On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence

2014 ◽  
Vol 756 ◽  
pp. 816-843 ◽  
Author(s):  
Marcello Meldi ◽  
Hugo Lejemble ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Initial Kinetic Energy ◽  
Grid Turbulence ◽  
Production Term ◽  
Turbulence Decay ◽  
Turbulence Production

AbstractThe present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$. A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$. Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.

scholarly journals Virtual motion of real particles

2010 ◽  
Vol 650 ◽  
pp. 1-4 ◽  
Author(s):  
G. TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Multiphase Flows ◽  
Isotropic Turbulence ◽  
Finite Size ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Length Scale ◽  
Turbulent Eddies

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

Sensitivity of stratified turbulence to the buoyancy Reynolds number

2013 ◽  
Vol 725 ◽  
pp. 1-22 ◽  
Author(s):  
P. Bartello ◽  
S. M. Tobias
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Froude Number ◽  
Relative Size ◽  
Stratified Flow ◽  
Reynolds Numbers ◽  
Stratified Turbulence ◽  
Integral Scale

AbstractIn this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

Stratified turbulence forced with columnar dipoles: numerical study

2015 ◽  
Vol 769 ◽  
pp. 403-443 ◽  
Author(s):  
Pierre Augier ◽  
Paul Billant ◽  
Jean-Marc Chomaz
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Stationary Flow ◽  
Length Scale ◽  
Computational Domain ◽  
Stratified Turbulence ◽  
Kinetic Energy Spectrum

This paper builds upon the investigation of Augier et al. (Phys. Fluids, vol. 26 (4), 2014) in which a strongly stratified turbulent-like flow was forced by 12 generators of vertical columnar dipoles. In experiments, measurements start to provide evidence of the existence of a strongly stratified inertial range that has been predicted for large turbulent buoyancy Reynolds numbers $\mathscr{R}_{t}={\it\varepsilon}_{\!K}/({\it\nu}N^{2})$, where ${\it\varepsilon}_{\!K}$ is the mean dissipation rate of kinetic energy, ${\it\nu}$ the viscosity and $N$ the Brunt–Väisälä frequency. However, because of experimental constraints, the buoyancy Reynolds number could not be increased to sufficiently large values so that the inertial strongly stratified turbulent range is only incipient. In order to extend the experimental results toward higher buoyancy Reynolds number, we have performed numerical simulations of forced stratified flows. To reproduce the experimental vortex generators, columnar dipoles are periodically produced in spatial space using impulsive horizontal body force at the peripheries of the computational domain. For moderate buoyancy Reynolds number, these numerical simulations are able to reproduce the results obtained in the experiments, validating this particular forcing. For higher buoyancy Reynolds number, the simulations show that the flow becomes turbulent as observed in Brethouwer et al. (J. Fluid Mech., vol. 585, 2007, pp. 343–368). However, the statistically stationary flow is horizontally inhomogeneous because the dipoles are destabilized quite rapidly after their generation. In order to produce horizontally homogeneous turbulence, high-resolution simulations at high buoyancy Reynolds number have been carried out with a slightly modified forcing in which dipoles are forced at random locations in the computational domain. The unidimensional horizontal spectra of kinetic and potential energies scale like $C_{1}{\it\varepsilon}_{\!K}^{2/3}k_{h}^{-5/3}$ and $C_{2}{\it\varepsilon}_{\!K}^{2/3}k_{h}^{-5/3}({\it\varepsilon}_{\!P}/{\it\varepsilon}_{\!K})$, respectively, with $C_{1}=C_{2}\simeq 0.5$ as obtained by Lindborg (J. Fluid Mech., vol. 550, 2006, pp. 207–242). However, there is a depletion in the horizontal kinetic energy spectrum for scales between the integral length scale and the buoyancy length scale and an anomalous energy excess around the buoyancy length scale probably due to direct transfers from large horizontal scale to small scales resulting from the shear and gravitational instabilities. The horizontal buoyancy flux co-spectrum increases abruptly at the buoyancy scale corroborating the presence of overturnings. Remarkably, the vertical kinetic energy spectrum exhibits a transition at the Ozmidov length scale from a steep spectrum scaling like $N^{2}k_{z}^{-3}$ at large scales to a spectrum scaling like $C_{K}{\it\varepsilon}_{\!K}^{2/3}k_{z}^{-5/3}$, with $C_{K}=1$, the classical Kolmogorov constant.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

1993 ◽  
Vol 251 ◽  
pp. 533-562 ◽  
Author(s):  
Sangsan Lee ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Shock Waves ◽  
Shock Front ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Isotropic Turbulence ◽  
Weak Shock ◽  
Linear Analysis ◽  
Weak Shock Wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

scholarly journals The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Antoine Briard ◽  
Thomas Gomez
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Total Energy ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Mhd Turbulence ◽  
Previous Prediction

Decaying homogeneous and isotropic magnetohydrodynamics (MHD) turbulence is investigated numerically at large Reynolds numbers thanks to the eddy-damped quasi-normal Markovian (EDQNM) approximation. Without any background mean magnetic field, the total energy spectrum $E$ scales as $k^{-3/2}$ in the inertial range as a consequence of the modelling. Moreover, the total energy is shown, both analytically and numerically, to decay at the same rate as kinetic energy in hydrodynamic isotropic turbulence: this differs from a previous prediction, and thus physical arguments are proposed to reconcile both results. Afterwards, the MHD turbulence is made imbalanced by an initial non-zero cross-helicity. A spectral modelling is developed for the velocity–magnetic correlation in a general homogeneous framework, which reveals that cross-helicity can contain subtle anisotropic effects. In the inertial range, as the Reynolds number increases, the slope of the cross-helical spectrum becomes closer to $k^{-5/3}$ than $k^{-2}$. Furthermore, the Elsässer spectra deviate from $k^{-3/2}$ with cross-helicity at large Reynolds numbers. Regarding the pressure spectrum $E_{P}$, its kinetic and magnetic parts are found to scale with $k^{-2}$ in the inertial range, whereas the part due to cross-helicity rather scales in $k^{-7/3}$. Finally, the two $4/3$rd laws for the total energy and cross-helicity are assessed numerically at large Reynolds numbers.

scholarly journals Experimental study on two oscillating grid turbulence with viscoelastic fluids based on PIV

2017 ◽  
Vol 95 (12) ◽  
pp. 1271-1277 ◽  
Author(s):  
Yue Wang ◽  
Wei-Hua Cai ◽  
Xin Zheng ◽  
Hong-Na Zhang ◽  
Feng-Chen Li
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Critical Concentration ◽  
Reduction Rate ◽  
Small Scale ◽  
Grid Turbulence ◽  
Viscoelastic Effect ◽  
Oscillating Grid

In this paper, to study the viscoelastic effect on isotropic turbulence without wall effects, a two oscillating grid turbulence is built to investigate this phenomenon using particle image velocimetry. In the experiments, the classical drag-reducing additives are chosen: polyacrylamide (PAM) and cetyltrimethyl ammonium chloride (CTAC), which have shown remarkable drag-reducing effect in wall-bounded turbulent flows. The results show that the existence of drag-reducing additives makes velocity field more anisotropic and reduces turbulent kinetic energy. We propose an intuitive and natural definition for a reduction rate of turbulent kinetic energy to show viscoelastic effect. It suggests that there exists a critical concentration for the reduction rate of turbulent kinetic energy in the CTAC solution case. Also, the small-scale vortex structures are inhibited, which suggests the drag-reducing mechanism in grid turbulence without wall effect.

On non-self-similar regimes in homogeneous isotropic turbulence decay

2012 ◽  
Vol 711 ◽  
pp. 364-393 ◽  
Author(s):  
Marcello Meldi ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Self Similarity ◽  
Velocity Correlation ◽  
Turbulence Decay ◽  
Long Time ◽  
Self Similar ◽  
Decay Exponent

AbstractBoth theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\ensuremath{\rightarrow} 0)$ or the velocity correlation function $f(r\ensuremath{\rightarrow} + \infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

On the Average Settling Rate of Heavy Particles in Decaying Homogeneous Isotropic Turbulence

1998 ◽  
Vol 14 (3) ◽  
pp. 111-118
Author(s):  
C. Y. Yang ◽  
U. Lei
Keyword(s):  
Time Scale ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Solid Particles ◽  
Settling Rate ◽  
Stationary Turbulence ◽  
Turbulence Decay ◽  
Decaying Turbulence ◽  
Inertia Response

ABSTRACTThe average settling rate of spherical solid particles, 〈vs〉, under a body force field is studied numerically in decaying homogeneous isotropic turbulent flows generated by the direct numerical simulation of the continuity and Navier-Stokes equations. The increase of the average settling rate, 〈Δvs〉, is maximized when Tp/Tk ≈ 1 and vd/u′ ≈ 0.5, and is of order 0.lu′, which is qualitatively similar to that in stationary turbulence. Here 〈Δvs〉 = 〈vs〉 − vd, Tp is the particle's relaxation time, Tk is the Kolmogorov time scale, vd is the settling rate of particles in still fluid, and u′ is the root mean square of the fluid velocity fluctuation. However, the magnitude of the maximum value of 〈Δvs〉 in decaying turbulence is substantially greater (about 40%) than that in the corresponding stationary turbulence due to the inertia response of particles to turbulence decay. Although 〈Δvs〉/u′ does not reach a stationary state as the flow is evolving, it is a slowly time varying function for the parameters of interest as Tp (≈ Tk when 〈Δvs〉 is maximized) is in general of one order less than the time scale of turbulence decay.

Spectra, Spatial Scales, and Predictability in a Quasigeostrophic Model

2009 ◽  
Vol 66 (10) ◽  
pp. 3115-3130 ◽  
Author(s):  
Rebecca E. Morss ◽  
Chris Snyder ◽  
Richard Rotunno
Keyword(s):  
Growth Rate ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Spatial Scales ◽  
Error Growth ◽  
Surface Perturbation ◽  
Kinetic Energy Spectrum ◽  
Quasigeostrophic Model ◽  
Perturbation Growth

Abstract Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

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