The horizontal far wake behind a heated or cooled body

Abstract

Buoyancy affects the horizontal wake far downstream of a heated or cooled body in an indirect manner via the hydrostatic pressure perturbation. Plane flow at large Reynolds and Péclet numbers is considered in this paper. The buoyancy effects are characterized by a Richardson number. Both laminar and turbulent flows are investigated to provide asymptotic solutions that are suitable as outflow boundary conditions in computational fluid dynamics. Similarity transformations, which are universal, lead to sets of ordinary differential equations. The interaction between the wake and the outer potential flow is taken into account by applying Bernoulli’s equation as a boundary condition. As the thermal energy equation and the boundary conditions for the temperature perturbation are homogeneous, the magnitude of the temperature perturbation is determined by the over-all thermal energy balance. The results of the analysis are in remarkable contrast to the classical non-buoyant wake solutions. Driven by the hydrostatic pressure disturbance, the flow does not decay in streamwise direction. The flow is governed by the total heat flow at the body, whereas the effect of the drag force is negligible. The set of ordinary differential equations is solved numerically. For laminar flow, two kinds of solutions are found for Richardson numbers below 0.734. One kind of solutions describes a flow field containing a reversed-flow region. For turbulent flow a turbulence model based on the turbulent kinetic energy balance is applied. In addition, the limit of weak buoyancy effects is considered, leading to power laws in terms of the Richardson number.