3.7 Temperature fluctuations

As clearly seen from Figure 12View Image, there is a huge temperature difference, a factor of almost two, at mean optical depth unity, between the warm upflows (∼ 10,000 K) and the cool downflows (∼ 6,000 K). Along with the sudden drop in entropy as the fluid begins to be exposed to space (Figure 5View Image), there is a corresponding sudden drop in the temperature of rising fluid parcels (Figure 13View Image). The temperature drop in individual fluid parcels when they can radiate away their energy is far steeper than the average temperature drop. The average includes the cool downflows whose temperature increases gradually as they exchange energy with their surroundings and entrain overturning entropy neutral material from the upflows. It is this drastic difference between the warm upflows and cool downflows at the same geometric height that is the cause of the tremendous temperature fluctuations at the surface.

The fluid is always approximately in radiative – convective equilibrium (∇ ⋅ (Fconv + Frad) ≈ 0) for the atmospheric structure through which it is moving. The upflows transfer their internal energy to radiation between optical depths τ ∼ 30 and τ ∼ 1. Between those depths they have a temperature gradient close to but slightly less than the grey radiative equilibrium value of 1∕4 T ∝ τ (Figure 14View Image). Their temperature gradient is slightly less than the radiative equilibrium value because the radiative flux is increasing as the optical depth decreases due to the transfer of energy from convection to radiation. This well known gradient on an optical depth scale corresponds to an extremely steep gradient on a geometric depth scale (Figure 13View Image), because of the extreme temperature sensitivity of the dominant H opacity.

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