Rayleigh-Taylor Unstable Flames: the Effect of Two-Mode Coupling

TL;DR

This study investigates how two-mode coupling influences the inverse cascade and growth dynamics of Rayleigh-Taylor unstable flames, revealing complex behaviors like stalling, pulsations, and metastability.

Contribution

It introduces a detailed simulation of two-mode coupling effects on RT flames, highlighting new flame behaviors and linking these dynamics to classical RT systems.

Findings

Mode coupling leads to long wavelength mode formation.

Flame behaviors include stalling, pulsations, and metastability.

Results unify dynamics across ablative, classical, and two-mode RT systems.

Abstract

In the classical Rayleigh-Taylor (RT) instability, initial conditions are forgotten and the growth of the mixing layer becomes self-similar when short wavelength modes couple to generate longer wavelength modes. In this paper, we explore how adding a reaction at the unstable interface affects this inverse cascade in wavenumber ("inverse k-cascade"). We simulate a 2D, Boussinesq, premixed model flame perturbed by a large amplitude primary mode ($k_1$) and a smaller amplitude secondary mode ($k_2$). Early on, the modes are uncoupled and the flame propagates as a metastable traveling wave. Once the secondary mode has grown large enough, the modes couple. The traveling wave is destabilized and the flame front bubbles rapidly grow. This inverse k-cascade, driven by two-mode coupling, ultimately generates a long wavelength mode with wavenumber GCD$(k_1,k_2)$, where GCD is the greatest common divisor. We identify five distinct flame growth solution types, and show that the flame may stall, develop coherent pulsations, or even become a metastable traveling wave again depending on GCD$(k_1,k_2)$. Finally, we compare our results with two-mode coupling in ablative and classical RT and show that all three systems may follow the same mode coupling dynamics.