The author considers the generation of time-averaged flows in nonuniform fluid due to high frequency vibrations of the container or due to oscillations of solid bodies embedded in the fluid. The general equation for time-averaged and pulsating components of hydrodynamical fields are obtained in the case when the nonuniformity of density is caused by nonuniform heating. It is shown that in the general case thermovibrational effect is linear with respect to the characteristic temperature difference, whereas in some particular situations (e.g., for a rigid-walled container completely filled with the fluid and not changing its orientation during the vibration period) the thermovibrational effect is quadratic.
The author applies his theory to the problem of the flow between two solid spheres when the inner sphere vibrates along a fixed direction and is kept at a temperature different from that of the outer sphere. However, no specific numerical results are presented for this problem. Therefore the paper is only of academic interest.