4.2 The primitive equations

The continuous equations solved by MOM are given by

       

$$- \nabla \cdot (u \, {\bf u}) + v \left(f + \frac{u\tan\phi}{a} \... ...ac{1}{a \, \rho_\circ \cdot \cos\phi} \right) p_\lambda + (\kappa_mu_z)_z + F^u$$ u_t = (4.1)

$$- \nabla \cdot (v \, {\bf u}) - u \left(f + \frac{u\tan\phi}{a} \right) -\left(\frac{1}{a \, \rho_\circ}\right) p_\phi + (\kappa_mv_z)_z + F^v$$ v_t = (4.2)

$$- \nabla_{h} \cdot {\bf u}_{h}$$ w_z = (4.3)

$$-\rho \, g$$ p_z = (4.4)

$$\theta_t - \nabla \cdot [ {\bf u} \, \theta + {\bf F}(\theta) ]$$ = (4.5)

$$- \nabla \cdot [ {\bf u} \, s + {\bf F}(s)]$$ s_t = (4.6)

$$\rho \rho(\theta,s,z).$$ = (4.7)

The coordinate $\phi$ is latitude, which increases northward and is zero at the equator. $\lambda$ is longitude, which increases eastward with zero defined at an arbitrary longitude (e.g., Greenwich, England). z is the vertical coordinate, which is positive upwards and zero at the surface of a resting ocean. Boldface characters represent vector quantities.