Some aspects of submesoscale processes in the ocean

This study clarifies two aspects of submesoscale processes (i) Unforced instabilities that give rise to submesoscale processes and (ii) Synthesizing several recent simulations to understand applications of Semi Geostrophic (SG) and Surface Quasi-Geostrophic (SQG) dynamics for submesoscale processes.

The unforced instabilities in the mixed layer where Rossby and Richardson numbers are O(1) investigated earlier by Stone in 1960s are different from the geostrophic baroclinic mode. The ageostrophic baroclinic instability problem of a sheared rotating stratified flow in thermal wind balance with a constant horizontal buoyancy gradient has been investigated by Molemaker et al. (2006) in the context of loss of balance. Bocaletti et al.(2007) investigate a similar instability problem, although with a reduced gravity bottom boundary condition. We clarify the connections between the ageostrophic mixed layer instability (Bocaletti et al.2006 and Fox-Kemper et al. 2007) and the geostrophic mode of Molemaker et al. 2006.

Lapeyre and Klein 2006 have recently suggested that the SQG dynamics captures submesoscale processes and the associated forward cascade of density variance. We attempt to clarify whether an SG or SQG framework is more appropriate for submesoscale dynamics. Several recent model results (e.g. Capet et al. 2007, Fox-Kemper et al. 2007, Thomas et al. 2007, Klein et al. 2007) imply that submesoscale processes are implicated in both forward and reverse energy cascade. The reverse cascade is physically manifest through the evolution of mixed layer eddies into larger ones, while the forward cascade is intimately tied to frontogenesis and frontal instabilities . Capet et al. (2007) show by detailed energetics analysis that the forward cascade by frontogenesis is almost entirely associated with advection by the horizontally divergent, ageostrophic component of the flow, which suggests that an SG model rather than an SQG model maybe more representative of submesoscale dynamics. In addition, the numerical models with submesoscale processes show a characteristic discontinuity energy spectra (-2 slope), associated with frontogenesis. It may be worth noting that SG dynamics leads to formation of frontal discontinuities in finite time, different from SQG.