Structure of turbulence prior to rapid-distortion

Rapid-distortion theory (RDT) uses linear analysis to study the interaction of turbulence with solid surfaces. It applies whenever the turbulence intensity is small and the length (or time) scale over which the interaction takes place is short compared to the length (or time) scale over which the turbulent eddies evolve. When both of these conditions are interpreted asymptotically, it implies that the upstream boundary condition that enters as an input to a scattering problem (given by the term,ωc, below) may be specified at an infinite distance from the surface discontinuity on the scale of the interaction but one that is still short on the scale of the turbulence evolution. In this paper we develop the mathematical theory for the leading edge interaction of turbulence by considering a canonical problem of a jet flow interacting with a semi-infinite infinitesimally thin flat plate positioned parallel to the level curves of the mean flow field. To fix ideas we consider a constant shear flow and derive a formula for the two-point velocity correlation function.