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

作者：Krechetnikov Rouslan^*

来源：Dynamics of Partial Differential Equations, 2011, 8(1): 47-67.

• Drop splash
• Rayleigh-Taylor instability

This work is a combination of physical and analytical considerations of linear 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 interface 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 f(tt) + 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.

• 出版日期2011-3