Turbulent plumes above a heated plate

Abstract

Our focus concerns the turbulent convective flow above a uniformly heated high-aspect-ratio rectangular plate on $z=0$ . Prior to this study, classic plume theory could not be applied directly as the Richardson number is ill-defined at the plate. Guided by observation, conservation equations are posed for the near-plate region where the attached buoyant flow is predominantly horizontal. Analytical solutions under the Boussinesq approximation reveal this to be a dynamically invariant region where the attached ‘plumes’ grow linearly toward the plate centreline, their merger forming an ‘apparent’ source for the vertical plume above. Coupling predictions with data from flow visualisation and temperature measurement, we deduce the half-width $0.72b_0$ , height ${z=0.46b_0}$ and finite Richardson number $({\sim }18)$ of an apparent source from which plume theory can be applied to model the plume above a heated plate of width $2b_0$ . Finally, practical implications of this advancement to the analytical theory of turbulent plumes are noted.