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 and with large-scale isotropic initial conditions using direct numerical simulations computed on grids of up to 40963 points. The Reynolds and Froude numbers are, respectively, equal to Re = 5.4 × 104 and Fr = 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 = ReFr2 ≈ 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. This scaling is also found for geostrophically balanced initial conditions on a run at a lower resolution and hence lower RB ≈ 4. Furthermore, we 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 local Richardson numbers and strong localized vortex tangles . Finally, a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.