Persistence and bimodality of large-scale turbulent structures across a Rayleigh-Taylor layer: Impact on transport and physical modelling through two-field-conditional correlations

TL;DR

This study investigates the bimodal distribution of turbulent fluctuations in Rayleigh-Taylor instability layers, providing new statistical analysis and data for validating two-structure turbulence models.

Contribution

It introduces a novel bimodal analysis method using indicator functions and applies it to simulation data, offering the first reference data for model validation.

Findings

Bimodal behavior observed near mixing zone edges.

Conditional averages reveal turbulence features for model calibration.

New statistical framework supports turbulence structure analysis.

Abstract

The distribution functions of field fluctuations of the turbulent mixing layer produced by a Rayleigh-Taylor instability (RTI) have long been hypothesized to involve bimodal effects. The present work reviews existing quantitative and qualitative evidence in support this conjecture, provides an associated theoretical framework, and measures the corresponding relevant statistical quantities on a simulation of a turbulent RTI at low Atwood number. The bimodal behaviour of fluctuations, readily observable close to the edges of the mixing zone, is less obvious within the mixing zone where indirect evidence comes from different sources, here gathered, discussed, and expanded: energy structure of buoyancy-drag equation, visual eduction from simulated RTI, two-fluid conditional analysis of energy balance, bulk non-dimensional turbulent numbers (Stokes, Knudsen, and Reynolds)... In order to carry out a bimodal analysis of the statistical quantities, two complementary indicator functions are here defined, the `light, upward moving' and `heavy downward moving' fluid zones. An adapted reconstruction is introduced here, based on the thresholding of a space- and time-filtered field (here the vertical velocity). The prescription for the two-structure-field segmentation was applied to a direct numerical simulation of an RTI and the corresponding structure-conditioned averages of the main quantities were obtained (concentrations, momentum, turbulent energies...). Notable features for turbulence understanding and modelling are then observed. The measured conditional averages provide the first know reference data for validation and calibration of so-called `two-structure' RANS turbulence models such as Youngs' (2015 Int. J. Heat Fluid Fl. 56, 233--250 and refs therein) and 2SFK (2003 Laser Part.\ Beams 21 (3), 311--315).