Study of convection in a liquid layer with vibrating forces

We consider convection in a gravity force field in a liquid enclosed in a vessel which is vibrating along the vertical axis according to the lawa/ sin t ( ).Time-averaged convection equations describing the basic motion in first approximation are derived in 1]. In addition, criteria are introduced in 1] which determine the initiation of convection in this case, and a model problem is considered: the case of spatially periodic disturbances. It is found that in this case high frequency vibrations stabilize the state of relative rest.In the present paper we consider convection in a liquid layer between two horizontal planes whose equations are z=±l/2.The temperatures T₁ and T₂ are specified on the upper and lower surfaces, respectively. It is shown (§1) that for small values of the vibrational criterion the principle of stability variation is satisfied. In this case there is a variational principle (§2) from which it follows that high frequency vibrations prevent the occurrence of convection in the horizontal liquid layer. With the aid of the variational principle a calculation is made of the dependence of the values of Rayleigh criterion on the vibrational criterion.The author wishes to thank I. B. Sinomenko and V. I. Yudovich for their continued interest in this study.