Divergence equation

From Glossary of Meteorology

divergence equation

An equation for the rate of change of horizontal divergence on a parcel (in analogy to the vorticity equation).

For frictionless flow this equation is
where ∇p · u is the horizontal divergence, J(u, v) is the Jacobian, ω is the material rate of change of pressure, β is the Rossby parameter, ζ is the vertical vorticity, and φ is the geopotential. All horizontal differentiations are carried out in a constant-pressure surface. The divergence equation is derived by taking the divergence of the vector equation of motion. When the two terms in the divergence are neglected, this equation becomes the balance equation.