Spatial decay bounds in a channel flow of 2‐D Boussinesq fluid with variable thermal diffusivity

Abstract

In this paper, the authors investigate the flow of an incompressible Boussinesq fluid in a semi‐infinite plane channel. An explicit spatial decay estimate in terms of the distance from finite end of the channel is obtained from an integro‐differential inequality for an energy integral. To make the result explicit, an upper bound for total energy is also obtained. The results of this paper may be thought of as a version of Saint‐Venant principle.