ocean.rst

Ocean

In the ocean we interpret:

r = z is the height

$$\dot{r}=\frac{Dz}{Dt}=w\text{ is the vertical velocity}$$

$$\phi=\frac{p}{\rho _{c}}\text{ is the pressure}$$

$$b(\theta ,S,r)=\frac{g}{\rho _{c}}\left( \rho (\theta ,S,r)-\rho _{c}\right) \text{ is the buoyancy}$$

where ρ_c is a fixed reference density of water and g is the acceleration due to gravity.

In the above:

At the bottom of the ocean: R_fixed(x, y) =  − H(x, y).

The surface of the ocean is given by: R_moving = η

The position of the resting free surface of the ocean is given by R_o = Z_o = 0.

Boundary conditions are:

w = 0 at r = R_fixed (ocean bottom)

$$w=\frac{D\eta }{Dt}\text{ at }r=R_{moving}=\eta \text{ (ocean surface)}$$

where η is the elevation of the free surface.

Then equations horiz-mtm- humidity-salt yield a consistent set of oceanic equations which, for convenience, are written out in z−coordinates in ocean_appendix - see eqs. eq-ocean-mom to eq-ocean-salt.