Surface-Interior interactions in baroclinic turbulence (and a theory for the observed energy spectrum of the atmosphere)
Shafer Smith (CIMS)

Motivated by observations of shallow mesoscale energy spectra in both the atmosphere and ocean, some basic results in the turbulence of geostrophically balanced flow are reconsidered.  It has long been known that surface quasigeostrophic (SQG) dynamics (the dynamics of temperature perturbations bounded vertically by regions of constant potential vorticity) exhibit a shallow forward cascade of energy at scales smaller than the forcing scale.  This lies in contrast to Charney's theory of
geostrophic turbulence, in which boundaries are neglected and (most of) the energy cascades to larger scale.  SQG is typically thought of as a rarely-realized special case, while geostrophic turbulence is assumed generic.  Here it will be show that, in fact, both interior and surface turbulent cascades can coexist and interact in realizable geophysical flows --- one need not have regions of homogenized PV to realize a shallow, forward energy cascade in geostrophically balanced flow.

Some of the results to be shown are: (1) Numerical simulations of quasigeostrophic turbulence that use low-vertical resolution finite-differencing will fail to resolve (or completely remove) eddy buoyancy cascades at the upper and lower surfaces.  (2) This problem can be ameliorated by using a PV inversion based on the Green's functions of the surface signals, plus a modal representation in the interior.  (3) A simplified model based on this framework (using two interior modes and two surfaces) is proposed as a useful alternative to the standard two-layer model.  (4) The simplified model can reproduce (for example) the observed atmospheric energy spectrum (Nastrom and Gage, 1985), which has a large-scale -5/3 slope, a synoptic-scale -3 slope and a mesoscale -5/3 slope (at horizontal scales less than 600 Km).  Moreover, the hybrid model exhibits a number of features more consistent with the data than competing models and theories.