Large-scale anisotropy in stably stratified rotating flows

Abstract

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

Absorption of waves by large-scale winds in stratified turbulence

“…For the run with Fr ≈ 0.04, the minimum of Ri is ≈ 14. Although this value is rather large for atmospheric flows, it has been reported in other simulations of stratified turbulence, and indicate that CL instability can be the reason for the nonlocal formation of large scale structures in stratified turbulence observed in [27][28][29].…”

“…This indicates the CL instability can be one of the mechanism behind the formation of large scales structures in stratified flows, often observed in simulations but whose origin is unclear [27][28][29]. Moreover, although Doppler shift is observed in all forcing functions considered, development of the CL instability requires the external forcing not to disrupt the development of mean horizontal winds.…”

“…It is known that stratified flows can generate large-scale vertically sheared horizontal winds (VSHW) [27], although the mechanism involved is not entirely understood. While evidence of energy flow toward large scales has been reported [28,29], several authors have argued that an inverse cascade is not possible [21,30] based on statistical mechanical arguments.…”

Influence of atmospheric stratification on the integral scale and fractal dimension of turbulent flows

“…Which is the mechanism responsible for the growth of this integral scale? It has been observed in previous works that under certain conditions the turbulent flows self-organize and develop large-scale structures that take place through an inverse cascade that occurs in stably stratified anisotropic flows (with or without rotation) (Smith and Waleffe, 2002;Marino et al, 2014). The inverse cascade mechanism might also be responsible for the growth of the integral scale in the stratified atmosphere.…”

Inverse cascades and resonant triads in rotating and stratified turbulence

“…Finally, for negligible or no rotation, although an increase of energy and of the integral vertical length scale was reported in simulations [37,38], Waite and Bartello [39,40] conclude against the presence of an inverse cascade using an argument based on statistical mechanics, similar to the one used by Kraichnan to predict the inverse cascade in 2D flows. More recently [60] showed, using a detailed analysis of anisotropic fluxes, that the growth of vertical length scales in this system is the result of highly anisotropic energy transfers associated with the formation of vertically sheared horizontal winds (VSHW, see [37]). …”