Session T30: Geophysical Fluid Dynamics: Oceanographic

Lagrangian transport by internal tides and their superharmonic cascade

Modulated internal tides induce both a Stokes drift and an Eulerian induced flow, the sum of which gives the Lagrangian transport of passive tracers, such as non-inertial microplastics.   In realistic ocean stratification, the Eulerian flow dominates over the Stokes drift and, at the surface, it flows retrograde to the direction of propagation of the waves.  This suggests that floating plastics are carried toward the source of the internal tide.   On the other hand, the internal tide also excites superharmonics with double the horizontal wavenumber of the internal tide and nearly double the frequency.  Particularly in the tropics where the Coriolis parameter is small, the superharmonics are nearly resonant with the internal tide, growing to large amplitude and themselves exciting superharmonics.  This cascade leads to the formation of solitary waves, which have an associated surface Lagrangian transport in the direction of the waves.  This work will present theory and numerical simulations illustrating the competition between the retrograde surface Eulerian transport of the parent internal tide and the prograde surface Lagrangian transport of the solitary waves it generates.   

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.   

Vortex dynamics in tidally modulated stratified wakes

Topographic features with steep slopes are sites of large energy conversion from the oscillating barotropic tide to internal waves and wake eddies. Large-eddy simulations of flow past an idealized conical obstacle with height h and bottom diameter D are undertaken to assess vortex dynamics initiated by a tidally modulated flow. The barotropic flow is composed of a uniform current (U_c) and a sinusoidal tidal modulation (U_tsin(2πf_tt)), where f_t is the tidal frequency. The topographic Froude number is O(0.1) so that an impinging steady current is driven laterally around the obstacle to generate eddies at a constant frequency f_s,c. The ratio f^*=f_s,c/f_t is varied to expose different regimes of tidal synchronization. The wake is found to change qualitatively such that far wake vortices are found at frequencies which differ from f_s,c and f_t. The frequency of wake vortices synchronize to the second subharmonic of the tidal frequency when 0.25 ≤ f^* < 0.5 (regime 1) and to its first subharmonic when 0.5 ≤ f^* ≤ 1 (regime 2). Qualitative changes also occur in the spatial organization of the near wake vortices due to flow separation initiated by tidal forcing. For instance, vortex shedding from the obstacle is laterally symmetric in regime 1 and strongly asymmetric in regime 2.   

Modeling the formation mechanism and growth rate of aggregates through Brownian dynamics

Microorganisms and particulates present near the ocean surface tend to form clusters when coming into contact with each other. The resulting marine aggregates exhibit a fractal structure and play a fundamental role in the oceanic carbon cycle. Our research aims to numerically model their formation using Brownian dynamics. In our model, aggregates undergo random translation and rotation, and they can also be allowed to settle under gravity. They attach to each other when within a predefined distance threshold. We quantify the fractal dimension and growth rate of the aggregates for constant and size-dependent diffusivities and for various settling speeds.   

Parameterizing eddy fluxes of reactive biogeochemical tracers

Motions at the mesoscale and below play a key role in setting the distribution of oceanic biogeochemical tracers. These motions are typically parameterized in global climate models using an eddy flux-gradient formulation, in which turbulent transport is represented in terms of large-scale gradients in the mean fields. However, this form of the eddy flux is not necessarily appropriate for reactive tracers, such as nutrients and phytoplankton. Using an idealized nutrient-phytoplankton system, we demonstrate that the eddy flux of an individual reactive tracer depends on the gradients of both tracers; including these "cross-fluxes" can significantly improve the representation of turbulent tracer transport in certain parameter regimes. We further show that the efficacy of the flux-gradient representation, even when appropriate for non-reacting tracers, requires separation between the flow and reaction timescales. This result has ramifications for the representation of tracer transport in reacting systems in general, and for ocean biogeochemistry in particular where the timescales of many biological processes are comparable to submesoscale motions.   

Statistical analysis and numerical modeling of shoaling internal waves offshore of La Jolla, CA

High-frequency internal wave (IW) trains with a period of approximately 10 min are observed at certain phases of the internal tide offshore of La Jolla, CA. The shoaling IWs structure is captured by an L-shaped temperature fiber optic sensing array. Despite the distinctive structure of the IWs, their intermittent and stochastic nature complicates the analysis. We apply conditional statistics to extract solitary wave characteristics like the dominant velocity (0.8 m/s), wave period (∼ 8 min), and wave propagation angle (∼15° to shore normal). Next, we demonstrate that wave trains with these characteristics are generated as solutions to the two-dimensional weakly nonlinear Kadomtsev–Petviashvili (KP) wave equation with cross-shore-varying bathymetry. The initial condition is, informed by the data, chosen as a 15° angled solitary wave of finite alongshore span. For a fixed initial wave amplitude, the density stratification is varied to investigate the evolution of the shoaling waves that are generated by the dispersion and advection of the initial soliton solution.   

Drifter deployment strategies to estimate surface dilation rate in submesoscale flows

Surface convergence in the ocean is associated with accumulation of buoyant pollutants as well as with subduction that is important to biological activity. Recent studies on submesoscale flows have shown that the finite-time Lagrangian average divergence (i.e., the dilation rate) is even better at identifying surface clustering regions and subduction conduits near density fronts than the instantaneous horizontal divergence field. Divergence can be derived from any velocity measurements, such as radar or ADCPs, but for the Lagrangian average, the most convenient methodology is based on the time rate of change of the area encompassed by drifter swarms. The technological advances that have enabled the deployment of large numbers of drifters in a single experiment have raised new questions about optimal deployment strategies for extracting dilation rate information with acceptable accuracy and as much spatial coverage as possible. Using a submesoscale-resolving operational model of the Mediterranean Sea, we analyze synthetic drifter trajectories to evaluate the impact the number of drifters and their initial separation have on the accuracy of the resulting dilation rate estimates. The results confirm that estimates improve as the swarm radius decreases and as more drifters are added, but with only a marginal improvement for swarms containing more than four drifters. GPS positions obtained from drifters in the ocean are subject to uncertainty on the order of 5-10 meters, and when this uncertainty is taken into account, an optimal initial separation distance can be identified that balances uncertainty from position measurements with that from the dilation rate estimation.  Finally, we investigate the effect of the initial configuration of drifter swarms using various shape parameters to classify the shapes of drifter triads and tetrads.   

Reynolds-averaged Simulation of Langmuir Turbulence in the Costal Ocean

Langmuir turbulence in the costal ocean is driven by winds and waves and is characterized by Langmuir cells (LCs) that can span the full depth of unstratified water columns. A solution strategy based on Reynolds averaging is introduced, relying on the coherency and persistence of full-depth LCs. Here the full-depth cells are treated as a secondary component to the wind and/or pressure gradient-driven primary flow. The resolved LCs and associated statistics will be compared with their counterparts in large-eddy simulation (LES). The comparison shows that the Reynolds-averaged approach can reproduce cell meandering and merging (i.e. the so called Y junctions), a requisite for capturing the proper crosswind scales of the LCs. The merging occurs less frequently over time as the cells grow after being spun from rest. The Reynolds-averaged approach will be extended to simulations involving a coastal boundary through coupling with a wave model predicting the Stokes drift velocity of the surface waves. Studies based on this approach will be presented investigating the impact of the costal shore and wave direction on the structure and intensity of the LCs in a surf-shelf transition zone. The impact of LCs on cross-shore mass transport will be investigated via a passive tracer.   

Reflection coefficients for reflecting internal wave beams

Tidally generated internal waves beams do not propagate far from the generation site and instabilities and other nonlinear processes may be the cause of this local dissipation of higher wave modes, but we find that the reflection coefficient, R≡Eout /Ein, for internal wave beams is always less than unity and approaches zero when the boundary angle matches the wave beam angle indicating that internal wave reflection may be an equally important dissipation mechanism for tidally generated wave beams. We use a 2D pseudo-spectral and a 2D finite volume code to solve the Navier-Stokes equations in the Boussinesq limit along with low Reynolds number experiments to find values of R for different conditions. We focus on beam angles where the only propagating modes are in the incoming and fundamental reflection (θ > 30^◦) to minimize nonlinear effects. We measure the decay rate due to viscous dissipation to separate its effects from the energy loss upon reflection. We also reduce the viscosity by two orders of magnitude, and even under these conditions, R falls off rapidly as the boundary angle increases indicating that high energy loss may be expected for many oceanic conditions.   

Not Participating

We use direct numerical simulations to study the dynamics of the turbulence produced by stratified shear instability in tilted coordinates where the tilt angle continuously oscillates in time. Such a setup might model, for example, a layer of strong density stratification in the ocean undergoing shear oscillations due to a horizontally propagating gravity wave. Previous work by Inoue and Smyth (2008, J. Phys. Oceanogr., 39) has demonstrated that the mixing properties may be modified by the timing of the deceleration of the shear induced by the tilt oscillation. Here, we investigate in detail how the time dependence of the forcing relative to the development of growing Kelvin-Helmholtz instabilities modifies the energetic pathways that lead to turbulence at a high Reynolds number. We look at the quantification of mixing in terms of the change in the background potential energy (BPE), and in terms of the mixing efficiency, here defined as the ratio of the rate of increase in BPE to the total energy expended in producing the mixing. We discuss the importance of transient flow behaviour for the parameterization of mixing and outline the implications of our results for the development of practical parameterizations used to infer mixing rates from observational data.