SPATIO-TEMPORAL GROWTH OF DISTURBANCES IN A BOUNDARY LAYER AND ENERGY BASED RECEPTIVITY ANALYSIS

T.K. Sengupta, A. Kameswara Rao and K.Venkatasubbaiah

Abstract

In fluid dynamical systems, it is not known a priori whether disturbances grow either in space or in time or as spatio -temporal structures. However, for boundary layers, it is customary to treat it as a spatial problem and some limited comparison between prediction and laboratory experiments exist. In the present work, the receptivity problem of a zero pressure gradient boundary layer excited by a localized harmonic source is investigated under the general spatio-temporal framework, using Bromwich contour integral method. While this approach has been shown to be equivalent to the spatial study, for unstable systems excited by a single frequency source [T. K. Sengupta, M. Ballav and S. Nijhawan, Phys. Fluids 6(3),1213(1994)], here we additionally show, how the boundary layer behaves when it is excited (i) at a single frequency that corresponds to stable condition (given by spatial normal-mode analysis) and (ii) by wide-band frequencies; that shows the possibility of flow transition due to a spatio-temporally growing fore-runner or wave-front. An energy based receptivity analysis tool is also developed as an alternative to traditional instability theory. Using this, we reinterpret the concept of critical layer-that was originally postulated to explain the mathematical singularity of inviscid disturbance field in traditional instability theory of normal modes.