Transfer matrix formalism for the growth of Rayleigh Taylor instability in compressible fluids

We extend a recently developed transfer-matrix formalism [1] to study the evolution of the Rayleigh-Taylor instability for a compressible fluid interface with smoothly varying density. We compare numerical results and approximate analytic solutions obtained from our formalism with a different approach developed by Dong et al.[2] for compressible non-viscous fluids using the Wentzel-Kramer-Brillouin approximation.

[1] P. Sharma, Rayleigh-Taylor instability in multiple finite- thickness fluid layers, Physical Review E 110, L063101 (2024).

[2] M. Dong, Z. Fan, and C. Yu, Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid inter- face with smoothly varying density. II. Asymptotic solution and its interpretation, Physical Review E 99, 013109 (2019).