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.