A statistically stationary minimal flow unit for self-similar Rayleigh–Taylor turbulence in the mode-coupling limit

Abstract

We propose a computational framework for simulating the self-similar regime of turbulent Rayleigh–Taylor (RT) mixing layers in a statistically stationary manner. By leveraging the anticipated self-similar behaviour of RT mixing layers, a transformation of the vertical coordinate and velocities is applied to the Navier–Stokes equations (NSE), yielding modified equations that resemble the original NSE but include two sets of additional terms. Solving these equations, a statistically stationary RT (SRT) flow is achieved. Unlike temporally growing Rayleigh–Taylor (TRT) flow, SRT flow is independent of initial conditions and can be simulated over infinite simulation time without escalating resolution requirements, hence guaranteeing statistical convergence. Direct numerical simulations (DNS) are performed at an Atwood number of 0.5 and unity Schmidt number. By varying the ratio of the mixing layer height to the domain width, a minimal flow unit of aspect ratio 1.5 is found to approximate TRT turbulence in the self-similar mode-coupling regime. The SRT minimal flow unit has one-sixteenth the number of grid points required by the equivalent TRT simulation of the same Reynolds number and grid resolution. The resultant flow corresponds to a theoretical limit where self-similarity is observed in all fields and across the entire spatial domain – a late-time state that existing experiments and DNS of TRT flow have difficulties attaining. Simulations of the SRT minimal flow unit span TRT-equivalent Reynolds numbers (based on mixing layer height) ranging from 500 to 10 800. The SRT results are validated against TRT data from this study as well as from Cabot & Cook (Nat. Phys., vol. 2, 2006, pp. 562–568).

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