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Triple‐deck regularization of weak laminar hydraulic jumps in a two layer shallow water flow
Author(s) -
Kluwick A.,
Viertl N.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510280
Subject(s) - inviscid flow , laminar flow , mathematics , mathematical analysis , nonlinear system , hydraulic jump , regularization (linguistics) , conservation law , limit (mathematics) , flow (mathematics) , mechanics , physics , geometry , quantum mechanics , artificial intelligence , computer science
The inviscid, weakly nonlinear, shallow‐water limit of the Navier–Stokes equations leads to a hyperbolic conservation law. In certain cases of a two‐layer flow the flux‐function is non‐convex, thus leading to the possibility of shocks (in physical terms hydraulic jumps) violating the Oleinik‐entropy criteria, so called non‐classical shocks. To rule out the inadmissible shocks their internal structure is studied, based on an asymptotic approach consistent with the Navier–Stokes equations. This leads to a triple‐deck problem with a novel, non‐linear interaction equation in the form of a forced, extended KdV‐equation. The limit of vanishing and weak influence of the displacement effect is studied analytically, and in addition representative numerical solutions of the full problem are presented. Of particular interest is a solution, which has a pronounced, almost vanishing minimum in he wall shear. Its local structure is studied in some detail. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)