MOM6
General coordinate equations

Transforming to a vertical coordinate \(r(z,x,y,t)\), with \(\dot{r} = \frac{\partial r}{\partial t}\) ...

The Boussinesq hydrostatic equations of motion in general-coordinate \(r\) are:

\f{eqnarray} \label{html:r-equations}\notag \ \rho_0 \left( \frac{\partial \mathbf{u}}{\partial t} + ( f + \zeta ) \, \hat{\mathbf{z}} \times \mathbf{u} +

{r} \, \frac{\partial \mathbf{u}}{\partial r} + \nabla_r \, K \right) &= -\nabla_r \, p - \rho \nabla_r \, \Phi + \boldsymbol{\mathcal{F}}