dorsal/arxiv
View SchemaLagrangian Averaging for Compressible Fluids
| Authors | H. S. Bhat, R. C. Fetecau, J. E. Marsden, K. Mohseni, M. West |
|---|---|
| Categories | |
| ArXiv ID | physics/0311086 |
| URL | https://arxiv.org/abs/physics/0311086 |
Abstract
This paper extends the derivation of the Lagrangian averaged Euler (LAE-$\alpha$) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-$\alpha$ equations is simplified and clarified. The derivation in this paper involves averaging over a tube of trajectories $\eta^\epsilon$ centered around a given Lagrangian flow $\eta$. With this tube framework, the Lagrangian averaged Euler (LAE-$\alpha$) equations are derived by following a simple procedure: start with a given action, Taylor expand in terms of small-scale fluid fluctuations $\xi$, truncate, average, and then model those terms that are nonlinear functions of $\xi$. Closure of the equations is provided through the use of \emph{flow rules}, which prescribe the evolution of the fluctuations along the mean flow.
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"abstract": "This paper extends the derivation of the Lagrangian averaged Euler\n(LAE-$\\alpha$) equations to the case of barotropic compressible flows. The aim\nof Lagrangian averaging is to regularize the compressible Euler equations by\nadding dispersion instead of artificial viscosity. Along the way, the\nderivation of the isotropic and anisotropic LAE-$\\alpha$ equations is\nsimplified and clarified.\n The derivation in this paper involves averaging over a tube of trajectories\n$\\eta^\\epsilon$ centered around a given Lagrangian flow $\\eta$. With this tube\nframework, the Lagrangian averaged Euler (LAE-$\\alpha$) equations are derived\nby following a simple procedure: start with a given action, Taylor expand in\nterms of small-scale fluid fluctuations $\\xi$, truncate, average, and then\nmodel those terms that are nonlinear functions of $\\xi$. Closure of the\nequations is provided through the use of \\emph{flow rules}, which prescribe the\nevolution of the fluctuations along the mean flow.",
"arxiv_id": "physics/0311086",
"authors": [
"H. S. Bhat",
"R. C. Fetecau",
"J. E. Marsden",
"K. Mohseni",
"M. West"
],
"categories": [
"physics.flu-dyn"
],
"title": "Lagrangian Averaging for Compressible Fluids",
"url": "https://arxiv.org/abs/physics/0311086"
},
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