Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

Abstract. This paper extends a turbulence closure-like model for stably stratified flows into a new dynamic domain in which turbulence is generated by internal gravity waves rather than mean shear. The model turbulent kinetic energy (TKE, K) balance, its first equation, incorporates a term for the energy transfer from internal waves to turbulence. This energy source is in addition to the traditional shear production. The second variable of the new two-equation model is the turbulent enstrophy (Ω). Compared to the traditional shear-only case, the Ω-equation is modified to account for the effect of the waves on the turbulence time and space scales. This modification is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean shear when turbulence is produced exclusively by internal waves. This paper is part 1 of a continuing theoretical development. It accounts for mean shear- and internal wave-driven mixing only in the two limits of mean shear and no waves and waves but no mean shear, respectively. The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000b). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. This is observed, for example, in the highly energetic tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

Dissipation and enstrophy in isotropic turbulence: Resolution effects and scaling in direct numerical simulations

Existing experimental and numerical data suggest that the turbulence energy dissipation and enstrophy (i.e., the square of vorticity) possess different scaling properties, while available theory suggests that there should be no differences at sufficiently high Reynolds numbers. We have performed a series of direct numerical simulations with up to 20483 grid points where advanced computational power is used to increase the Reynolds number (up to 650 on the Taylor scale) or to resolve the small scales better (down to 1∕4 of a Kolmogorov scale). Our primary goal is to assess the differences and similarities between dissipation and enstrophy. Special attention is paid to the effects of small-scale resolution on the quality and reliability of the data, in view of recent theoretical work [V. Yakhot and K. R. Sreenivasan, “Anomalous scaling of structure functions and dynamic constraints on turbulence simulations,” J. Stat. Phys. 121, 823 (2005)] which stipulates the resolution needed to obtain a moment of a given order. We also provide error estimates as a function of small-scale resolution. Probability density functions of dissipation and enstrophy at high Reynolds number reveal the presence of extreme events several thousands times of the mean. The extreme events in dissipation and enstrophy fields appear to scale alike, substantially overlap in space, and are nearly statistically isotropic, while fluctuations of moderate amplitudes, at least for the present Reynolds numbers, show persistent differences. Conditional sampling shows that intense dissipation is likely to be accompanied by similarly intense enstrophy, but intense enstrophy is not always accompanied by intense dissipation.

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability

Weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer–Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher-order higher-resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z+ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Reτ = 1,160, while the DNS data are extracted from a channel flow at Reτ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.

External turbulence interaction with a columnar vortex

A study was performed using direct numerical simulation to examine the interaction of external turbulence with a nominally columnar, large-scale vortex at a vortex Reynolds number . A multi-step procedure is used to generate initial conditions in which the external turbulence has the wrapped, nearly azimuthal form characteristic of turbulence around a large-scale vortex structure. The proper-orthogonal decomposition method is used to extract specific modes of the vortex turbulence that dominate the kinetic energy and enstrophy fields. The effect of turbulence initial intensity and length scale on the turbulence structure and its influence on the large-scale vortex are examined. It is observed that the external turbulence wraps around the large-scale vortex and advects radially inward toward the vortex core. The dominant axial length scale of the external turbulence appears to scale with the vortex core diameter, with the mode with the largest enstrophy having a wavelength of about twice the core diameter. The turbulence induces a bending wave on the vortex core with axial wavelength approximately equal to the dominant wavelength of the external turbulence. The turbulent enstrophy decays according to a power-law expression for cases with moderate initial turbulence intensity. For sufficiently strong initial turbulence intensity, the turbulence breaks up the large-scale vortex core, creating strong turbulence within the vortex core.