THE INFLUENCE OF ROUGHNESS ON BOUNDARY LAYER STABILITY

摘要

A theory is proposed for the influence of shallow two-dimensional periodic roughness on the stability of waves in a boundary layer The approach is based on the linearized perturbation equations for disturbances in a locally parallel flow. The mean flow induced by two-dimensional ripples is modelled by Fourier expansions in the stream direction coupled with a Taylor series in the direction normal to the wall The required no-slip boundary condition that applies over the ripple surface is transferred, through the Taylor expansion, to the r-axis It turns out that even for quite small roughness heights it is necessary to use more than the first term of the Taylor expansion to define the boundary condition adequately The resulting mean boundary layei is then defined by the usual boundary layer equations, but with a negative slip boundary value on the x-axis The slip velocity arises from the nonlinear coupling between the Fourier terms in the definition of the ripple shape and the perturbation velocities. Although the slip velocity is small, it does have a significant effect on the stability of Tollmien-Schlichting waves Wind tunnel measurements of the effect of two-dimensional ripples on the evolution of Iollmien-Schlichting waves have been made for a range of ripple heights.