Session L27: Geophysical Fluid Dynamics: Oceanographic II

Internal wavepacket tunnelling across a thermohaline staircase

Due to double diffusive processes below the thermocline in the Arctic Ocean, vertical density profiles exhibit a staircase structure in which successive layers of near-uniform density are separated by sharp density jumps. Earlier work [Sutherland, PR Fluids (2016)] theoretically predicted the transmission and reflection of a vertically propagating internal gravity wave incident from above upon a density staircase with an arbitrary number of steps. That work assumed a plane incident wave, being monochromatic in wavenumber and frequency. For waves with given frequency, the transmission coefficient exhibited a series of spikes depending upon the depth of steps relative to the horizontal wavelength. Here we use numerical simulations to examine the transmission of a vertically propagating internal wavepacket that interacts transiently with a staircase. Rather than exhibit successive transmission spikes, the simulations show a smooth transition between perfect and zero transmission as the relative step size increases. This results from internal waves exciting leaky internal modes of the staircase that retransmit waves above and below the staircase slowly over time, as can be predicted by theory.   

Prandtl number effects on extreme mixing events in forced stratified turbulence

`Strongly' stratified turbulent flows can self-organise into a  `layered anisotropic stratified turbulence' (LAST) regime, characterised by staircases of relatively deep and well-mixed density `layers' separated by relatively thin `interfaces' of enhanced density gradient. Understanding their mixing dynamics is important for parameterizing heat transport in the world's oceans. It is challenging to simulate such `LAST' mixing, which is associated with Reynolds numbers Re=U L/ν >> 1  and Froude numbers Fr=(2 π U)/(L N) << 1, (U and L being characteristic velocity and length scales, ν being the kinematic viscosity and N the buoyancy frequency).  As a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is still required, the buoyancy Reynolds number Re<sub>b</sub>=ε/(ν N<sup>2</sup>) >> 1, where ε is the TKE dissipation rate. This requirement is exacerbated for oceanic flows,  as the Prandtl number Pr =ν/κ=O(10) in thermally-stratified water (κ is the thermal diffusivity), thus leading (potentially) to even finer denisty field structure. We report on four fully-resolved direct numerical simulations of stratified turbulence  with different Fr=2,0.5 and Pr=1,7, forced so that Re=9216 and Re<sub>b</sub> =50, with resolutions up to 30240 x 30240 x 3780, investigating how variation of bulk parameters affects mixing properties.   We find that as Pr increases, stably stratified interfaces are finer and their contribution to bulk mixing characteristics decreases. Neverthelesss, `extreme' mixing events (with highly elevated and exceptionally `efficient' buoyancy variance destruction rates χ, dominating the total mixing budget) are still preferentially found in strongly stratified interfaces.   

On the use and misuse of the Osborn model: Implications for improved estimates of ocean mixing rates

The Osborn model is widely used for quantification of diapycnal diffusivity K_ρ in in oceanic flows.Two main simplifications are routinely made when estimating mixing rates in stably stratified flows when using the Osborn model. First, a constant value is frequently assumed for the mixing coefficient Γ. Second, dissipation rates of turbulent kinetic energy ε are inferred using either the Thorpe length scales or from microstructure measurements using the isotropy assumption. Data from three independent direct numerical simulations of homogeneous stratified turbulence are used as a testbed to highlight impacts of these assumptions on estimates of K_ρ. A systematic analysis is used to evaluate the inferred diffusivities to exact DNS diffusivities as a function of the turbulent Froude number Fr_t. Use of a constant mixing coefficient Γ results in an under-prediction of K_ρ by up to a factor of 5 for strongly stratified conditions (i.e., at low Fr_t) and an over-prediction of K_ρ by up to two orders of magnitude in weakly stratified conditions (i.e., high Fr_t). The use of inferred dissipation rates ε based on the assumption of isotropy results in an over-prediction of K_ρ by a factor of 2 for low Fr_t and converges on the exact K_ρ for Fr_t > 1. However, the use of kinematic length scales, such as the Thorpe scale, to infer ε result in significant errors. The implications of these findings for improved estimates of ocean mixing rates are illustrated using an example application.   

Estimates of Mode-1 Internal Tide Harmonic Generation in the Global Ocean

Recent theoretical and experimental work has demonstrated the generation of nonlinear harmonics when internal waves propagate in non-uniform stratification, if the harmonic frequency is near resonance. This effect may impact the evolution of low-mode internal tides in the ocean, possibly leading to the formation of strongly nonlinear waves. Here, measured ocean stratification profiles are used to quantify the potential for nonlinear harmonic generation for mode 1 semi-diurnal internal tides. The results show that the first harmonic, with double the wavenumber of the parent mode, is often expected to attain a significant amplitude in the Equatorial Pacific due to near-resonance, but not in the Atlantic. This is because weaker and more shallow Atlantic pycnoclines do not provide a sufficient harmonic forcing. Hence near-resonance is found to be a necessary, but not sufficient, condition for harmonic generation in measured ocean stratifications. A second criterion, based on pycnocline depth and density change, is proposed as an additional condition for harmonic generation.   

Internal tides at the coast: energy flux of baroclinic tides propagating into the deep ocean in the presence of supercritical shelf topography

The generation of internal tides at coastal margins is an important mechanism for the loss of energy from the barotropic tide. Although some previous studies attempted to quantify energy loss from the barotropic tides into the deep ocean, global estimates are complicated by the coastal geometry and spatio-temporally variable stratification. We explore the effects of supercritical, finite amplitude bottom topography, which is difficult to solve analytically, by conducting a suite of 2D linear numerical simulations of barotropic tide interacting with a coastal shelf that is uniform in the along-shore direction. We explore the effects of latitude, topographic parameters, and non-uniform stratification on the baroclinic tidal energy flux propagating into the deep ocean away from the shelf. By varying the pycnocline depth and width, we approximate the deep permanent pycnocline rather than shallow and infinitesimally thin pycnoclines previously studied. We find that the topographic criticality parameter used in previous studies, i.e., ratio of the topographic slope to the characteristic slope of the mode-1 internal tide, is not a suitable scaling for the baroclinic energy flux magnitude. Instead, we derive a new scaling that combines the latitudinal effects, stratification-dependent barotropic tidal forcing, and various physical parameters that describe the topographic shape.   

Heat and mass transfer in the North Atlantic Ocean: insights from turbulence and convection resolving simulations

The large-scale circulation attributes to the horizontal geostrophic circulation which is often localized near the ocean surface in the form of gyre and zonal flows and the overturning circulation associated with vertical motion. Mechanical forcing (e.g. wind, tide etc.) has long been known as the primary driver of the meridional overturning or gyre circulations. However, the modern laboratory experiments and high fidelity simulations have revealed the important role of buoyancy forcing in deriving the ocean circulation and maintaining the stratification in the subtropical regions. However, critical questions still remain on the contributions of each parameter to driving the meridional overturning circulation (MOC), gyre circulation, and the processes governing heat and mass transfer in the ocean. In the present work, we investigate the role of buoyancy and wind in driving ocean circulation in the North Atlantic Ocean (NAO) using direct numerical simulations of an idealized ocean at a wide range of surface wind stress and buoyancy forcing. In our model, buoyancy forcing (given by Rayleigh number, Ra ~O( 10^{11} -10^{14}) ) is large enough to sustain turbulent convection and a rich baroclinic eddy field. By varying surface forcing, we can quantify its effect on the heat and mass transfer (strength of the vertical and horizontal stream functions) in the model. The simulations show that the buoyancy forcing can solely drive both horizontal gyre and vertical overturning circulations. Moreover, the evaluation of scaling indicates that the meridional overturning transport scales with thermal wind balance along with the vertical advection-diffusion balance in the thermal boundary layer without considering the surface wind forcing. It shows the negligible effect of the surface wind on the overturning transport in the range of the wind stress investigated in the present work which is comparable to the atmospheric wind forcing relative to the buoyancy forcing. The results show that the horizontal gyre circulation strongly depends on the surface wind stress as it has a component which is linearly proportional to the wind. However, it has another term which associates with the meridional overturning transport which has long been neglected in previous works and the relevant theories.   

Numerical simulations of `pure' Langmuir turbulence

Langmuir turbulence, engendered by the interaction of surface gravity waves and mean Eulerian currents, is a prominent upper ocean mixing process. A coarse-grained description of this phenomenon is provided by the reduced Craik-Leibovich (rCL) equations, which can be derived via multiple-scales asymptotic analysis of the governing Craik-Leibovich (CL) equations in the strong CL vortex-force limit. The rCL equations self-consistently suppress nonlinear advection by the (Eulerian) downwind velocity and, thus, the mechanisms responsible for the sustenance of shear-flow turbulence in the extit{absence} of waves. Crucially, the rCL equations also obviate the need to temporally resolve rapid-distortion transients driven by the wave Stokes drift, in principle facilitating simulation of Langmuir turbulence over long times and in spatially extended domains. Unfortunately, prior simulations of the rCL equations in this `pure' Langmuir turbulence regime have been stymied by the occurrence of spurious cross-wind banding in the downwind velocity field. In this work, we resolve this issue and characterize rCL dynamics in the pure Langmuir turbulence regime, highlighting a 2:1 spatial resonance that dominates surface patterning.   

Evaporation induced convection increases upper ocean turbulence and mixing.

The upper ocean surface layer is directly affected by the air-sea fluxes which vary spatiotemporally. The diurnal timescale (24 hr) is one of the most prominent sources of the variability of upper ocean turbulence and mixing, in response to these air-sea fluxes. In this study, we use large-eddy simulation to quantify the role of surface evaporation (haline fluxes) in the modulation of diurnal mixed layer turbulence and mixing. During daytime when the upper ocean boundary layer becomes thermally stratified, a salinity inversion layer forms near the surface, leading to double diffusive salt-fingering instability. During nighttime, convection due to surface buoyancy loss from both surface cooling and evaporation deepens the mixed layer. During transitions between day to night, the flow instability changes from salt-fingering to gravitationally unstable convection and vice versa. In a total sense, surface evaporation increases the mixed layer depth and irreversible mixing through convection, both during nighttime and daytime, and leads to better prediction of dynamical variables like sea surface salinity (SSS) and sea surface temperature (SST).   

Dynamical Parameter Estimation for LES Closure Models

We present an algorithm for dynamically estimating the parameters of chaotic systems. The algorithm uses partial observations of a system of dissipative differential equations to estimate the state of the system and relevant physical parameters simultaneously. The algorithm was first applied to the Lorenz system, and then to Rayleigh Benard convection to estimate the Rayleigh and Prandtl numbers. In both cases, convergence of parameter estimation was established both numerically and analytically. We first review the implementation and results of parameter recovery in these two settings to illustrate the general approach, and then move to applying this algorithm to estimating parameters for turbulence closure models for ocean large eddy simulations (LES). This problem requires a new approach both in the numerics and the theory as the desired parameter doesn't have a 'unique true' value. Rather than converging to the true value, the parameter estimation algorithm instead converges to the optimal approximate one.   

A new physically-motivated vertical mixing scheme for ocean surface boundary layer turbulence

In this study, we present a physically-motivated Assumed-Distribution Higher-Order Closure (ADC) scheme to parameterize small-scale vertical mixing in the ocean surface boundary layer (OSBL). The ADC is a hybrid mass-flux and high-order closure scheme that achieves turbulence closure by reconstructing all the required second-order and higher-order moments exactly from a subset of moments that are evolved prognostically. In addition, this ADC parameterization has energetic constraints and includes non-local fluxes, which are a significant source of vertical mixing in the upper ocean boundary layer. We have implemented the ADC scheme within the Model for Prediction Across Scales-Ocean (MPAS-Ocean), the ocean component of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). We evaluated this scheme against three dimensional large-eddy simulations (LES) using a single-column model formulation for general ocean-relevant forcing. Results show that the new scheme can efficiently simulate upper ocean vertical mixing produced by various processes including surface wave-, buoyancy-, and wind-driven mixing.   

Eulerian modeling of neutrally buoyant tracers in global oceans

Evaluating the distribution of plastic debris in the ocean has been an intriguing but challenging task. Previous studies using Lagrangian models have identified the effect of convergent surface flow to tracer accumulation, and have revealed the presence of five garbage patches in subtropical ocean gyres. In this work, aiming to eventually enable assimilation of remote-sensing data, we developed an Eulerian model for plastic transport in the global ocean. The model was built for neutrally buoyant tracers, in our case microplastic, in the framework of MITgcm. It incorporates the ECCOv4r4 climate data, which was obtained in a data-constraint global ocean simulation, and is integrated for 24-years from 1992 to 2017. Comparison with previous model and measurement data, and sensitivity test of the result to configuration of sources/sinks of plastics will be presented.   

Chaotic advection by a vortex in a polygonal bay

This talk discusses the motion of a point vortex in the presence of a bay and a coastal current, as well as the ensuing water exchange between the bay and the open sea. The bay is either a rectangle or a polygonal idealization of Todos Santos Bay in northwestern Mexico; the coastal current is uniform and parallel to the coast. Complex variable theory was used to compute the path function of the point vortex and the stream function of the flow. In the rectangular bay the path function exhibits five different topologies depending on the aspect ratio of the bay and the relative intensity of the vortex. Wide bays efficiently trap vortices, even strong ones: most initial conditions inside the bay result in periodic trajectories entirely contained in the bay. Narrow bays are ineffective vortex traps: most initial conditions inside the bay lead to infinite trajectories with the vortex moving upstream along the coast. Todos Santos Bay, with its irregular coastline, exhibits a variety of path-function topologies, but it is in general an ineffective vortex trap. The exchange of water between the bay and the open sea was studied using classical dynamical systems theory. With parameter values realistic for Todos Santos Bay, a vortex whose orbital radius is εc, where c is the square root of the bay area, produces a water exchange of about 1.4εc² during each period of the vortex motion.