MECHANICAL QUASI-EQUILIBRIUM AND THERMOVIBRATIONAL CONVECTIVE INSTABILITY IN AN INCLINED FLUID LAYER

The linear stability of mechanical quasi-equilibrium of a long incline d plane fluid layer, in the presence of a constant temperature gradien t, subject to a static gravity field and high frequency vibration is i nvestigated theoretically. The layer is oriented in an arbitrary respe ct to the vertical. The boundaries of the layer are assumed to be rigi d and highly conducting. Each of two vectors-the temperature gradient and the axis of vibration-can have one of the four orientations: verti cal (t), longitudinal (l), horizontal (h), and transversal (t). Thus a total of sixteen situations are studied. The consideration is based o n the equations system describing mean (averaged) fields in the frame of an averaging method. The possibility and necessary conditions of me chanical quasi-equilibrium existance are studied. The spectral amplitu de 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 expansi on. In the case of an arbitrary value of wave number, the spectral pro blem is solved numerically. The boundaries of stability and critical d isturbance characteristics are determined for all the sixteen cases me ntioned before.