A Submesoscale k^-2 Kinetic Energy Spectrum from Surface Quasigeostrophic Theory with Variable Stratification

Submesoscale (1-100 km) surface kinetic energy (KE) spectra are closely correlated with mixed-layer depths: shallow summertime mixed-layers are associated with a steep k^-3  KE spectrum while deep wintertime mixed-layers are associated with a shallow k^-2 KE spectrum. Yet, despite the geostrophic nature of wintertime submesoscale turbulence, classical geostrophic turbulence theory is unable to account for the k^-2 KE spectrum. Here, we show that surface quasigeostrophic (SQG) dynamics are acutely sensitive to the prevailing ocean stratification with non-uniform stratification modifying the familiar, linear-in-wavenumber, SQG inversion relation. Deep wintertime mixed-layers thus lead to a regime of SQG turbulence whose locality is intermediate between two-dimensional turbulence and the well-known constant stratification SQG turbulence. Moreover, the predicted wintertime KE spectrum in the forward cascade inertial range is close to the observed wintertime k^-2 spectrum. We therefore suggest that the shallower wintertime spectrum may not be due to the inverse cascade of energy associated with mixed-layer baroclinic instability, as some authors have suggested, but is rather due to the modified nature of wintertime SQG turbulence in the forward cascade of buoyancy variance.