On the Applicability of Low-Dimensional Models for Convective Flow Reversals at Extreme Prandtl Numbers

TL;DR

This study investigates how the nature of flow reversals in convective fluids varies with Prandtl number, showing that low-dimensional deterministic models are only applicable at zero Prandtl number and not at infinite Prandtl number.

Contribution

The paper demonstrates that the applicability of low-dimensional models for flow reversals depends on the Prandtl number, highlighting the limitations of universal models across parameter regimes.

Findings

Flow reversals at zero Prandtl number show low-dimensional deterministic signatures.

Flow reversals at infinite Prandtl number lack low-dimensional deterministic signatures.

A single low-dimensional model cannot describe flow reversals across all Prandtl numbers.

Abstract

Constructing simpler models, either stochastic or deterministic, for exploring the phenomenon of flow reversals in fluid systems is in vogue across disciplines. Using direct numerical simulations and nonlinear time series analysis, we illustrate that the basic nature of flow reversals in convecting fluids can depend on the dimensionless parameters describing the system. Specifically, we find evidence of low-dimensional determinism in flow reversals occurring at zero Prandtl number, whereas we fail to find such signatures for reversals at infinite Prandtl number. Thus, even in a single system, as one varies the system parameters, one can encounter reversals that are fundamentally different in nature. Consequently, we conclude that a single general low-dimensional deterministic model cannot faithfully characterize flow reversals for every set of parameter values.