SHEAR SHELTERING AND THE CONTINUOUS-SPECTRUM OF THE ORR-SOMMERFELD EQUATION

The expansion into eigenfunctions of a general disturbance in a viscou s flow is possible only when both the discrete and continuous modes of the Orr-Sommerfeld equation are employed. Proper implementation of th e boundary conditions and a method for computation of the continuous m odes are developed. The unique phenomenon known as shear sheltering is discussed and illustrated. It is shown that the penetration depth of disturbances into the boundary layer has a dependence on frequency and Reynolds number similar to that of a Stokes layer. A simple model tha t captures this dependence is developed. (C) 1998 American Institute o f Physics.