dorsal/arxiv
View SchemaSelf-Similarity in Decaying Two-Dimensional Stably Stratified Adjustment
| Authors | Jai Sukhatme, Leslie M. Smith |
|---|---|
| Categories | |
| ArXiv ID | physics/0607045 |
| URL | https://arxiv.org/abs/physics/0607045 |
| DOI | 10.1063/1.2717514 |
Abstract
The evolution of large-scale density perturbations is studied in a stably stratified, two-dimensional flow governed by the Boussinesq equations. As is known, intially smooth density (or temperature) profiles develop into fronts in the very early stages of evolution. This results in a frontally dominated $k^{-1}$ potential energy spectrum. The fronts, initially characterized by a relatively simple geometry, spontaneously develop into severely distorted sheets that possess structure at very fine scales, and thus there is a transfer of energy from large to small scales. It is shown here that this process culminates in the establishment of a $k^{-5/3}$ kinetic energy spectrum, although its scaling extends over a shorter range as compared to the $k^{-1}$ scaling of the potential energy spectrum. The establishment of the kinetic energy scaling signals the onset of enstrophy decay which proceeds in a mildly modulated exponential manner and possesses a novel self-similarity. Specifically, the self-similarity is seen in the time invariant nature of the probability density function (\pdf{}) associated with the normalized vorticity field. Given the rapid decay of energy at this stage, the spectral scaling is transient and fades with the emergence of a smooth, large-scale, very slowly decaying, (almost) vertically sheared horizontal mode with most of its energy in the potential component -- i.e. the Pearson-Linden regime.
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"abstract": "The evolution of large-scale density perturbations is studied in a stably\nstratified, two-dimensional flow governed by the Boussinesq equations. As is\nknown, intially smooth density (or temperature) profiles develop into fronts in\nthe very early stages of evolution. This results in a frontally dominated\n$k^{-1}$ potential energy spectrum. The fronts, initially characterized by a\nrelatively simple geometry, spontaneously develop into severely distorted\nsheets that possess structure at very fine scales, and thus there is a transfer\nof energy from large to small scales. It is shown here that this process\nculminates in the establishment of a $k^{-5/3}$ kinetic energy spectrum,\nalthough its scaling extends over a shorter range as compared to the $k^{-1}$\nscaling of the potential energy spectrum. The establishment of the kinetic\nenergy scaling signals the onset of enstrophy decay which proceeds in a mildly\nmodulated exponential manner and possesses a novel self-similarity.\nSpecifically, the self-similarity is seen in the time invariant nature of the\nprobability density function (\\pdf{}) associated with the normalized vorticity\nfield. Given the rapid decay of energy at this stage, the spectral scaling is\ntransient and fades with the emergence of a smooth, large-scale, very slowly\ndecaying, (almost) vertically sheared horizontal mode with most of its energy\nin the potential component -- i.e. the Pearson-Linden regime.",
"arxiv_id": "physics/0607045",
"authors": [
"Jai Sukhatme",
"Leslie M. Smith"
],
"categories": [
"physics.flu-dyn",
"physics.ao-ph"
],
"doi": "10.1063/1.2717514",
"title": "Self-Similarity in Decaying Two-Dimensional Stably Stratified Adjustment",
"url": "https://arxiv.org/abs/physics/0607045"
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