International audienceDirect numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re " 1 and horizontal Froude number Fh Gt; 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter R = ReFh2. When R " 1, viscous forces are nimportant and lv scales as lv ~ U/N (U is a characteristic horizontal velocity and N is the Brunt - Väis¨alä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When R " 1, vertical viscous shearing is important so that lv ~ lh/Re1/2 (lh is a characteristic horizontal length scale). The parameter R is further shown to be related to the buoyancy Reynolds number and proportional to (lO/?) 4/3, where lO is the Ozmidov length scale and ? the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when R " 1: the scales larger than lO are strongly influenced by the stratification while those between lO and ? are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being R. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of R but they tend to be smooth for R > 1, while for R > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for R > 1 but tends to isotropy as R increases above unity. When R > 1, the horizontal and vertical energy spectra are very steep while, when R > 1, the horizontal spectra of kinetic and potential energy exhibit an pproximate kh-5/3-power-law range and a clear forward energy cascade is observed. © 2007 Cambridge University Press

Key Words absolute/convective instabilities, transient growth, fronts, Global modes, passive and active control ■ Abstract The objective of this review is to critically assess the different approaches developed in recent years to understand the dynamics of open flows such as mixing layers, jets, wakes, separation bubbles, boundary layers, and so on. These complex flows develop in extended domains in which fluid particles are continuously advected downstream. They behave either as noise amplifiers or as oscillators, both of which exhibit strong nonlinearities (Huerre & Monkewitz 1990). The local approach is inherently weakly nonparallel and it assumes that the basic flow varies on a long length scale compared to the wavelength of the instability waves. The dynamics of the flow is then considered as a superposition of linear or nonlinear instability waves that, at leading order, behave at each streamwise station as if the flow were homogeneous in the streamwise direction. In the fully global context, the basic flow and the instabilities do not have to be characterized by widely separated length scales, and the dynamics is then viewed as the result of the interactions between Global modes living in the entire physical domain with the streamwise direction as an eigendirection. This second approach is more and more resorted to as a result of increased computational capability. The earlier review of Huerre & Monkewitz (1990) emphasized how local linear theory can account for the noise amplifier behavior as well as for the onset of a Global mode. The present survey first adopts the opposite point of view by demonstrating how fully global theory accounts for the noise amplifier behavior of open flows. From such a perspective, there is strong emphasis on the very peculiar nonorthogonality of linear Global modes, which in turn allows a novel interpretation of recent numerical simulations and experimental observations. The nonorthogonality of linear Global modes also imposes severe constraints on the extension of linear global theory to the fully nonlinear régime. When the flow is weakly nonparallel, this limitation is so severe that the linear Global mode theory is of little help. It is then much more appropriate to develop a fully nonlinear formulation involving the presence of a front separating the base state region from the bifurcated state region.

International audienceIt is well-known that strongly stratified flows are organized into a layered pancake structure in which motions are mostly horizontal but highly variable in the vertical direction. However, what determines the vertical scale of the motion remains an open question. In this paper, we propose a scaling law for this vertical scale Lu when no vertical lengthscales are imposed by initial or boundary conditions and when the fluid is strongly stratified, i.e., when the horizontal Froude number is small: Fh=U/NLh " 1, where U is the magnitude of the horizontal velocity, N the Brunt-Vïsälä frequency and Lh the horizontal lengthscale. Specifically, we show that the vertical scale of the motion is Lv=U/N by demonstrating that the inviscid governing equations in the limit Fh?O, without any a priori assumption on the magnitude of Lu, are self-similar with respect to the variable zN/U, where z is the vertical coordinate. This self-similarity fully accounts for the layer characteristics observed in recent studies reporting spontaneous layering from an initially vertically uniform flow. For such a fine vertical scale, vertical gradients are large, O(1/FhLh). Therefore, even if the magnitude of the vertical velocity is small and scales like FhU, the leading order governing equations of these strongly stratified flows are not two-dimensional in contradiction with a previous conjecture. The self-similarity further suggests that the vertical spectrum of horizontal kinetic energy of pancake turbulence should be of the form E(kz)?N2kz-3, giving an alternative explanation for the observed vertical spectra in the atmosphere and oceans. © 2001 American Institute of Physics