dorsal/arxiv
View SchemaEnergy and enstrophy dissipation in steady state 2-d turbulence
| Authors | Alexandros Alexakis, Charles R. Doering |
|---|---|
| Categories | |
| ArXiv ID | physics/0605090 |
| URL | https://arxiv.org/abs/physics/0605090 |
| DOI | 10.1016/j.physleta.2006.07.048 |
Abstract
Upper bounds on the bulk energy dissipation rate $\epsilon$ and enstrophy dissipation rate $\chi$ are derived for the statistical steady state of body forced two dimensional turbulence in a periodic domain. For a broad class of externally imposed body forces it is shown that $\epsilon \le k_{f} U^3 Re^{-1/2}(C_1+C_2 Re^{-1})^{1/2}$ and $\chi \le k_{f}^{3}U^3 (C_1+C_2 Re^{-1})$ where $U$ is the root-mean-square velocity, $k_f$ is a wavenumber (inverse length scale) related with the forcing function, and $Re = U /\nu k_f$. The positive coefficients $C_1$ and $C_2$ are uniform in the the kinematic viscosity $\nu$, the amplitude of the driving force, and the system size. We compare these results with previously obtained bounds for body forces involving only a single length scale, or for velocity dependent a constant-energy-flux forces acting at finite wavenumbers. Implications of our results are discussed.
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"abstract": "Upper bounds on the bulk energy dissipation rate $\\epsilon$ and enstrophy\ndissipation rate $\\chi$ are derived for the statistical steady state of body\nforced two dimensional turbulence in a periodic domain. For a broad class of\nexternally imposed body forces it is shown that $\\epsilon \\le k_{f} U^3\nRe^{-1/2}(C_1+C_2 Re^{-1})^{1/2}$ and $\\chi \\le k_{f}^{3}U^3 (C_1+C_2 Re^{-1})$\nwhere $U$ is the root-mean-square velocity, $k_f$ is a wavenumber (inverse\nlength scale) related with the forcing function, and $Re = U /\\nu k_f$. The\npositive coefficients $C_1$ and $C_2$ are uniform in the the kinematic\nviscosity $\\nu$, the amplitude of the driving force, and the system size. We\ncompare these results with previously obtained bounds for body forces involving\nonly a single length scale, or for velocity dependent a constant-energy-flux\nforces acting at finite wavenumbers. Implications of our results are discussed.",
"arxiv_id": "physics/0605090",
"authors": [
"Alexandros Alexakis",
"Charles R. Doering"
],
"categories": [
"physics.flu-dyn",
"physics.geo-ph"
],
"doi": "10.1016/j.physleta.2006.07.048",
"title": "Energy and enstrophy dissipation in steady state 2-d turbulence",
"url": "https://arxiv.org/abs/physics/0605090"
},
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