Nonlinear bubble behaviours of compressible Rayleigh-Taylor instability with isothermal stratification in cylindrical geometry

TL;DR

This paper investigates the nonlinear behaviors of compressible Rayleigh-Taylor instability in cylindrical geometry, revealing how density stratification, vorticity, and flow compressibility influence bubble growth across different Atwood and Mach numbers.

Contribution

It introduces an improved nonlinear model that incorporates density variation, vorticity, and compressibility, validated by numerical simulations across various regimes.

Findings

Density stratification affects acceleration at low Atwood and Mach numbers.

Vorticity dominates bubble acceleration in convergent cases at low Atwood and Mach numbers.

Flow compressibility primarily influences acceleration at high Atwood and Mach numbers.

Abstract

Nonlinear evolutions of two-dimensional single-mode compressible Rayleigh--Taylor instability (RTI) with isothermal stratification are investigated in cylindrical geometry via direct numerical simulation for different Atwood numbers ($A_T=0.1-0.9$) and Mach numbers ($Ma=0.1-0.9$). It is found that the nonlinear bubble growth involves the effects of density stratification, vorticity accumulation and flow compressibility and shows considerable differences between convergent (acceleration acting radially inward) and divergent (acceleration acting radially outward) cases. Specifically, the density stratification leads to non-acceleration at low $A_T$ and high $Ma$. The accelerations in convergent cases are dominated by vorticity accumulation at low $A_T$ and low $Ma$ and by flow compressibility at high $A_T$ and high $Ma$ whereas the accelerations in divergent cases are purely induced by flow compressibility at high $A_T$ and high $Ma$. Based on the nonlinear theory of incompressible cylindrical RTI with uniform-density background~(Zhao et al., J. Fluid Mech., vol. 900, 2020, A24), an improved model is proposed by taking the density variation, vorticity accumulation and flow compressibility into consideration. This model is verified by numerical results and well reproduces the bubble evolution for different $A_T$ and $Ma$ from linear to highly nonlinear regimes.