Spatial inhomogeneity of kinetic and magnetic dissipations in thermal convection

TL;DR

This study examines how kinetic and magnetic dissipations vary spatially in thermal convection, revealing significant inhomogeneity that impacts the modeling of small-scale magnetic fields and dynamo processes.

Contribution

It provides detailed analysis of dissipation inhomogeneity in thermal convection, highlighting the effects of magnetic fields and the importance for small-scale dynamo modeling.

Findings

More dissipation occurs near the bottom of the domain, especially with magnetic fields.

Dissipation in downflows exceeds 80% of total, increased by magnetic fields.

Kinetic and magnetic dissipations are not well correlated despite similar PDFs.

Abstract

We investigate the inhomogeneity of kinetic and magnetic dissipations in thermal convection using high-resolution calculations. In statistically steady turbulence, the injected and dissipated energies are balanced. This means that a large amount of energy is continuously converted to internal energy via dissipation. As in thermal convection downflows are colder than upflows, the inhomogeneity of the dissipation potentially changes the convection structure. Our investigation on the inhomogeneity of the dissipation shows the following. 1. More dissipation is seen around the bottom of the calculation domain, and this tendency is promoted with the magnetic field. 2. The dissipation in the downflow is much larger than that in the upflow. The dissipation in the downflow is more than 80% of the total at maximum. This tendency is also promoted with the magnetic field. 3. Although 2D probability density functions of the kinetic and magnetic dissipations versus the vertical velocity are similar, the kinetic and magnetic dissipations are not well correlated. Our result suggests that the spatial inhomogeneity of the dissipation is significant and should be considered when modeling a small-scale strong magnetic field generated with an efficient small-scale dynamo for low-resolution calculations.