Modifying shallow-water equations as a model for wave-vortex turbulence. Mohanan, A. V., Augier, P., & Lindborg, E. In December, 2017. ![Modifying shallow-water equations as a model for wave-vortex turbulence [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex 1 download The one-layer shallow-water equations is a simple two-dimensional model to study the complex dynamics of the oceans and the atmosphere. We carry out forced-dissipative numerical simulations, either by forcing medium-scale wave modes, or by injecting available potential energy (APE). With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers F\textlessSUB\textgreaterf\textless/SUB\textgreater = ∊ /(k\textlessSUB\textgreaterf\textless/SUB\textgreater c), where ∊ is the energy dissipation rate, k\textlessSUB\textgreaterf\textless/SUB\textgreater the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k\textlessSUP\textgreater-2\textless/SUP\textgreater and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .\u\) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k\textlessSUP\textgreater-5/3\textless/SUP\textgreater spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k\textlessSUP\textgreater-3\textless/SUP\textgreater spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. Divergence and potential temperature fields of shallow-water (top row) and toy model (bottom row) simulations.
@inproceedings{mohanan_modifying_2017,
title = {Modifying shallow-water equations as a model for wave-vortex turbulence},
url = {https://ui.adsabs.harvard.edu/abs/2017AGUFMNG14A..07M/abstract},
abstract = {The one-layer shallow-water equations is a simple two-dimensional model to study the complex dynamics of the oceans and the atmosphere. We carry out forced-dissipative numerical simulations, either by forcing medium-scale wave modes, or by injecting available potential energy (APE). With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers F{\textless}SUB{\textgreater}f{\textless}/SUB{\textgreater} = ∊ /(k{\textless}SUB{\textgreater}f{\textless}/SUB{\textgreater} c), where ∊ is the energy dissipation rate, k{\textless}SUB{\textgreater}f{\textless}/SUB{\textgreater} the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k{\textless}SUP{\textgreater}-2{\textless}/SUP{\textgreater} and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .\{u\}) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k{\textless}SUP{\textgreater}-5/3{\textless}/SUP{\textgreater} spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k{\textless}SUP{\textgreater}-3{\textless}/SUP{\textgreater} spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. Divergence and potential temperature fields of shallow-water (top row) and toy model (bottom row) simulations.},
language = {en},
urldate = {2021-05-20},
author = {Mohanan, A. V. and Augier, P. and Lindborg, E.},
month = dec,
year = {2017},
keywords = {\#cv},
}
Downloads: 1
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With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers F\\textlessSUB\\textgreaterf\\textless/SUB\\textgreater = ∊ /(k\\textlessSUB\\textgreaterf\\textless/SUB\\textgreater c), where ∊ is the energy dissipation rate, k\\textlessSUB\\textgreaterf\\textless/SUB\\textgreater the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k\\textlessSUP\\textgreater-2\\textless/SUP\\textgreater and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .\\u\\) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k\\textlessSUP\\textgreater-5/3\\textless/SUP\\textgreater spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k\\textlessSUP\\textgreater-3\\textless/SUP\\textgreater spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. 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The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .\\{u\\}) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k{\\textless}SUP{\\textgreater}-5/3{\\textless}/SUP{\\textgreater} spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k{\\textless}SUP{\\textgreater}-3{\\textless}/SUP{\\textgreater} spectrum. 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