Existence of the stationary solution of a Rayleigh-type equation
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A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the stationary solution of a Rayleigh-type equation, which describes oscillations of the vertical velocity component in the classical boundary layer.
Keywordsdouble-deck structure boundary-layer theory fluid mechanics Navier–Stokes equations Rayleigh-type equation eigenvalue problem
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