A class of 3D boundary layer profiles with independent streamwise and spanwise shear supports Navier-Stokes eigenmodes growing at rate exp(C alpha^3 t/sqrt(nu)), an instability absent in two dimensions.
Mack modes in supersonic boundary layer
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abstract
Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.
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Unstable mode around the 3D boundary layer flow
A class of 3D boundary layer profiles with independent streamwise and spanwise shear supports Navier-Stokes eigenmodes growing at rate exp(C alpha^3 t/sqrt(nu)), an instability absent in two dimensions.