Numerical experiments on strongly stratified homogeneous shear turbulence
نویسنده
چکیده
Turbulence in strongly stable density stratification is a common phenomenon in atmosphere and in oceans and other large water bodies. Stably and strongly stratified turbulence have been studied in many experimental and numerical studies. A characteristic feature of strongly stratified turbulence observed in several studies is the formation of quasi-horizontal layers. During the last decade, the dynamics of the layered structure in absense of mean shear was revealed by Billant & Chomaz (Phys. Fluids 13, 1645-1651, 2001) and by Brethouwer et al. (J. Fluid Mech. 585, 343-368, 2007). They found that the layer thickness scales by U/N where U is the magnitude of the horizontal turbulent velocity and N is the Brunt-Väisälä frequency N=(g/T0 dT/dz)1/2. Brethouwer et al. (2007) concluded in their DNS study that, in the absense of mean shear, strongly stratified turbulence has two very different regimes depending on the parameter R=Fh2Re related to buoyant Reynolds number. Here Fh is the horizontal Froude number Fh=ε/(UN) characterizing the ratio of vertical and horizontal length scales, and Re is the usual turbulent Reynolds number Re=Ek/(εν), with Ek being the turbulent kinetic energy and ε its dissipation rate. In strongly stratified flows, Fh<<1. If R<1, the layers become quasi laminar, thus no small-scale turbulent motion is sustained and no forward energy cascade exists. On the other hand, if R>1, healthy small-scale threedimensional turbulent motion is observed embedded in the layer structure and forward energy cascade occurs. The latter is the situation typical in nature, but it is not so easy to achieve in laboratory and in DNS as Fh must be small and R=Fh Re must be large or at least larger than about one. Brethouwer et al. applied artificial forcing of the lowest horizontal Fourier modes instead of mean shear in their DNS to sustain statistically stationary turbulence. So far, the dynamics of strongly stratified turbulence with mean shear has not been studied from this point of view (whereas weakly stratified shear turbulence has been studied in many works). In the present study, strongly stratified homogeneous turbulence with imposed constant mean shear is numerically studied in the light of the findings by Brethouwer et al. Preliminary results suggest that the U/N-scaling applies to horizontal velocity components also in the presence of mean shear but that the vertical velocity structures show larger length scale not scaling by U/N. The vertical velocities are clearly larger than in non-sheared cases, although still being smaller than the horizontal components. This difference can be explained by the fact that in sheared flow, where Ek slowly decays, reversed energy flux from potential to kinetic energy occurs intermittently whereas in the artificially forced non-sheared case energy always flows from kinetic to potential energy. The reversed energy flux occurs through the vertical velocity component and therefore this component is sustained unlike in the non-sheared case. This difference is likely to be connected to the observed difference in the vertical velocity structures (see Fig. 1). Nevertheless the overall behavior is quite similar to that observed by Brethouwer et al. The two distinct regimes according to R are clearly observed also in this study.
منابع مشابه
Diapycnal diffusivities in homogeneous stratified turbulence
[1] Quantifying diapycnal mixing in stably stratified turbulence is fundamental to the understanding and modeling of geophysical flows. Data of diapycnal mixing from direct numerical simulations of homogeneous stratified turbulence and from grid turbulence experiments, are analyzed to investigate the scaling of the diapycnal diffusivity. In these homogeneous flows the instantaneous diapycnal di...
متن کاملBuoyancy Fluxes in a Stratified Fluid
Direct numerical simulations of the time evolution of homogeneous stably stratified shear flows have been performed for mean flow Richardson numbers in the range from 0.075 to 1.00 and for Prandtl numbers ranging from 0.1 to 2. The local or instantaneous results indicate that when the turbulent Froude number FrT = 1 the peak value of mixing efficiency is Rf ≈ 0.25, a result independent of the P...
متن کاملThe Effect of Stable Stratification on Turbulence Anisotropy in Uniformly Sheared Flow
Direct numerical simulation of uniform shear flow is used to study the anisotropy of fluctuating motion in a stably stratified medium with uniform mean shear. Turbulence is found to be three dimensional over a wjde range of gradient Richardson numbers in the two Bows investigated here: vertical mean shear ($$-) and horizontal mean shear (g). The role of the turbulent F’roude number in establish...
متن کاملBounded Energy States in Homogeneous Turbulent Shear Flow—An Alternative View
The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown th...
متن کاملTurbulent mixing in strongly stratified shear flows
Motivated by the importance of irreversible mixing in geophysical and environmental flows, we seek to understand the dependence of its efficiency under strongly stratified conditions through a seris of direct numerical simulation of Holmboe wave instability under various initial conditions. Our numerical findings demonstrate that while mixing is enhanced when the density layer is much sharper t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010