Va. Demin et al., MECHANICAL QUASI-EQUILIBRIUM AND THERMOVIBRATIONAL CONVECTIVE INSTABILITY IN AN INCLINED FLUID LAYER, International journal of heat and mass transfer, 39(9), 1996, pp. 1979-1991
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.