Exponentially-varying, unsteady standing waves in parallel-flow boundary layers

Fluctuations which oscillate in time and grow or decay exponentially in the streamwise direction are found as solutions of the Orr-Sommerfield equation. The x-wavenumber is purely imaginary; the frequency is real. Since these disturbances do not propagate in the streamwise direction, they are called standing waves. In the direction normal to the wall, they behave as two travelling waves of unequal strengh. Inside the boundary layer and near the edge, the flow field has fluctuating vorticity. The disturbance in the distant free stream is irrotational. Inside the boundary layer, the vorticity originates primarily from the production term, through viscous diffusion to/from the wall, and by convection. Near the wall, an unsteady viscous sublayer forms. Analytical solutions for fluctuations in a uniform mean flow near a wall are presented, along with numerical solutions obtained for Falkner-Skan boundary layers. The mean boundary layer can be influenced by the mean pressure gradient and surface roughness. The feature which distinguishes these solutions from the instability waves, and also distinguishes these solutions from those with free-stream vorticity fluctuations, is the characteristic irrotational fluctuations in the free stream. The standing waves are other means for upstream and downstream influence in the boundary layer.