larger than that in Equation (\[eq:vterm\]). Both of the above factors may prevent the falling WFC’s from attaining $V_t>C_h$. Because the WFC’s are pressure confined, however, their internal sound speed $C_w = D_\rho ^{-1/2} C_h =0.1 \ll V_t$, and so internal shock dissipation is likely to occur within the WFC’s. In order to examine the role of the relative magnitudes of the speeds, we choose, in model 4, $S (y_0) =0.1$, $g=0.05$, and $D_\rho (y_0) = 25$ such that $V_t < C_h$ throughout the computational domain. Shock dissipation does not occur in the RHG, but it is present interior to the WFC.

In Model 3, we assume the same initial condition as model 1, but adopt an effectively isothermal equation of state for the WFC’s by allowing the gas to cool to 10$^4$ K. The resulting energy drainage would lead to a greater dissipation rate within the WFC’s but it should not significantly modify the energy deposition rate into the RHG.

Numerical Method
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The models discussed below are calculated using Cosmos, a multi-dimensional, chemo-radiation-hydrodynamics code developed at Lawrence Livermore National Laboratory (Anninos, Fragile & Murray 2003). For the current models, radiative emission is not included. In order to maximize 