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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}
}