The influence of high-frequency vibrations on the convection of a liquid in an infinitely long horizontal cylinder of square cross-section, which undergoes vertical vibrations, is investigated. The problem was solved numerically on the basis of the averaged equations of thermal vibrational convection, written in terms of the vorticity of the average velocity and stream functions of the average and pulsating flows. The influence of vibrations on the system was determined by a dimensionless vibration parameter V proportional to the ratio of vibrational acceleration to gravitational acceleration and independent of the temperature difference. The values V ≥ 1 correspond to the case of low gravity conditions. The intensity of gravitational convection was characterized by the Grashof number Gr. All calculations were performed for the fixed value of the Prandtl number Pr = 100. For values 0 ≤ V ≤ 10 the evolution of average convective regimes was studied and a map of these regimes was plotted on the Gr—V parameter plane. The stability boundary of stationary average convection is determined. It is shown that after the loss of stability by a stationary average flow in a cavity, two oscillatory average convective regimes with different symmetries can be realized.

研究了高频振动对承受垂直振动的无限长方形横截面水平圆柱体内液体对流的影响。该问题是在热振动对流的平均方程的基础上以数值方式解决的，该方程根据平均速度和平均流和脉动流的流函数的涡量来写。振动对系统的影响由无量纲振动参数V决定，该参数与振动加速度与重力加速度的比率成正比，并且与温差无关。值V ≥ 1 对应于低重力条件的情况。引力对流强度由格拉肖夫数 Gr 表征。所有计算均针对 Prandtl 数 Pr = 100 的固定值进行。对于值 0 ≤  V  ≤ 10，研究了平均对流状态的演变，并在 Gr- V参数平面上绘制了这些状态的地图。确定了平稳平均对流的稳定边界。结果表明，在空腔中的静止平均流动失去稳定性后，可以实现具有不同对称性的两种振荡平均对流状态。