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Cite Details

Susan Kurien and Leslie Smith, "Effect of rotation and domain aspect-ratio on layer formation in strongly stratified Boussinesq flows", Journal of Turbulence, vol. 15:4, pp. 241 - 271, 2014

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 are 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 Fr = Fro ≈ 0.002. The first set of runs fixes δ = 1 and varies the Rossby number Fro≤ Ro≤ 32 Fro. 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 Ro = Fro. 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 Bu = Ro⁄Fro = Nδ⁄f = 1 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 Bu=1 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 Bu = 1. 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⁄N behavior observed for scale measurements in prior studies. The study is a first attempt to systematically characterize how both external aspect-ratio δ and N⁄f determine the internal scales and aspect-ratios of the structures formed in such flows.

BibTeX Entry

@article{kurien-2014-effect,
author = {Susan Kurien and Leslie Smith},
title = {Effect of rotation and domain aspect-ratio on layer formation in strongly stratified Boussinesq flows},
year = {2014},
urlpdf = {http://math.lanl.gov/~skurien/papers/KurienSmith_JOT14_public.pdf},
journal = {Journal of Turbulence},
volume = {15:4},
pages = {241 - 271}
}