Potential vorticity

Potential vorticity combines a fluid’s absolute rotation with its density stratification or layer thickness. It is materially conserved for inviscid, adiabatic motion under suitable assumptions.

Ertel potential vorticity: A three-dimensional potential-vorticity measure formed from absolute vorticity and the gradient of a materially conserved scalar. It gives the general three-dimensional form of the conservation principle.
Rossby wave: A large-scale wave in a rotating fluid whose restoring influence is the variation of planetary vorticity with latitude. Its propagation follows from parcels conserving potential vorticity as they move north or south.
Vorticity: A measure of local rotation in a fluid, represented by the curl of its velocity field. It is the rotational ingredient combined with stratification or thickness.
Potential temperature: The temperature an air parcel would have if brought adiabatically to a standard reference pressure. It can be conserved in adiabatic flow, but unlike potential vorticity it does not include rotation.
Shallow-water equations: Equations describing a thin fluid layer with horizontal scales much larger than its depth. Layer thickness supplies the stretching factor that changes relative vorticity while conserving potential vorticity.
Stratospheric sudden warming: A rapid wintertime rise in polar stratospheric temperatures associated with a major disruption of the westerly circulation. Potential-vorticity maps reveal the wave-driven rearrangement of the polar vortex.
Coriolis parameter: Twice the local vertical component of Earth’s angular rotation rate, varying with latitude. It supplies planetary vorticity in rotating Earth-fluid applications.
Enstrophy: A measure proportional to the spatial integral of squared vorticity in a fluid. It summarizes vorticity across a flow rather than combining parcel rotation with stratification.
Absolute vorticity: The sum of a fluid parcel’s relative vorticity and planetary vorticity. Potential vorticity uses absolute, not merely relative, rotation.
Orographic Rossby wave: A Rossby wave generated when large-scale flow crosses topography and experiences a potential-vorticity disturbance. Mountains create potential-vorticity changes that launch planetary-scale waves.

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