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- W2070791750 abstract "We study Dhanak's model [J. Fluid Mech. 269, 265 (1994)]10.1017/S0022112094001552 of a viscous vortex sheet in the sharp limit, to investigate singularity formations and present nonlinear evolutions of the sheets. The finite-time singularity does not disappear by giving viscosity to the vortex sheet, but is delayed. The singularity in the sharp viscous vortex sheet is found to be different from that of the inviscid sheet in several features. A discontinuity in the curvature is formed in the viscous sheet, similarly as the inviscid sheet, but a cusp in the vortex sheet strength is less sharpened by viscosity. Exponential decay of the Fourier amplitudes is lost by the formation of the singularity, and the amplitudes of high wavenumbers exhibit an algebraic decay, while in the inviscid vortex sheet, the algebraic decay of the Fourier amplitudes is valid from fairly small wavenumbers. The algebraic decay rate of the viscous vortex sheet is approximately −2.5, independent of viscosity, which is the same rate as the asymptotic analysis of the inviscid sheet. Results for evolutions of the regularized vortex sheets show that the roll-up is weakened by viscosity, and the regularization parameter has more significant effects on the fine-structure of the core than does viscosity." @default.
- W2070791750 created "2016-06-24" @default.
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- W2070791750 date "2013-01-01" @default.
- W2070791750 modified "2023-10-01" @default.
- W2070791750 title "Singularity formation and nonlinear evolution of a viscous vortex sheet model" @default.
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- W2070791750 doi "https://doi.org/10.1063/1.4789460" @default.
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