Observations and Modelling of Fronts and Frontogenesis

vorticity ('pseudo-potential vorticity') equation, and
inferred the existence and spectral form of an inertial
subrange in quasigeostrophic motion from the results of
Kraichnan (1967) on two dimensional Navier-Stokes turbulence.
In this subrange, enstrophy (half-squared vorticity) is
cascaded to small scales, rather than energy as in
three-dimensional turbulence. Charney (1971) introduced the
phrase 'geostrophic turbulence' to describe the energetic,
low frequency, high wavenumber, three-dimensional,
near-geostrophic motions to which this theory applies. The
phrase is now also used more generally to describe the
'chaotic, nonlinear motion of fluids that are near to a state
of geostrophic and hydrostatic balance' (Rhines, 1979) but in
which anisotropic waves (e.g., Rossby waves) may also
propagate.
In the predicted inertial subrange, the energy spectrum
E(k) has the form
E(k) = c ,2/3 k3,
where C is a universal constant, r is the enstrophy cascade
rate, and k is an isotropic wavenumber. Total energy is
equally distributed between the potential energy and each of
the two components of kinetic energy. For a spatially
oriented wavenumber (e.g., wavenuniber along a tow track), the
power law dependence is unchanged, but the transverse
velocity kinetic energy component contains three times the
22