Viscous Flow Analysis of the Kelvin-Helmholtz Instability for Short Waves

In this paper a mathematical model for the formation of nanostructures in the material under an intensive external action due to the occurrence of Kelvin-Helmholtz instability is provided. The model is based on the linearized Navier-Stokes and Euler equations, kinematic and dynamic boundary conditions. A dispersion equation is obtained and analyzed in the short-wave approximation. It is found that the dependence of the decrement in the wave number has two maxima. The first maximum occurs at the wave number corresponding to the microrange wavelength, and the second maximum takes place at the wave number corresponding to the nanorange. Analytical dependences of the wave number, which account for the maximum decrement of input parameters of the problem (viscosity, density of the material of the first and second layers, relative velocity of layers, and surface tension) are found. A range of the parameters for which the bimodal Kelvin-Helmholtz instability appears is specified.