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On the Nonlinear Development of Small Three‐Dimensional Perturbations in Plane Poiseuille Flow: Single‐Mode Approach
Author(s) -
Shanthini Rajaratnam
Publication year - 1991
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/sapm199184293
Subject(s) - vorticity , hagen–poiseuille equation , amplitude , perturbation (astronomy) , physics , nonlinear system , reynolds number , mathematical analysis , vorticity equation , classical mechanics , mechanics , vortex , mathematics , flow (mathematics) , turbulence , optics , quantum mechanics
Nonlinear aspects of developing three‐dimensional perturbations in plane Poiseuille flow have been elucidated at the primary, instead of the conventional secondary, level. Three‐dimensional perturbation velocities generate normal vorticity by stretching and tilting the basic‐flow vorticity. The amplitude of the induced normal vorticity, and hence that of the streamwise perturbation velocity, can grow temporally to significant peak values before the exponential decay predicted by the linear theory sets in. These growths, according to the linear theory, do not influence the amplitudes of the normal perturbation velocity that are monotonically decaying with time. It is shown in this study that the normal velocity continues to be oblivious to the development of induced normal vorticity, even in the nonlinear regime, if the perturbation velocities are described by waves traveling in a single oblique direction. Also, the Reynolds number dependence of the amplitude of the normal vorticity is discussed.