We study the existence conditions for a double-deck structure of a boundary layer in typical problems of incompressible fluid flow along surfaces with small irregularities (periodic or localized) for large Reynolds number. We obtain characteristic scales (a power of a small parameter included in a solution) which lead to the double-deck structure, and we obtain a formal asymptotic solution of a problem of a flow inside an axially-symmetric pipe and a two-dimensional channel with small periodic irregularities on the wall. We prove that a quasistationary solution of a Rayleigh-type equation (which describes the flow oscillation on the “upper deck” of the boundary layer with the double-deck structure, i.e. in the classical Prandtl boundary layer) exists and is stable. We obtain a formal asymptotic solution with the double-deck structure for the problem of fluid flow along a plate with small localized irregularities such as hump, step or small angle. We construct a numerical solution algorithm for all equations which we obtained and we show the results of their applications.
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique in the Prandtl boundary layer, and the stability of the solution is investigated at large times. The results of numerical modeling are given. Supported by the Basic Research Program of the National Research University “Higher School of Economics.” © 2015, Pleiades Publishing, Ltd.
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure.
We consider a non-stationary problem of an incompressible viscous fluid flow along surfaces with small irregularities for large Reynolds number, which have a formal asymptotic solution with a double-deck structure of the boundary layer.