\hypertarget{Notation_Symbols}{}\doxysection{Symbols for variables}\label{Notation_Symbols}
$z$ refers to elevation (or height), increasing upward so that for much of the ocean $z$ is negative.

$x$ and $y$ are the Cartesian horizontal coordinates.

$\lambda$ and $\phi$ are the geographic coordinates on a sphere (longitude and latitude respectively).

Horizontal components of velocity are indicated by $u$ and $v$ and vertical component by $w$.

$p$ is pressure and $\Phi$ is geo-\/potential\+:

\[ \Phi = g z .\]

The thermodynamic state variables are usually salinity, $S$, and potential temperature, $\theta$ or the absolute salinity and conservative temperature, depending on the equation of state. $\rho$ is in-\/situ density.\hypertarget{Notation_vector_notation}{}\doxysection{Vector notation}\label{Notation_vector_notation}
The three-\/dimensional velocity vector is denoted $\boldsymbol{v}$

\[\boldsymbol{v} = \boldsymbol{u} + \widehat{\boldsymbol{k}} w ,\]

where $\widehat{\boldsymbol{k}}$ is the unit vector pointed in the upward vertical direction and $\boldsymbol{u} = (u, v, 0)$ is the horizontal component of velocity normal to the vertical.

The gradient operator without a suffix is three dimensional\+:

\[\boldsymbol{\nabla} = ( \boldsymbol{\nabla}_z, \partial_z ) .\]

but a suffix indicates a lateral gradient along a surface of constant property indicated by the suffix\+:

\[\boldsymbol{\nabla}_z = \left( \left. \partial_x \right|_z, \left. \partial_y \right|_z, 0 \right) .\]