The effect of time-dependent gravity with multiple frequencies on the thermal convective stability of a fluid layer

The effect of a time-dependent gravity vector with a double frequency on the thermal stability of a fluid layer is explained physically and by way of a calculation. The analogy of this problem to the time-dependent acceleration of the base plate or pivot of a simple linear pendulum is made clear. Specifically it is shown that if a fluid layer that is heated from below is unstable to a time-dependent gravity field for two different frequencies, it may regain stability if both frequencies act in concert with each other.