Jets and other planar perturbations of parallel basic flows

Laminar two-dimensional planar flow of a viscous incompressible fluid is considered in a half-plane bounded by a straight wall. The basic flow is parallel to the wall with constant velocity in Case I, and a shear flow in Case II. The dispersion of a jet is analyzed by use of boundary layer assumptions and eigenfunction expansions in both Cases I and II. Provided an initial perturbation is given in a cross section normal to the wall, the decay of the momentum of the resulting perturbation downstream can be studied by use of eigenfunction expansions. Special eigenfunctions are employed to construct bounds for the solution of the total nonlinear problem.