Response of the Blasius boundary layer to free-stream vorticity

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Abstract
Two- and three-dimensional vortical modes that solve the linearized Navier-Stokes equations in the free stream are used in the present theory to represent some of the key features of low-level turbulence. Excluding the leading edge, the effect of these modes on the Blasius boundary layer is investigated using the parabolized stability equations (PSE). When the vortical modes are steady, or have low frequencies, the PSE analysis is started at a location x0 from the solution to a new set of ordinary differential equations. This solution is able to satisfy the linearized Navier-Stokes equations in a rather large neighborhood of x0. When the vortical modes have frequencies equal to those of unstable Tollmien-Schlichting waves, the scattering of the vortical modes by surface undulation produces only a weak response in the boundary layer, in agreement with other investigations. However, when steady and low-frequency vortical modes are considered, the analysis yields results that successfully reproduce a number of the experimental measurements of Kendall [AIAA Paper 90-1504 (1990)] on streaky structures, known as Klebanoff modes, that cause a periodic spanwise modulation of the streamwise velocity.