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Interactive boundary layer in a Hele Shaw cell
Author(s) -
Lagrée P.Y.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200610331
Subject(s) - laminar flow , boundary layer , blasius boundary layer , reynolds number , mathematics , boundary layer thickness , flow separation , singularity , nonlinear system , mathematical analysis , hele shaw flow , flow (mathematics) , navier–stokes equations , boundary (topology) , boundary value problem , mechanics , physics , geometry , open channel flow , turbulence , quantum mechanics , compressibility
The steady laminar flow in a rectangular Hele Shaw cell is considered at high Reynolds number. The lower thin wall layer is perturbed by a small bump. Averaged equations obtained in averaging the Navier Stokes equations across the thin direction are used. This procedure allows to recover the nonlinear convective term in the equations. First a classical Boundary Layer theory is constructed, the weak coupling leads to a singularity. An Interacting Boundary Layer theory is then constructed in order to compute the strong coupling of the “Averaged ideal fluid” and the “Averaged boundary layer”. The “triple deck” counter part is presented as well. An asymptotic nonlinear approximation of the flow can be computed with short computation time. Positive comparisons of computation of the full Averaged Navier Stokes equation and Interacting Boundary Layer theory are shown. For instance, the boundary layer separation over a bump is obtained when either the bump height or the Reynolds number is increased.