Abstract– The hydrodynamic instability of a system of vertical motions initiated by spatially periodic distributions of heat sources is investigated. The Galerkin method with three basis trigonometric functions is used to describe the perturbation dynamics. The nonlinear system of equations for finding the expansion coefficients is formulated. It is found that the vertical motions are unstable in the absence of dissipation if the Richardson number is less than one eighth. A weakly nonlinear model of inviscid instability is developed. It is shown that the loss of stability in the presence of dissipation can lead to formation of either steady-state or time-oscillating secondary flow with nontrivial streamline topology.

中文翻译：

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热源空间周期性分布激发的垂直运动的水动力不稳定性

摘要– 研究了由热源空间周期性分布引发的垂直运动系统的水动力不稳定性。具有三个基三角函数的伽辽金方法用于描述扰动动力学。公式化了用于寻找膨胀系数的非线性方程组。发现如果理查森数小于八分之一，则在没有耗散的情况下，垂直运动是不稳定的。开发了无粘性不稳定性的弱非线性模型。结果表明，存在耗散时稳定性的丧失会导致形成具有非平凡流线拓扑的稳态或时间振荡二次流。