dorsal/arxiv
View SchemaSharp vorticity gradients in two-dimensional hydrodynamic turbulence
| Authors | E. A. Kuznetsov, V. Naulin, A. H. Nielsen, J. Juul Rasmussen |
|---|---|
| Categories | |
| ArXiv ID | physics/0407101 |
| URL | https://arxiv.org/abs/physics/0407101 |
Abstract
The appearance of sharp vorticity gradients in two-dimensional hydrodynamic turbulence and their influence on the turbulent spectra is considered. We have developed the analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines. Compressibility of this mapping can be considered as the main reason for the formation of the vorticity discontinuities at high Reynolds numbers. For two-dimensional turbulence in the case of strong anisotropy the vorticity discontinuities can generate spectra with the fall-off at large $k$ proportional to $k^{-3}$ resembling the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the $k$ dependence of the spectrum due to discontinuities coincides with that of the Saffman spectrum: $k^{-4}$. We have compared the analytical predictions with direct numerical solutions of the two-dimensional Euler equation for decaying turbulence. We observe that the di-vorticity is reaching very high values and is distributed locally in space along piecewise straight lines. Thus, indicating strong anisotropy and accordingly we found a spectrum close to the $k^{-3}$-spectrum.
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"abstract": "The appearance of sharp vorticity gradients in two-dimensional hydrodynamic\nturbulence and their influence on the turbulent spectra is considered. We have\ndeveloped the analog of the vortex line representation as a transformation to\nthe curvilinear system of coordinates moving together with the di-vorticity\nlines. Compressibility of this mapping can be considered as the main reason for\nthe formation of the vorticity discontinuities at high Reynolds numbers. For\ntwo-dimensional turbulence in the case of strong anisotropy the vorticity\ndiscontinuities can generate spectra with the fall-off at large $k$\nproportional to $k^{-3}$ resembling the Kraichnan spectrum for the enstrophy\ncascade. For turbulence with weak anisotropy the $k$ dependence of the spectrum\ndue to discontinuities coincides with that of the Saffman spectrum: $k^{-4}$.\nWe have compared the analytical predictions with direct numerical solutions of\nthe two-dimensional Euler equation for decaying turbulence. We observe that the\ndi-vorticity is reaching very high values and is distributed locally in space\nalong piecewise straight lines. Thus, indicating strong anisotropy and\naccordingly we found a spectrum close to the $k^{-3}$-spectrum.",
"arxiv_id": "physics/0407101",
"authors": [
"E. A. Kuznetsov",
"V. Naulin",
"A. H. Nielsen",
"J. Juul Rasmussen"
],
"categories": [
"physics.flu-dyn"
],
"title": "Sharp vorticity gradients in two-dimensional hydrodynamic turbulence",
"url": "https://arxiv.org/abs/physics/0407101"
},
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