  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.
