Secondary instability of the spike-bubble structures induced by nonlinear Rayleigh-Taylor instability with a diffuse...

Area of Science:

• Fluid Dynamics
• Plasma Physics
• Turbulence Research

Background:

• Rayleigh-Taylor (RT) flows exhibit laminar-turbulent transition driven by spike-bubble structures.
• Kelvin-Helmholtz instability is widely accepted to cause secondary instability in RT flows due to velocity shears.
• The precise role of acceleration and the quantitative description of secondary instability in RT flows remain underexplored.

Purpose of the Study:

• To quantitatively investigate the secondary instability in two-dimensional diffuse-interface Rayleigh-Taylor (RT) nonlinear flows.
• To elucidate the combined contributions of Rayleigh-Taylor and Kelvin-Helmholtz regimes to secondary instability.
• To analyze the impact of diffuse interfaces on secondary instability modes.

Main Methods:

• Employed Arnoldi iteration and generalized Rayleigh quotient iteration methods for quantitative analysis.
• Utilized two-dimensional diffuse-interface RT nonlinear flow simulations.
• Conducted direct numerical simulations to validate linear growth and evolution to turbulence.

Main Results:

• Observed sinuous and varicose instability modes with high growth rates.
• Confirmed that both Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) regimes contribute to secondary instability.
• Demonstrated that the diffuse interface leads to multiple secondary instability modes, with higher-order modes showing more local extremes.

Conclusions:

• Secondary instability in RT flows is driven by a combination of RT and KH instabilities.
• The RT regime, influenced by the 'rising bubble' effect, dominates early instability, while the KH regime becomes significant over time.
• The diffuse interface promotes a multiplicity of secondary instability modes, contributing to the transition to a turbulent-mixing state.