a function of the speed and geometry of the WFC’s, and of their density contrast with the RHG.

Parameters for the Residual Halo Gas
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We consider four models. The parameters are listed in Table \[tab:models\], which lists, for each model, value of $g$, the polytropic index for the cloud, $\gamma_w$, the density contrast between the cloud and the background, $D_\rho$, and the initial downward speed of the cloud, normalized to the sound speed of the background. In all cases, the RHG is initialized with the same temperature throughout, but thereafter evolves with a polytropic equation of state, in which $P_h = K_h \rho_h ^{\gamma_h}$ where $K_h$ is the adiabatic constant, and the polytropic index $\gamma_h=5/3$ for each model. We also assume that the RHG is initially in hydrostatic equilibrium, such that $$\rho_h=\rho_0{\rm e}^{{g\over{C_h^2}}\left(y-y_0\right)},
\label{eq:den}$$ where $\rho_0$ is the density at a reference height $y_0$, and $C_h$ is the isothermal sound speed of the RHG. Because the RHG initially has the same temperature throughout, the magnitude of $K_h$ is a function of $y$, such that $$K_h = C_h^2 \rho(y)^{1-\gamma_h}.$$ The density scale height of the RHG is $$r_h = { C_h^2 \over g}.$$

In all models the velocities are normalized 