Reactive Rayleigh–Taylor turbulence

Abstract

The Rayleigh–Taylor (RT) instability develops and leads to turbulence when a heavy fluid falls under the action of gravity through a light one. We consider a model in which the RT instability is accompanied by a reactive transformation between the fluids. We study the model using direct numerical simulations (DNSs), focusing on the effect of the reaction (flame) on the turbulent mixing. We discuss ‘slow’ reactions in which the characteristic reaction time exceeds the temporal scale of the RT instability, τ ≫ tinst. In the early turbulent stage, tinst ≲ t ≲ τ, effects of the flame are distributed over a maturing mixing zone, whose development is weakly influenced by the reaction. At t ≳ τ, the fully mixed zone transforms into a conglomerate of pure-fluid patches of sizes proportional to the mixing zone width. In this ‘stirred flame’ regime, temperature fluctuations are consumed by reactions in the regions separating the pure-fluid patches. This DNS-based qualitative description is followed by a phenomenology suggesting that thin turbulent flame is of a single-fractal character, and thus distribution of the temperature field is strongly intermittent.