Understanding the different scaling behavior in various shell models proposed for turbulent thermal convection

TL;DR

This paper investigates the scaling behaviors in shell models of turbulent thermal convection, revealing how buoyancy influences whether temperature acts as an active or passive scalar and affects the observed statistical properties.

Contribution

It demonstrates that buoyancy's relevance determines the scaling law (Bolgiano-Obukhov or Kolmogorov) and clarifies the origin of intermittency corrections in these models.

Findings

Buoyancy relevance dictates the scaling behavior in shell models.

Intermittency corrections originate from entropy transfer fluctuations when buoyancy is relevant.

Temperature acts as an active scalar when buoyancy influences the statistical properties.

Abstract

Different scaling behavior has been reported in various shell models proposed for turbulent thermal convection. In this paper, we show that buoyancy is not always relevant to the statistical properties of these shell models even though there is an explicit coupling between velocity and temperature in the equations of motion. When buoyancy is relevant (irrelevant) to the statistical properties, the scaling behavior is Bolgiano-Obukhov (Kolmogorov) plus intermittency corrections. We show that the intermittency corrections of temperature could be solely attributed to fluctuations in the entropy transfer rate when buoyancy is relevant but due to fluctuations in both energy and entropy transfer rates when buoyancy is irrelevant. This difference can be used as a criterion to distinguish whether temperature is behaving as an active or a passive scalar.