### Cite Details

Susan Kurien and Leslie Smith, "Asymptotics of unit Burger number rotating and stratified
flows for small aspect ratio
", *Physica D*, vol. 241, pp. 149 - 163, 2012

### Abstract

Rotating and stably stratified Boussinesq flow
is investigated for Burger number unity in domain aspect ratio
(height/horizontal length) *δ<1* and
*δ= 1*. To achieve Burger number unity, the
non-dimensional rotation and stratification frequencies (Rossby
and Froude numbers, respectively) are both set equal to a second
small parameter *ε<1*. Non-dimensionalization of
potential vorticity distinguishes contributions proportional to
*(εδ)*^{−1},
δ^{−1} and
*O(1)*. The
*(εδ)*^{−1} terms are
the linear terms associated with the pseudo-potential vorticity of
the quasi-geostrophic limit. For fixed *δ=1/4* and
a series of decreasing *ε*, numerical simulations
are used to assess the importance of the
*δ*^{−1} contribution of
potential vorticity to the potential enstrophy. The change in the
energy spectral scalings is studied as *ε* is
decreased. For intermediate values of *ε*, as the
flow transitions to the
*(εδ)*^{−1} regime in
potential vorticity, both the wave and vortical components of the
energy spectrum undergo changes in their scaling behavior. For
sufficiently small *ε*, the
*(εδ)*^{−1}
contributions dominate the potential vorticity, and the vortical
mode spectrum recovers *k*^{−3}
quasi-geostrophic scaling. However, the wave mode spectrum shows
scaling that is very different from the well-known
*k*^{−1} scaling observed for
the same asymptotics at *δ=1*. Visualization of the
wave component of the horizontal velocity at
*δ=1/4* reveals a tendency toward a layered
structure while there is no evidence of layering in the
*δ=1* case. The investigation makes progress
toward quantifying the effects of aspect ratio *δ*
on the *ε→0* asymptotics for the wave component of
unit Burger number flows. At the lowest value of
*ε=0.002*, it is shown that the horizontal kinetic
energy spectral scalings are consistent with phenomenology that
explains how linear potential vorticity constrains energy in the
limit *ε→0* for fixed *δ*.

### BibTeX Entry

@article{kurien-2012-asymptotics,

author = {Susan Kurien and Leslie Smith},

title = {Asymptotics of unit Burger number rotating and stratified
flows for small aspect ratio
},

year = {2012},

urlpdf = {http://math.lanl.gov/~skurien/papers/KurSmi_Burger_PhysD12.pdf},

journal = {Physica D},

volume = {241},

pages = {149 - 163}

}