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Convert gather to 4 equation envs for xml output
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Jake Langham committed Jan 15, 2024
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Expand Up @@ -132,18 +132,20 @@ increase in the solids concentration.
\label{fig:schematic}](schematic.pdf){width=8.5cm}

In two spatial dimensions, the governing equations that `Kestrel` solves are
\begin{gather}\frac{\partial H}{\partial t} +
\nabla\cdot(H\bar{\mathbf{u}}) = \mathcal{E} - \mathcal{D} + \mathcal{Q}_H,\label{eq:governing eqs 1}\\
\begin{equation}\frac{\partial H}{\partial t} +
\nabla\cdot(H\bar{\mathbf{u}}) = \mathcal{E} - \mathcal{D} + \mathcal{Q}_H,\label{eq:governing eqs 1}\end{equation}
\begin{equation}
\frac{\partial~}{\partial t}(H\bar{\psi}) +
\nabla\cdot(H\bar{\mathbf{u}}\bar{\psi}) = \psi_b (\mathcal{E} - \mathcal{D}) +
\mathcal{Q}_H\mathcal{Q}_{\psi},\\
\mathcal{Q}_H\mathcal{Q}_{\psi},\end{equation}
\begin{equation}
\frac{\partial ~}{\partial t}(\bar{\rho} H \bar{\mathbf{u}}) +
\nabla\cdot(\rho H\bar{\mathbf{u}}\otimes\bar{\mathbf{u}}) +
\frac{g}{2\cos\theta}\nabla_s\left(\bar{\rho} H^2\cos^2\theta \right) =
-\bar{\rho} gH \nabla_s b - \mathcal{T} + \nabla\cdot(\nu \bar{\rho} H \nabla \bar{\mathbf{u}}), \\
\frac{\partial b}{\partial t} = \frac{\mathcal{D} - \mathcal{E}}{\cos\theta},
-\bar{\rho} gH \nabla_s b - \mathcal{T} + \nabla\cdot(\nu \bar{\rho} H \nabla \bar{\mathbf{u}}), \end{equation}
\begin{equation}\frac{\partial b}{\partial t} = \frac{\mathcal{D} - \mathcal{E}}{\cos\theta},
\label{eq:governing eqs 4}
\end{gather}
\end{equation}
where $\bar{\rho} = \bar{\psi}\rho_s + (1-\bar{\psi})\rho_f$ is the flow
density, $\rho_s$, $\rho_f$, $\psi_b$, $g$ and $\nu$ are user-defined modelling
parameters, $\theta(\mathbf{x},t)$ is the local slope angle between the bed
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