Attenuation by uniform suction of compressible Görtler vortices induced by free stream vortical disturbances

The effect of uniform wall suction on compressible Görtler vortices excited by free stream vortical disturbances is studied via asymptotic and numerical methods. The flow is described by the boundary-region framework, written and solved herein for non-similar boundary layers. The suction, applied downstream of an impermeable region, reduces the amplitude of steady and unsteady Görtler vortices. The vortices are attenuated more when the boundary layer has reached the asymptotic-suction condition than when it is streamwise-dependent. The impact of suction weakens as the free stream Mach number increases. As the boundary layer becomes thinner, the exponential growth of the vortices is prevented because the disturbance spanwise pressure gradient and spanwise viscous diffusion are inhibited. The flow is described by the boundary-layer equations in this case, for which the wall-normal momentum equation is uninfluential at leading order and the curvature effects responsible for the inviscid pressure-centrifugal imbalance are therefore negligible. The influence of unsteadiness weakens as suction intensifies because, in the limit of a thin boundary layer, the boundary-region solution simplifies to a regular-perturbation series whose first terms are described by the steady boundary-layer equations. Suction broadens the stability regions and may favour the presence of oblique Tollmien–Schlichting waves at the expense of more energetic Görtler vortices for relatively high frequencies and moderate Mach numbers.