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Kelvin-Helmholtz instability in magnetic fluids with surface adsorption: Linear and nonlinear theory. (English) Zbl 0763.76028

Summary: The linear and nonlinear stability of the Kelvin-Helmholtz problem for magnetic fluids with surface adsorption is studied by employing the multiple scale method. The phenomenon of nonlinear focusing or collapse is considered. It is shown that the evolution of the amplitude is governed by a two-dimensional Schrödinger equation with cubic nonlinearity. This equation gives rise to a self-focusing singularity when the velocity difference is in the subcritical regime. Also from its equation, we obtain the condition for the existence of the modulational instability. The various regions of stability and instability are indicated.

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30 Nonlinear effects in hydrodynamic stability
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