Variable-Density Self-Similar Rayleigh-Taylor Turbulence, and the Path to Get There

Author: Goh, Chian Yeh

Year: 2027

Degree: Dissertation (Ph.D.)

Advisor: Blanquart, Guillaume

Committee Members: Colonius, Tim; Bae, H. Jane; Blanquart, Guillaume; Pullin, Dale Ian

Option: Mechanical Engineering

Abstract

The Rayleigh-Taylor (RT) instability arises when a denser fluid is accelerated into a lighter fluid, which eventually transitions into a buoyancy-driven turbulent mixing layer. At sufficiently late times, simple dimensional arguments predict that the mixing-layer height grows self-similarly and quadratically with time. Despite this simple prediction, the self-similar regime is difficult to realize and study in practice.

The late-time behavior of temporally growing RT (TRT) mixing layers can be strongly dependent on initial conditions, which are difficult to control in experiments. Consequently, theoretical self-similarity has not yet been demonstrated experimentally. Meanwhile, direct numerical simulations of conventional TRT flow become increasingly expensive as the mixing layer grows, and statistical fluctuations with limited sampling can obscure physical trends. At high density ratios, the approach to self-similarity is further delayed and more expensive simulations are required. This thesis addresses these limitations by developing an improved semi-Lagrangian scalar transport algorithm for variable-density flows and a statistically stationary RT (SRT) configuration that enables the self-similar regime to be studied over long sampling times at fixed flow conditions.

The SRT configuration is derived through a transformation of the governing equations and further simplifying assumptions, resulting in a statistically stationary mixing layer at a prescribed height. Under certain domain constraints, a minimal flow unit is identified and shown to reproduce the statistics of self-similar TRT, reducing domain-size requirements significantly. The resulting framework is used to investigate the effects of Reynolds number, Atwood number, and multiple lengthscales on RT turbulence. The results demonstrate that non-Boussinesq RT dynamics are more effectively characterized by the logarithm of the density ratio than by the Atwood number, and that the late-time TRT approach to self-similarity can be characterized using an eddy-column model driven by multiple lengthscales. Finally, a classical one-dimensional turbulent diffusivity model is revisited and shown to capture several features of RT turbulence that were observed independently much later in the literature, including asymmetric growth and shifts in velocity statistics.

Overall, the results establish SRT not merely as a cheaper alternative to TRT, but as a complementary framework with unique advantages for isolating physical mechanisms and obtaining well-converged statistics in a scalable and tractable manner.