A new approach to the Rayleigh-Taylor instability is presented that yields exact solutions for the simplest cases and provides approximate but still very accurate analytical expressions for important and more complex cases involving nonideal fluids. The approach is based on Newton’s second law and allows for an intuitive and physically appealing explanation of the mechanisms underlying the instability.
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Hide (Ref. 19) independently found the same formula by using a variational method. After this publication Ride (Ref. 20) pointed out that Hide’s derivation of Eq. (23) was in error and published a corrected version that resulted in a less accurate approximation than Eq. (23). More recently, Mikaelian (Ref. 16) obtained Eq. (23) by using a moment equation approach that used the inviscid velocity field approximation that we have used here and that was also used by Hide and Ride [Eq. (19) with ]. Mikaelian has shown that the other approximations introduced in Hide’s derivation were consistent with using such a velocity field and demonstrated that Hide’s derivation was actually correct.
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2006
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