Journal of Chemical Technology and Applications

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Journal of Chemical Technology and Applications 44 7897 074717

Kelvin-Helmholtz Instability Theory Pre Reviewed

The success of viscous potential flow in the analysis of Rayleigh-Taylor instability has motivated the analysis of the Kelvin-Helmholtz (KH) theory given here. It is well known that the instability that arises when surface tension and viscosity are neglected is catastrophic; short waves with wavelengths λ=2π/k amplify` without control like e power kt. The instability grows exponentially as the wavenumber k→∞no matter. how small-time t. This kind of catastrophic instability is called Hadamard instability In the case of inviscid fluids, this instability is regularized by surface tension which stabilizes the shortwaves surface tension is very important. The question is whether viscosity, without surface tension, would regularize the Hadamard instability of a vortex sheet on an unbounded domain.

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