Dynamical Decomposition Of Multiscale Oceanic Motions

Oceanic flows are characterized by a variety of dynamical regimes,with each regime encompassing multiple spatiotemporal scales.In the real ocean such motions interact with one another to different degrees.A practical decomposition of multiscale motions in realistic oceanic settings is crucial to advancing dynamical interpretation and prediction of oceanic processes but remains a major challenge.Conventional approaches focus on time-scale or space-scale decomposition.Based on the fundamentals of ocean dynamics,this study explores physical characteristics of each dynamical regime following two lines of thought,extends conventional approaches to the time-space domain and finally proposes theoretically solid and practically reliable decomposition methodologies that are capable of accurately identifying various dynamical regimes.First,methodologies are developed to decompose variables for the full flow into six dynamical regimes(i.e.,large-scale currents,barotropic tides,lowmode internal gravity waves(IGWs),mesoscale flows,high-mode IGWs and submesoscale flows)based on their respective physical characteristics,taking the IGW aliasing effect into account.Specifically,large-scale currents and barotropic tides are characterized by the largest horizontal scales but with distinctly different frequencies;low-mode IGWs are well constrained by linear dispersion relations,whereas mesoscale flows are of relatively low frequency and with horizontal scales above the first baroclinic deformation radius;the intrinsic frequency of high-mode IGWs(submesoscale flows)is above(well below)the inertial frequency.Particular attempts are made to tackle the challenging problem of separating submesoscale flows from high-mode IGWs based on the relative magnitude of the relative vorticity and horizontal divergence in spectral space.Second,the classic framework of(un)balanced motions is generalized and the dynamical graining is devised to decompose variables for the full flow into two dynamical regimes,namely generalized balanced(including the large-scale circulation,mesoscale processes and submesoscale currents)and unbalanced(including barotropic tides and IGWs)motions.Correspondingly,governing equations and kinetic energy equations for generalized(un)balanced motions are rigorously derived through dynamical graining.Note that generalized(un)balanced motions themselves have multiple space/time scales which could be further separated according to conventional spatial/temporal approaches(e.g.,Fourier,Leonard or Liang filtering).For example,combing spatially high-pass filtering with generalized balanced motions(variables or primitive equations)isolates submesoscale flows.Those two lines of thought are illustrated in the South China Sea using model outputs extracted from a global,tide-resolving and submesoscale-admitting configuration of the MITgcm(i.e.,LLC4320)and are shown to work well.The established theoretical and methodological framework of decomposing multiscale motions in this study could be fully exploited to reveal the mechanisms of scale-interaction and associated energy transfers in the ocean.