Premium
Large‐Reynolds‐Number Asymptotics of the Berman Problem
Author(s) -
Cox S. M.,
King J. R.
Publication year - 2004
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.0022-2526.2004.01512.x
Subject(s) - reynolds number , mathematics , limit (mathematics) , flow (mathematics) , ordinary differential equation , boundary value problem , type (biology) , mathematical analysis , suction , viscous liquid , nonlinear system , magnetic reynolds number , geometry , mechanics , physics , differential equation , thermodynamics , turbulence , biology , ecology , quantum mechanics
Similarity flow of a viscous fluid in a channel is considered, driven by uniform withdrawal of the fluid through the channel walls. The nonlinear ordinary differential boundary value problem that results has several branches of solutions; those of Types III, III 1 , and I 1 are investigated here, in the limit of large wall‐suction Reynolds number. This paper gives a markedly more accurate Type III asymptotic solution than previously available, and describes the true asymptotics of the other branches for the first time. The asymptotic structure of the Type III 1 solution is particularly subtle, requiring matching between seven different layers. Numerical solutions of the boundary value problem provide support for the asymptotic solutions obtained.