A large direct numerical simulation of rotating stably stratified turbulence: Evidence for Bolgiano-Obukhov scaling

Annick Pouquet
National Center for Atmospheric Research

A. Pouquet, R. Marino, P. Mininni and D. Rosenberg

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 $Re=5.4\times 10^4$ and $Fr=0.0242$. The ratio of the Brunt-V\"ais\"al\"a 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 $R_B=ReFr^2=32$, 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 large-scale 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.

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