Mechanical quasi-equilibrium and thermovibrational convective instability in an inclined fluid layer

Abstract

The linear stability of mechanical quasi-equilibrium of a long inclined plane fluid layer, in the presence of a constant temperature gradient, subject to a static gravity field and high frequency vibration is investigated theoretically. The layer is oriented in an arbitrary respect to the vertical. The boundaries of the layer are assumed to be rigid and highly conducting. Each of two vectors-the temperature gradient and the axis of vibration-can have one of the four orientations: vertical ( v), longitudinal ( l), horizontal ( h), and transversal ( t). Thus a total of sixteen situations are studied. The consideration is based on the equations system describing mean (averaged) fields in the frame of an averaging method. The possibility and necessary conditions of mechanical quasi-equilibrium existance are studied. The spectral amplitude problem for small two-dimensional normal disturbances is formulated. In the case of long-wave instability, the spectral problem is solved asymptotically using the wave number as a small parameter for expansion. In the case of an arbitrary value of wave number, the spectral problem is solved numerically. The boundaries of stability and critical disturbance characteristics are determined for all the sixteen cases mentioned before.