On the scaling of temperature fluctuations induced by frictional heating

TL;DR

This paper investigates how temperature fluctuations caused by viscous dissipation in turbulence scale with Reynolds number, revealing discrepancies with existing models and highlighting the importance of dissipation rate fluctuations.

Contribution

It demonstrates that existing models underestimate frictional temperature fluctuation variance by a factor proportional to the square of the Reynolds number, due to anomalous dissipation scaling.

Findings

Scaling of temperature fluctuations differs from previous predictions.

Dissipation rate fluctuations exhibit anomalous scaling.

Models underpredict temperature fluctuation variance significantly.

Abstract

The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuations by a factor proportional to the square of the Taylor-scale Reynolds number.