Temperature-driven turbulence in compressible fluid flows

TL;DR

This paper investigates the long-term behavior of temperature-driven compressible flows, demonstrating convergence of numerical solutions to continuous attractors and providing insights into turbulence characteristics.

Contribution

It proves the convergence of discrete attractors to continuous ones in compressible flows and offers numerical validation for turbulence-related hypotheses.

Findings

Discrete attractors consist of entire trajectories.

Numerical solutions converge to continuous attractors.

Invariant measures are Gaussian, contrasting previous conjectures.

Abstract

We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories. Further, we prove the convergence of discrete attractors to their continuous counterparts. Theoretical results are illustrated by extensive numerical simulations of the well-known Rayleigh-Benard problem. The numerical results also indicate the validity of the ergodic hypothesis and imply that a non-zero Reynolds stress persist for long time. Finally, we also observe that any invariant measure is of Gaussian type in sharp contrast with the conjecture proposed by [Glimm et al., SN Applied Sciences 2, 2160 (2020)].