Rotational and irrotational freestream disturbances interacting inviscidly with a semi-infinite plate

This report is part of a search for all possible classes of linear disturbances that can arise in a flowfield and thus serve as descriptive elements for a general disturbance flowfield. This report examines the velocity and pressure fields of disturbances that exist in a full two-dimensional unsteady incompressible inviscid flowfield about a semi-infinite flat plate. The permissible classes of disturbances include rotational as well as irrotational disturbances. Because of the linearity of the treatment, superpositions of these are also included. In general, the disturbances do not vanish far from the plate and in some instances are unbounded at infinite distances from the plate. These unbounded disturbances are retained, since they are relevant to applications involving finite domains, for example, in wind tunnels. In this elliptic problem, the semi-infinite plate exerts an irrotational upstream influence which is composed of a pattern of standing waves. Downstream of the leading edge, the flowfield is also altered by an irrotational flow, but this irrotational flow is composed of both standing and traveling waves.