Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments

Abstract

This paper investigates the receptivity of boundary layers due to distributed roughness interacting with free-stream disturbances. Both acoustic and vortical perturbations are considered. An asymptotic approach based on the triple-deck formulation has been developed to determine the initial amplitude of the Tollmien–Schlichting wave to the O(R−1/8) accuracy, where R is the global Reynolds number. In the case of vortical disturbances, we show that the dominant contribution to the receptivity comes from the upper deck as well as from the so-called edge layer centred at the outer reach of the boundary layer. It is found that for certain forms of disturbances, the receptivity is independent of their vertical structure and can be fully characterized by their slip velocity at the edge of the boundary layer. A typical case is the vortical disturbance in the form of a convecting wake, for which the same conclusion as above has been reached by Dietz (1999) on the basis of measurements. Our theoretical predictions are compared with the experimental data of Dietz (1999), and a good quantitative agreement has been found. Such a comparison is the first to be made for distributed vortical receptivity. Further calculations indicate that the vortical receptivity in general is much stronger than was suggested previously. In the case of acoustic disturbances, it is found that our first-order theory is in good agreement with experiments as well as with previous theoretical results. But the second-order theory over-predicts, and the possible reasons for this are discussed.