Geostrophic Adjustment of an Isolated Diapycnal Mixing Event and Its Implications for Small-Scale Lateral Dispersion

Abstract

In this first of two companion papers, the time-dependent relaxation of an isolated diapycnal mixing event is examined in detail by means of numerical simulations, with an emphasis on the energy budget, particle displacements, and their implications for submesoscale oceanic lateral dispersion. The adjustment and dispersion characteristics are examined as a function of the lateral extent of the event L relative to the Rossby radius of deformation R. The strongest circulations and horizontal displacements occur in the regime R/L Ϸ O(1). For short times, less than an inertial period, horizontal displacements are radial. Once the adjustment is completed, displacements become primarily azimuthal and continue to stir fluid over several to tens of inertial periods. The cumulative effect of many such events in terms of the effective lateral dispersion that they induce is examined in the companion paper.

The fully nonlinear stratified geostrophic adjustment problem

“…We then focus on the geostrophic state in detail, specifically examining the change in kinetic energy and the change in potential energy for different initial widths, as well as the changes in the kinetic energy in the geostrophic state and the propagating wave train as the Rossby number varies. These results make the closest contact with the work of Lelong and Sundermeyer (2005). Finally we draw a number of conclusions based on our findings and identify directions for future work.…”

“…However, for a given initial condition it is not immediately obvious what the precise split is between the portion of the initial state that propagates away and the portion left behind. While the case in which the disturbance that emanates from the initial condition is small enough to be well described by linear wave theory has been studied in detail by Lelong and Sundermeyer (Lelong and Sundermeyer, 2005), the significant amount of literature on the combined effects of nonlinearity, dispersion, and rotation, and especially the experimental results in Grimshaw et al (2013), suggest that the initial value problem should be reconsidered without a priori approximations. Using our definition of the Rossby number, we find that the experiments presented in Grimshaw et al (2013), with a Coriolis parameter of f = 0.105 s −1 , had a corresponding Rossby number of 0.667.…”

“…those from Lelong and Sundermeyer (2005), who performed 3-D numerical simulations of the adjustment problem. Lelong and Sundermeyer (2005) focused on the energetics of the geostrophic state that are generated by a wellmixed region of intermediate density fluid.…”

“…Lelong and Sundermeyer (2005) focused on the energetics of the geostrophic state that are generated by a wellmixed region of intermediate density fluid. Though not exactly the same case, Lelong and Sundermeyer (2005) performed their simulations using the full set of equations and thus provide an apt point of comparison. To facilitate this comparison between our work and theirs, Table 2 provides a translation of our notation to that of Lelong and Sundermeyer (2005).…”

“…More recently, Ledwell et al (2004) and Oakey and Greenan (2004), as part of the Coastal Mixing and Optics experiment, showed the presence of patches of well-mixed regions (density anomalies) throughout a background of stable fluid along the New England shelf. The specifics of this adjustment were investigated in Lelong and Sundermeyer (2005). The authors performed fully 3-D numerical simulations of moderate resolution, using the nonhydrostatic equations under the Boussinesq approximation, of the adjustment process resulting from one of these density anomaly patches.…”