Ocean Waves and Density Fronts

Recently, numerical simulations coupled with observations have highlighted that oceanic motions associated with horizontal scales smaller than 50 km mainly comprise of horizontal jets, fronts, filaments and vortices. Collectively, they represent the strongest submesoscale currents in the upper ocean. Normally, these currents are approximately in geostrophic, hydrostatic balance with the sea level, pressure and buoyancy fields and represent ‘coherent structures’ that are in a dynamically preferred state. Surface gravity waves have important influences on near-surface and/or near-shore currents, often referred to as wave effects on currents. For the purpose of oceanic circulation models, wave breaking is often subsumed in the surface wind-stress representation except for the depth-induced breaking in the surf zone. In line with this, the problem of Langmuir turbulence has been proposed and studied extensively. Unfortunately, little focus has been given to the interaction between surface waves and submesoscale currents.

In a recent publication, Professor James C. McWilliams from the Department of Atmospheric and Oceanic Sciences at the University of California extended the Secondary Circulation and Frontogenetic Tendency (SCFT) methodology so as to incorporate wave effects on currents as expressed in wave-averaged equations for the current dynamics in the presence of a specified wave field and its associated Stokes drift. He thoroughly analyzed the representative diagnostic solutions. His research work is currently published in the Journal of Fluid Mechanics.

In brief, the research method employed commenced with the presentation and review of a generalized SCFT model. Next, he posed specific problems for the two-dimensional fronts and filaments. He then recalled a turbulent thermal-wind secondary circulation and frontogenetic tendency solution for comparison with the new wave effects on currents results that he had obtained from his model and simulations. Lastly, he made a brief analysis of current effects on waves near submesoscale fronts and filaments.

He observed that the wave’s Stokes-drift velocity induced SCFT effects that were dominant in strong swell with weak turbulent mixing, and they combined with Ekman and turbulent thermal wind influences in more general situations near wind-wave equilibrium. In addition, he noted that the complementary effect of the submesoscale currents on the waves was weak for longer waves near the wind-wave or swell spectrum peak, but it remained strong for shorter waves. Moreover, he recorded that the SCFT behavior was essentially the same for fronts and for dense filaments, apart from their obvious structural pattern difference.

In summary, Prof. James C. McWilliams presented a detailed diagnostic analysis for the ageostrophic secondary circulation, buoyancy flux and frontogenetic tendency in upper-ocean submesoscale fronts and dense filaments under the combined influences of boundary-layer turbulent mixing, surface wind stress and surface gravity waves. His analysis was based on a momentum-balance approximation that neglects ageostrophic acceleration, where the surface wave effects are represented with a wave-averaged asymptotic theory based on the time scale separation between wave and current evolution. Altogether, it is best to conclude that, since the reality of nature is messy as winds and waves are often in disequilibrium, and still there exists a large uncertainty about how to best represent turbulent mixing in the presence of waves and submesoscale flows, the goal of demonstrating a detailed correspondence between modelled and measured individual events may prove difficult and elusive.