  The analysis of vibration effect on non-isothermal fluid in closed cavity is
important for planning technological experiments in space. Control and
optimization of these processes critically depend on the understanding of
liquid response to the vibrations. With this aim the theoretical investigation
for infinite plane and cylindrical fluid layers are performed. We investigated
simple case of the fluid response-thermal vibrational convection in a
cylindrical fluid layer with rigid conducting boundaries. It is found that
steady modes of thermal vibrational convection are subjected to various
bifurcations. Bifurcations cause sharp changes in heat transfer. The Lorenz
model is generalized (GLM) and used to conduct the analysis of bifurcations
caused by the changing of the cavity shape and vibrational Rayleigh number. The
shape of steady-state surface in 3D space of the streamfunction of mean flow,
vibrational Rayleigh number and the cavity curvature is found. The numerical 2D
solution is performed for plane and cylindrical fluid layers. The results of
the analysis based on the GLM model are compared with the data obtained by
direct numerical simulation. The bifurcation curve with extremum is found.
Thus, bifurcations of complex shape could be observed. Comparisons with space
experiments and its discussions are presented.
