Pure single-mode Rayleigh-Taylor instability for arbitrary Atwood numbers

Area of Science:

• Fluid Dynamics
• Plasma Physics
• Astrophysical Phenomena

Background:

• Nonlinear Rayleigh-Taylor instability (RTI) is crucial in various scientific fields.
• Previous weakly nonlinear solutions for single-mode RTI have limitations.
• Accurate theoretical models are needed for predicting fluid interface evolution.

Purpose of the Study:

• To rigorously solve the single-mode Rayleigh-Taylor instability (RTI) up to the third order.
• To address the deficiencies in classical weakly nonlinear solutions.
• To develop an improved theoretical model for RTI applicable to arbitrary Atwood numbers.

Main Methods:

• Utilized the method of potential functions to solve the nonlinear RTI equations.
• Incorporated both stimulating and inhibiting RTI terms in the potential solution.
• Employed Taylor expansion to simplify expressions and extend the solution's validity range.
• Validated results through comparison with 2D Euler equation numerical simulations.

Main Results:

• The potential solution accurately captures both accelerating and decelerating RTI effects, unlike classical models.
• The derived solution shows better agreement with numerical simulations than the classical approach before saturation.
• The improved theory, using Taylor expansion, effectively predicts interface evolution across linear, weakly nonlinear, and later nonlinear stages.

Conclusions:

• The refined potential function method provides a more accurate theoretical framework for single-mode nonlinear RTI.
• The improved model enhances predictive capabilities for fluid mixing and interface dynamics.
• This work offers a valuable tool for studying phenomena driven by RTI, from laboratory experiments to astrophysical processes.