### 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=H*_{d}/L_{d}
where *H*_{d}
(*L*_{d}) 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 =
Fr*_{o} ≈ 0.002. The first set of
runs fixes *δ = 1* and varies the Rossby number
*Fr*_{o}≤ Ro≤ 32
Fr_{o}. 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 =
Fr*_{o}. 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⁄Fr*_{o} = 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}

}