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The effect of profile symmetry on the nonlinear stability of mixing layers. (English) Zbl 0707.76044
Summary: The nonlinear stability of arbitrary mixing-layer profiles in an incompressible, homogeneous fluid is studied in the high-Reynolds-number limit where the critical layer is linear and viscous. The type of bifurcation from the marginal state is found to depend crucially on the symmetry properties of the basic-state profile. When the velocity profile on the mean flow is perfectly symmetric, the bifurcation is stationary. When the symmetry of the profile is broken, the bifurcation is Hopf. The nonsymmetry of the mixing layer also introduces some changes in the critical layer and the matching of flow quantities across it.

76E30 Nonlinear effects in hydrodynamic stability
76E05 Parallel shear flows in hydrodynamic stability
35Q35 PDEs in connection with fluid mechanics
Full Text: DOI
[1] Churilov, Nonlinear stability of a zonal shear flow, Geophys. Astrophys. Fluid Dynamics 36 pp 31– (1986) · Zbl 0626.76060 · doi:10.1080/03091928608208796
[2] Churilov, Note on weakly nonlinear stability theory of a free mixing layer, Proc. Roy. Soc. London Ser. A 409 pp 351– (1987) · Zbl 0631.76050 · doi:10.1098/rspa.1987.0020
[3] Churilov, The nonlinear development of disturbances in a zonal shear flow, Geophys. Astrophys. Fluid Dynamics 38 pp 145– (1987) · Zbl 0644.76063 · doi:10.1080/03091928708219202
[4] Djordjevic, AIAA 2nd Shear Flow Conference, in: AIAA Paper 89-1020 pp 13– (1989)
[6] Haberman, Critical layers in parallel flows, Stud. Appl. Math. 51 pp 139– (1972) · Zbl 0265.76052 · doi:10.1002/sapm1972512139
[7] Huerre, On the Landau constant in mixing layers, Proc. Roy. Soc. London Ser. A 409 pp 369– (1987) · Zbl 0631.76035 · doi:10.1098/rspa.1987.0021
[8] Huerre, Absolute and convective instabilities in free shear layers, J. Fluid Mech. 159 pp 151– (1985) · Zbl 0588.76067 · doi:10.1017/S0022112085003147
[9] Huerre, Local and global instabilities in spatially-developing flows, Annual Rev. Fluid Mech. 22 pp 473– (1990) · doi:10.1146/annurev.fl.22.010190.002353
[10] Huerre, Lectures in Appl. Math. 159 pp 151– (1983)
[11] Huerre, Effects of critical layer structure on the nonlinear evolution of waves in free shear layers, Proc. Roy. Soc. London Ser. A 371 pp 509– (1980) · Zbl 0447.76035 · doi:10.1098/rspa.1980.0094
[12] Ho, Perturbed free shear layers, Annual Rev. Fluid Mech. 16 pp 365– (1984) · doi:10.1146/annurev.fl.16.010184.002053
[13] Maslowe, Critical layers in shear flows, Annual Rev. Fluid Mech. 18 pp 405– (1986) · Zbl 0634.76046 · doi:10.1146/annurev.fl.18.010186.002201
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