Transfer-matrix formalism for linear growth of fluid instability.

We use a recently developed transfer-matrix formalism [1] to study the evolution of the Rayleigh-Taylor instability for a viscous 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 non-viscous fluids using the Wentzel-Kramer-Brillouin approximation.

[1] P. Sharma, Rayleigh Taylor Instability in Multiple Finite-Thickness Fluid Layers. arXiv:2403.12271 [physics.flu-dyn]

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