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The motion induced by a radially stretching membrane in a rotating fluid system
Author(s) -
Weidman Patrick D.
Publication year - 2015
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.201500094
Subject(s) - mechanics , physics , boundary layer , ordinary differential equation , classical mechanics , ekman number , angular velocity , flow (mathematics) , equations of motion , viscous liquid , stokes flow , differential equation , quantum mechanics
The flow induced above an impermeable sheet undergoing linear radial stretching in a system rotating at angular velocity Ω is investigated. The problem is governed by the single parameter σ = Ω / a , where a is the stretching rate of the membrane. A similarity reduction of the Navier‐Stokes equations leads to a pair of nonlinearly‐coupled ordinary differential equations which are numerically solved over the range 0 ≤ σ ≤ 10 . Coriolis forces acting on the radially stretching flow in the vicinity of the wall induces azimuthal flow in the boundary layer. A large‐σ analysis of the system leads to the Ekman equations describing the balance of Coriolis and viscous forces for which an exact solution is presented. Numerical results for the radial and azimuthal shear stresses, along with the magnitude of the velocity induced into the boundary layer, are shown to be in good agreement with the large‐σ asymptotic results.