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The vorticity equation is an important prognostic equation in the atmospheric sciences. Vorticity is a vector, therefore, there are three components. The equation of vorticity (three components in the canonical form) 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, component η, using the pressure system:
Here, ρ is density, u, v, and ω 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.
Additional recommended knowledge
The vorticity equation describes the evolution of the vorticity of a fluid element as it moves around. The vorticity equation can be derived from the conservation of momentum equation. In its general vector form it may be expressed as follows,
where, is the velocity vector, ρ is the density, p is th pressure, is the viscous stress tensor and is the body force term.
Equivalently in tensor notation,
where, we have used the Einstein summation convention, and eijk is the Levi-Civita symbol.
Thus for an inviscid, barotropic fluid with conservative body forces, the vorticity equation simplifies to, 
Alternately, in case of incompressible, inviscid fluid with conservative body forces,
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Vorticity_equation". A list of authors is available in Wikipedia.|