×

zbMATH — the first resource for mathematics

Secondary instability of wall-bounded shear flows. (English) Zbl 0556.76039
The process by which a laminar shear flow undergoes transition to turbulence is of fundamental fluid dynamical interest. In this paper, this question is addressed from the view point of stability theory. The primary instabilities of wall-bounded shear flows and the canonical cases of plane Poiseuille flow and pipe Poiseuille flow are discussed. The nonlinear saturation process of primary instability is also treated. The concept of linear secondary instability is introduced and applied to the canonical Poiseuille flows. The structure and dynamics of the secondary instability are analyzed and the theory is applied to plane Couette flow and the boundary layer over a flat plate. The extent to which the secondary instability introduced in the paper relates the actual transition process of laminar shear flow to turbulence is also examined.
Reviewer: T.K.V.Iyengar

MSC:
76F10 Shear flows and turbulence
76E99 Hydrodynamic stability
PDF BibTeX Cite
Full Text: DOI
References:
[1] DOI: 10.1017/S0022112062000014 · Zbl 0131.41901
[2] DOI: 10.1017/S0022112077000780 · Zbl 0362.76091
[3] DOI: 10.1017/S0022112069001613 · Zbl 0184.53202
[4] DOI: 10.1063/1.862643
[5] DOI: 10.1017/S0022112073001217 · Zbl 0255.76047
[8] DOI: 10.1017/S0022112074001571 · Zbl 0291.76019
[10] Carlson, Flow Dynamics Research Lab. (Dept of Aero, and Astro., M.I.T.) Rep. 20 pp 1– (1981)
[11] DOI: 10.1103/PhysRevLett.47.832
[12] DOI: 10.1007/BF01591113 · Zbl 0164.29003
[13] DOI: 10.1063/1.861737
[14] DOI: 10.1103/PhysRevLett.45.989
[16] DOI: 10.1063/1.1706101
[17] DOI: 10.1017/S0022112071002842 · Zbl 0237.76027
[18] Grohne, A.V.A. Göttingen Rep. 357 pp 10– (1969)
[19] Gorman, Ann. N. Y. Acad. Sci. 357 pp 10– (1980)
[21] Stuart, AGARD Rep. 9 pp 11– (1965)
[22] DOI: 10.1007/BF01205039 · Zbl 0465.76050
[23] Stuart, J. Fluid Mech. 9 pp 11– (1960)
[24] DOI: 10.1063/1.861156 · Zbl 0308.76030
[25] Squires, Proc. R. Soc. Lond. A 142 pp 621– (1933)
[27] DOI: 10.1017/S0022112071000284 · Zbl 0245.76038
[28] DOI: 10.1007/BF01646553 · Zbl 0223.76041
[29] DOI: 10.1017/S0022112075003254
[30] Metcalfe, Flow Research Rep. 122 pp 123– (1973)
[32] Manneville, Physica 98 pp 219– (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.