Effect of rotation and domain aspect-ratio on layer formation in strongly stratified Boussinesq flows

Abstract

We present a numerical study of layer formation in forced, rotating, stably stratified Boussinesq flows. All flows are strongly stratified such that the buoyancy timescale 1/N is much faster than the turbulence timescale. The Coriolis timescale 1/f is chosen to be comparable to the turbulence timescale or faster. Furthermore, all simulations are in an asymptotic parameter regime defined by quadratic potential enstrophy. The aspect-ratio of the domain is δ = Hd/Ld where Hd (Ld) is the vertical height (horizontal length) of the domain, and the Froude (Rossby) number is defined using vertical (horizontal) scale and a velocity scale, both based on the large-scale force. Two sets of simulations are studied, both with fixed Froude number . The first set of runs fixes δ = 1 and varies the Rossby number . These unit aspect-ratio runs show a transition from flow with a quasi-geostrophic component to a layered flow as the Rossby number is increased from . The layering appears first in the wave component of the flow, but is gradually dominated by the vortical component for large-enough Rossby number. Partly motivated by mid-latitude geophysical flows, the second set of runs fixes the Burger number and varies the domain aspect-ratio 1/16 ≤ δ ≤ 1 (correspondingly 16 ≥ N/f ≥ 1). Wave-mode layering is also present in the runs with and δ < 1, with vortical-mode layering appearing only as δ < 1/4. Comparing the two sets of simulations for fixed N/f > 1, energy is suppressed in the vortical-mode component for the δ = f/N as compared to δ = 1. In general, as N/f increases from unity, there is a steady increase in the relative energy in the vortical modes at sub-forcing scales, but the rate of increase is slower if the aspect-ratio is decreased simultaneously so as to keep . The characteristic scales of the wave and vortical modes are measured using correlation lengths in the vertical and horizontal. As N/f increases, the vortical-mode thickness decreases as f/N while the wave-mode thickness increases as ≃ (N/f)1/2. The latter contribution may well provide a correction to the f/Nbehaviour observed for scale measurements in prior studies. The study is the first attempt to systematically characterise how both external aspect-ratio δ and N/f determine the internal scales and aspect-ratios of the structures formed in such flows.