Linear temporal stability analysis on cross sheared flow: the stabilization effects via cross shear

Xiao, Yuan, and Lin, Wenxian (2022) Linear temporal stability analysis on cross sheared flow: the stabilization effects via cross shear. Physics of Fluids, 34. 034101.

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Abstract

The stability features of the inviscid, homogenous, and free cross sheared flow, with base flow velocities U = tanh(z) in the primary direction, which is unstable, and V = nz^3 in the orthogonal direction, which is stable, are thoroughly examined with linear temporal stability analysis, where z is the transverse coordinate perpendicular to the flow and n is the cross shear ratio which is the ratio of the characteristic magnitudes of V to U. The map of the unstable regions directly related to v = n(b=a) is obtained, where (b=a) is the ratio between the orthogonal and primary wavenumbers. Further examination of the eigenfunctions shows that the eigenfunction structures divide into the orthogonal wavenumber (OW) mode where (b=a) dominates and the cross shear (CS) mode where n dominates. The cross shear is found necessary for stabilization in spite of different fashions for the OW and CS modes. The transition from the OW mode to the CS mode shows that the developments of the two modes inherently compete with each other, so that when w = (b=a)=n decreases the enhanced cross shear needs to deteriorate the OW mode before it helps the growth of the CS mode. Based on the magnitudes of the associated eigenfunctions in the enstrophy budget, the map of the OW, CS, and hybrid modes, which includes the mixed features of both the OW and CS modes, is produced and discussed.

Item ID: 72699
Item Type: Article (Research - C1)
ISSN: 1089-7666
Keywords: Linear stability analysis, Perturbation analysis, Flow control, Flow instabilities
Copyright Information: © 2022 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Phys. Fluids 34, 034101 (2022); https://doi.org/10.1063/5.0083687 and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0083687.
Date Deposited: 07 Jun 2022 00:17
FoR Codes: 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401207 Fundamental and theoretical fluid dynamics @ 40%
40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401209 Hydrodynamics and hydraulic engineering @ 60%
SEO Codes: 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280110 Expanding knowledge in engineering @ 100%
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