geostrophic momentum approximation

The selective approximation of true momentum by the corresponding geostrophic momentum. The approximation is usually made in conjunction with the assumption that the Coriolis parameter f is a constant, in which case it takes the form

where u, v, and w are the eastward, northward, and upward components of the total wind, ρ is the density, p the pressure, and

the eastward and northward components of the geostrophic wind. In the geostrophic momentum approximation the geostrophic wind is the advected quantity but the advection is by the total (geostrophic plus ageostrophic) wind. When the geostrophic momentum approximation is combined with geostrophic coordinates, the resulting equations are termed the semigeostrophic equations.