# Vorticity equation

The

**vorticity equation** is an important

*prognostic equation* in the

atmospheric sciences. It describes the total derivative (that is, the local change due to local change with time and

advection) of

vorticity, and thus can be stated in either

*relative* or

*absolute* form.

The more compact version is that for *absolute vorticity*, , using the pressure system:

Here, is

density,

*u*,

*v*, and are the components of wind

velocity, and is the 2-dimensional (i.e. horizontal-component-only)

del.

The terms on the RHS denote the positive or negative generation of *absolute vorticity* by divergence of air, twisting of the axis of rotation, and baroclinity, respectively.