Secondary convective motions in a plane inclined layer

Abstract

A linear theory of stability of a plane-parallel convective flow between infinite isothermal planes heated to different temperature was developed in [1–6]. At moderate Pr values the instability is monotonic and leads to the development of steady secondary motions. These motions for the case of a vertical layer have been investigated by the net [7, 8] and small-parameter [9] methods. In this paper steady secondary motions in an inclined layer are investigated. The small-parameter and net methods are used. The hard nature of excitation of secondary motions in a defined range of tilt angles is established. There are two types of secondary motions, whose regions of existence overlap — vortices at the boundary of countercurrent streams and convection rolls; the hard instability is due to the development of convection rolls. The analog of the Squire transformation obtained in [4] for infinitely small disturbances of a plane-parallel convective flow is extended to secondary motions of finite amplitude.