Sharp vorticity gradients in two-dimensional hydrodynamic turbulence

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dc.creatorKuznetsov, E. A.
dc.creatorNaulin, V.
dc.creatorNielsen, A. H.
dc.creatorRasmussen, J. Juul
dc.date2004-07-19
dc.date.accessioned2026-07-07T05:52:19Z
dc.date.available2026-07-07T05:52:19Z
dc.descriptionThe 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.
dc.description24 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/physics/0407101
dc.identifierhttp://arxiv.org/abs/physics/0407101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/86284
dc.subjectFluid Dynamics
dc.titleSharp vorticity gradients in two-dimensional hydrodynamic turbulence
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