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 = H_d/L_d where H_d (L_d) 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.

Keywords:

• Boussinesq
• rotating turbulence
• stratified turbulence
• small aspect-ratio flows

Acknowledgements

The authors thank two anonymous reviewers whose comments were instrumental in developing Section 4 of the paper.

Additional information

Funding

The resources of the Argonne Leadership Computing Facility at Argonne National Laboratory were used, which are supported by the Office of Science of the US DOE [grant number DE-AC02-06CH11357]. Funding for this effort came from the NSF programme Collaboration in Mathematical Geosciences [grant number NSF CMG-1025188] (S. Kurien was funded via the New Mexico Consortium). This research was performed under the auspices of the US DOE at Los Alamos National Laboratory (LANL) [grant number DE-AC52-06NA25396].