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.
Context. Mixing by convective overshooting has long been suggested to play an important role for the amount of hydrogen available to nuclear burning in convective cores of stars. The best way to model this effect is still debated. Aims. We suggest an improved model for the computation of the dissipation rate of turbulent kinetic energy which can be used in non-local models of stellar convection and can readily be implemented and self-consistently used in 1D stellar evolution calculations. Methods. We review the physics underlying various models to compute the dissipation rate of turbulent kine…
This paper was originally published in June 2013 in JFM (vol. 725). There was one result concerning an expression of viscous dissipation in convective flows and a second result on the condition of applicability of the anelastic liquid equation ($γ- 1 \ll 1$). We then found that this second result was wrong and the explanation why this is so was published as a corrigendum in July 2014 in JFM (vol. 751). In a few words, the origin of the error is that we have derived an expression for dissipation in the framework of the exact equations and subsequently used it in the framework of the anelastic m…
Recent advances in helioseismology, numerical simulations and mean-field theory of solar differential rotation have shown that the meridional circulation pattern may consist of two or more cells in each hemisphere of the convection zone. According to the mean-field theory the double-cell circulation pattern can result from the sign inversion of a nondiffusive part of the radial angular momentum transport (the so-called $Λ$-effect) in the lower part of the solar convection zone. Here, we show that this phenomenon {can result} from the radial inhomogeneity of the Coriolis number, which depends o…
Tidal interactions are important in driving spin and orbital evolution in planetary and stellar binary systems, but the fluid dynamical mechanisms responsible remain incompletely understood. One key mechanism is the interaction between tidal flows and convection. Turbulent convection is thought to act as an effective viscosity in damping large-scale tidal flows, but there is a long-standing controversy over the efficiency of this mechanism when the tidal frequency exceeds the turnover frequency of the dominant convective eddies. This high frequency regime is relevant for many applications, suc…
The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new i…
Turbulent convection models are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied in calculations of stellar structure and evolution. In order to understand the physical processes of the convective overshooting and to simplify the application of turbulent convection models, a semi-analytic solution is necessary. We obtain the approximate solution and asymptotic solution of the turbulent convection model in the overshooting region, and find some important properties of the convective overshooting: I. The oversh…
In this paper, we investigate the upward overshooting by three-dimensional numerical simulations. We find that the above convectively stable zone can be partitioned into three layers: the thermal adjustment layer (mixing both entropy and material), the turbulent dissipation layer (mixing material but not entropy), and the thermal dissipation layer (mixing neither entropy nor material). The turbulent dissipation layer is separated from the thermal adjustment layer and the thermal dissipation layer by the first and second zero points of the vertical velocity correlation. The simulation results a…
The partial ionization of the solar plasma causes several nonideal effects such as the ambipolar diffusion, the Hall effect, and the Biermann battery effect. Here we report on the first three-dimensional realistic simulations of solar local dynamo where all three effects were taken into account. The simulations started with a snapshot of already saturated battery-seeded dynamo, where two new series were developed: one with solely ambipolar diffusion and another one also taking into account the Hall term in the generalized Ohm's law. The simulations were then run for about 4 hours of solar time…
Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency $|ω_t|$ exceeds the turnover frequency $ω_{cν}$ of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equ…
All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that th…
We investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh-Bénard convection using direct numerical simulations. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport, and dissipation associated with large and small-scale dynamos. This energy balance-based characterization reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries.
