Hot disk issues

March 18, 2020, Revision: 1.3

1 Convection develops

Convection does develop after all; see Fig. 1. This can be seen nicely in \overline{ρu_{y}}. However, the timestep became very short and the velocity is still increasing; see Fig. 2. Toward the end, however, the timestep becomes somewhat longer again.

Figure 1: Contours of \overline{ρu_{y}}. Convection starts first in the lower disk half.

Figure 2: Evolution of timestep and rms velocity.

2 Early energy fluxes

At these early time, the convective flux, i.e., the sum of enthalpy and kinetic flux, goes still inward, i.e., it does not contribute to outward energy transport; see Fig. 4. We have to wait longer (but it is expensive). The temperature profile looks normal; see Fig. 4.

Figure 3: Profiles if total flux (black), radiative flux (red), convective [=kinetic+enthalpy] flux (green), and just kinetic flux (blue) at the last time.

Figure 4: Temperature profile at the last time. The positions where the optical depth is unity are marked as red dots.

∇ − ∇_{ad} ≡ \frac{ds/c_{p}}{d ln P}

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