Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Abstract

Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent Navier–Stokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.