Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

Abstract

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to 4096 3 points. The Reynolds and Froude numbers are respectively equal to Re = 5.4×10 4 and F r = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f , is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReF r 2 = 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the largescale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, with local overturning events indicated by small Richardson numbers, and a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

“…In Figure (top), we plot vorticity structures in RST with large‐scale eddies due to the influence of rotation, at the border of which strong small‐scale vortex lanes develop because of instabilities such as Kelvin‐Helmoltz or those due to shear. The plot is for a flow with , for a decay run on a grid of 4,096 3 points, integrating the Boussinesq equations (see Rosenberg et al, , and references therein for more details).…”

“…Rotating stratified flows. (top) Vorticity strength on three planes for the decay run analyzed in Rosenberg et al (), where the color map is also given. The grid has 4,096 3 points, N / f = 5, R e = 55,000, F r = 0.024.…”

Correction to: Variations of characteristic time scales in rotating stratified turbulence using a large parametric numerical study

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After publication of the paper, an error in computing the ratio γ of kinetic to potential energy transfer times has been detected, which has led the authors to amend two figures, as explained below.Energy dissipation rates, v,p = |D t E v,p |, were computed with isotropic one-dimensional Fourier data, when 2D spectra should have been used [1]. The difference is particularly stark for the strongly anisotropic density dissipation p , with sharp fronts.

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“…Energy dissipation rates, v,p = |D t E v,p |, were computed with isotropic one-dimensional Fourier data, when 2D spectra should have been used [1]. The difference is particularly stark for the strongly anisotropic density dissipation p , with sharp fronts.…”

Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition

“…The initial conditions of the runs analyzed in this paper all have velocity modes only, and they are centered in the large scales. We know that balanced initial conditions also give a similar scaling with an identical value of k EQ [34]. In the future, we plan to analyze the stationary case, using both isotropic and balanced forcing; this will also allow for longer time statistics.…”