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This work is a combination of physical and analytical considerations of lin- ear stability pictures on time-invariant and time-dependent spatial domains with symmetry. The discussion is offered in the context of the Rayleigh-Taylor instability (of a fluid inter- face accelerated in the direction of a heavier phase) applied to the drop splash problem, which provides a natural ground for developing stability theory on time-dependent spatial domains with O(2) symmetry. The peculiarity of the underlying linear model common in a number of other interfacial instabilities - linear oscillator ftt + a(k)f = 0 in the wavenumber k-space - allows one to establish a direct correspondence between stability pictures on time-invariant and time-dependent spatial domains. The stability analysis also leads to a notion of frustration in (linear) stability patterns.

A linear stability theory on time-invariant and time-dependent spatial domains with symmetry: the drop splash problem