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Solutions of the Ginzburg‐Landau Equation of Interest in Shear Flow Transition
Author(s) -
Landamn Michael J.
Publication year - 1987
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 - 10.1002/sapm1987763187
Subject(s) - quasiperiodic function , hagen–poiseuille equation , laminar flow , reynolds number , mathematics , instability , flow (mathematics) , shear flow , nonlinear system , amplitude , plane (geometry) , mathematical analysis , physics , mathematical physics , classical mechanics , mechanics , geometry , turbulence , quantum mechanics
The Ginzburg‐Landau equation may be used to describe the weakly nonlinear 2‐dimensional evolution of a disturbance in plane Poiseuille flow at Reynolds number near critical. We consider a class of quasisteady solutions of this equation whose spatial variation may be periodic, quasiperiodic, or solitarywave‐ like. Of particular interest are solutions describing a transition from the laminar solution to finite amplitude states. The existence of these solutions suggests the existence of a similar class of solutions in the Navier‐Stokes equations, describing pulses and fronts of instability in the flow.