Rayleigh-Taylor instability in multiple finite-thickness fluid layers

Area of Science:

• Fluid Dynamics
• Plasma Physics
• Geophysics

Background:

• The Rayleigh-Taylor instability is a fundamental phenomenon in fluid dynamics.
• Understanding its growth rate is crucial for various scientific and engineering applications.
• Previous models often simplify fluid properties, limiting their applicability.

Purpose of the Study:

• To develop a general transfer-matrix formalism for analyzing Rayleigh-Taylor instability.
• To apply this formalism to stratified heterogeneous fluids with spatially varying density and viscosity.
• To derive analytical solutions using approximations for specific fluid viscosity limits.

Main Methods:

• Development of a general transfer-matrix formalism.
• Analytical and numerical treatment of stratified heterogeneous fluids.
• Introduction of the inviscid-flow approximation for uniform kinematic viscosity.
• Analysis of the large-viscosity limit.

Main Results:

• A general transfer-matrix formalism for Rayleigh-Taylor instability growth rate determination.
• Analytical solutions for stratified heterogeneous fluids under inviscid and large-viscosity approximations.
• Numerical validation of the analytical findings.

Conclusions:

• The developed transfer-matrix formalism offers a versatile tool for studying fluid instabilities.
• The analytical solutions provide valuable insights into the behavior of heterogeneous fluids.
• The study highlights the importance of considering spatial variations in fluid properties.