Spatio-temporal growth of disturbances in a boundary layer and energy based receptivity analysis

Sengupta, T.K., Kameswara Rao, A. and Venkatasubbaiah, K. (2006) Spatio-temporal growth of disturbances in a boundary layer and energy based receptivity analysis. Physics of Fluids, 18 (9), 94101. (doi:10.1063/1.2348732).

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 the 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. Fluids6, 1213 (1994)], here we additionally show, how the boundary layer behaves when it is excited (i) at a single frequency that corresponds to a stable condition (given by spatial normal-mode analysis) and (ii) by wideband frequencies, that shows the possibility of flow transition due to a spatio-temporally growing forerunner or wave front. An energy based receptivity analysis tool is also developed as an alternative to traditional instabilitytheory. Using this, we reinterpret the concept of critical layer that was originally postulated to explain the mathematical singularity of inviscid disturbance field in traditional instabilitytheory of normal modes.

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