Dynamic Instability of Accelerated Fluids

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Abstract
The asymmetrical growth of an interface separating two fluids of different densities, under the influence of an imposed acceleration (Rayleigh‐Taylor instability), is shown to be mainly a nonlinear phenomenon. When the initial disturbance is a simple sinusoidal wave and is started from rest, it is found that the growth of the interface depends explicitly on two dimensionless parameters of the initial disturbance, namely, the dimensionless amplitude (i.e., the amplitude‐to‐wave‐length ratio) and the dimensionless wave number (i.e., the wave number of the initial disturbance to the ``cutoff'' wave number of the medium under the prevailing experimental condition). Results of the analysis show that the asymmetrical development of the interface occurs much earlier for disturbances of larger amplitudes and lower wave numbers than those of smaller amplitudes and higher wave numbers, i.e., those with wave numbers near the ``cutoff.'' Surface tension shows a definite stabilizing effect. Because of the nonlinear effect, for a sinusoidal initial disturbance, a generation of higher harmonics as well as a feed‐back to the fundamental is noted. Contrary to the prediction of the linearized theory, the present analysis, based on higher order approximations, reveals an ``over‐stable'' phenomenon for disturbances having initial wave numbers beyond the ``cutoff.''

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