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Effect of compliant walls on secondary instabilities in boundary-layer transition. (English) Zbl 0754.76025
In the present study, Herbert’s theory [T. Herbert, Ann. Rev. Fluid Mech. 20, 487-526(1988)] is used to predict the development of secondary instabilities over isotropic and nonisotropic compliant walls. Because oblique waves may be dominant over compliant walls, a secondary theory extention is made to allow for these 3-D primary instabilities. The effect of variations in primary amplitude, spanwise wavenumber, and Reynolds number on the secondary instabilities are examined. As in the rigid wall case, over compliant walls the subharmonic mode of secondary instability dominates for low-amplitude primary disturbances. Both isotropic and nonisotropic compliant walls lead to reduced secondary growth rates compared with the rigid wall results.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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