Rigid Sets and Coherent Sets in Realistic Ocean Flows

This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new “diffeomorphism-based” criterion to extract “rigid sets”, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.

Effects of strongly eddying oceans on multidecadal climate variability in the Community Earth System Model

Climate variability on multidecadal timescales appears to be organized in pronounced patterns with clear expressions in sea surface temperature, such as the Atlantic Multidecadal Variability and the Pacific Decadal Oscillation. These patterns are now well studied both in observations and global climate models and are important in the attribution of climate change. Results from CMIP5 models have indicated large biases in these patterns with consequences for ocean heat storage variability and the global mean surface temperature. In this paper, we use two multi-century Community Earth System Model simulations at coarse (1∘) and fine (0.1∘) ocean model horizontal grid spacing to study the effects of the representation of mesoscale ocean flows on major patterns of multidecadal variability. We find that resolving mesoscale ocean flows both improves the characteristics of the modes of variability with respect to observations and increases the amplitude of the heat content variability in the individual ocean basins. In the strongly eddying model, multidecadal variability increases compared to sub-decadal variability. This shift of spectral power is seen in sea surface temperature indices, basin-scale surface heat fluxes, and the global mean surface temperature. This implies that the current CMIP6 model generation, which predominantly does not resolve the ocean mesoscale, may systematically underestimate multidecadal variability.

Observing and quantifying kinematic properties and lagrangian coherent structures of ocean flows using drifter experiments

This thesis analyzes data from two types of unique drifter experiments in order to characterize two aspects of ocean flows that are often difficult to study. First, vertical velocities and their associated transport processes are often challenging to observe in the real ocean since vertical velocities are typically orders of magnitude smaller than horizontal velocities in mesoscale and submesoscale flows. Second, Lagrangian coherent structures (LCS) are features which categorize ocean flows into regimes of distinct behavior. These structures are also difficult to quantify in the real ocean, since sets of gridded trajectories from real ocean data (rather than model fields) are rarely available. The first experiment uses drifters drogued at multiple depths in the Alboran Sea to observe and characterize the ocean’s vertical structure, particularly near a strong front where vertical velocities are expected to be much stronger than other regions of the Ocean. The second experiment uses a roughly gridded pattern of surface drifters in the Gulf of Mexico to study LCSs as quantified by methods from dynamical systems such as finitetime Lyapunov exponents (FTLEs), trajectory arc-length, correlation dimension, dilation, Lagrangian-averaged vorticity deviation (LAVD), and spectral clustering. This thesis includes the first attempt to apply these dynamical systems techniques to real drifters for LCS detection. Overall, these experiments and the methods used in this paper are shown to be promising new techniques for quantifying both the vertical structure of ocean flows and Lagrangian Coherent Structures of flows using real drifter data. Future work may involve modified versions of the experiments, with denser sets of ocean drifters in the horizontal and/or vertical directions.

Modeling Multiscale and Multiphysics Coastal Ocean Processes: A Discussion on Necessity, Status, and Advances

Coastal ocean flows are interconnected by a complex suite of processes. Examples are inlet jets, river mouth effluents, ocean currents, surface gravity waves, internal waves, wave overtopping, and wave slamming on coastal structures. It has become necessary to simulate such oceanographic phenomena directly and simultaneously in many disciplines, including coastal engineering, environmental science, and marine science. Oceanographic processes exhibit distinct behaviors at specific temporal and spatial scales, and they are multiscale, multiphysics in nature; these processes are described by different sets of governing equations and are often modeled individually. In order to draw the attention of the scientific community and promote their simulations, a Special Issue of the Journal of Marine Science and Engineering entitled “Multiscale, Multiphysics Modelling of Coastal Ocean Processes: Paradigms and Approaches” was published. The papers collected in this issue cover physical phenomena, such as wind-driven flows, coastal flooding, turbidity currents, and modeling techniques such as model comparison, model coupling, parallel computation, and domain decomposition. This article outlines the needs for modeling of coastal ocean flows involving multiple physical processes at different scales, and it discusses the implications of the collected papers. Additionally, it reviews the current status and offers a roadmap with numerical methods, data collection, and artificial intelligence as future endeavors.

Broadband Submesoscale Vorticity Generated by Flow around an Island

An array of moorings deployed off the coast of Palau is used to characterize submesoscale vorticity generated by broadband upper-ocean flows around the island. Palau is a steep-sided archipelago lying in the path of strong zonal geostrophic currents, but tides and inertial oscillations are energetic as well. Vorticity is correspondingly broadband, with both mean and variance O(f) in a surface and subsurface layer (where f is the local Coriolis frequency). However, while subinertial vorticity is linearly related to the incident subinertial current, the relationship between superinertial velocity and superinertial vorticity is weak. Instead, there is a strong nonlinear relationship between subinertial velocity and superinertial vorticity. A key observation of this study is that during periods of strong westward flow, vorticity in the tidal bands increases by an order of magnitude. Empirical orthogonal functions (EOFs) of velocity show this nonstationary, superinertial vorticity variance is due to eddy motion at the scale of the array. Comparison of kinetic energy and vorticity time series suggest that lateral shear against the island varies with the subinertial flow, while tidal currents lead to flow reversals inshore of the recirculating wake and possibly eddy shedding. This is a departure from the idealized analog typically drawn on in island wake studies: a cylinder in a steady flow. In that case, eddy formation occurs at a frequency dependent on the scale of the obstacle and strength of the flow alone. The observed tidal formation frequency likely modulates the strength of submesoscale wake eddies and thus their dynamic relationship to the mesoscale wake downstream of Palau.

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows.

Palaeolithic voyage for invisible islands beyond the horizon

How Palaeolithic maritime transportation originated and developed is one of the key questions to understand the world-wide dispersal of modern humans that began 70,000–50,000 years ago. However, although the earliest evidence of maritime migration to Sahul (Australia and New Guinea) has been intensively studied, succeeding development of Paleolithic maritime activity is poorly understood. Here, we show evidence of deliberate crossing of challenging ocean that occurred 35,000–30,000 years ago in another region of the western Pacific, the Ryukyu Islands of southwestern Japan. Our analysis of satellite-tracked buoys drifting in the actual ocean demonstrated that accidental drift does not explain maritime migration to this 1200 km-long chain of islands, where the local ocean flows have kept the same since the late Pleistocene. Migration to the Ryukyus is difficult because it requires navigation across one of the world’s strongest current, the Kuroshio, toward an island that lay invisible beyond the horizon. This suggests that the Palaeolithic island colonization occurred in a wide area of the western Pacific was a result of human’s active and continued exploration, backed up by technological advancement.

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

Partitioning ocean flows into regions dynamically distinct from their surroundings based on material transport can assist search-and-rescue planning by reducing the search domain. The spectral clustering method partitions the domain by identifying fluid particle trajectories that are similar. The partitioning validity depends on the accuracy of the ocean forecasting, which is subject to several sources of uncertainty: model initialization, limited knowledge of the physical processes, boundary conditions, and forcing terms. Instead of a single model output, multiple realizations are produced spanning a range of potential outcomes, and trajectory clustering is used to identify robust features and quantify the uncertainty of the ensemble-averaged results. First, ensemble statistics are used to investigate the cluster sensitivity to the spectral clustering method free-parameters and the forecast parameters for the analytic Bickley jet, a geostrophic flow model. Then, we analyze an operational coastal ocean ensemble forecast and compare the clustering results to drifter trajectories south of Martha’s Vineyard. This approach identifies regions of low uncertainty where drifters released within a cluster predominantly remain there throughout the window of analysis. Drifters released in regions of high uncertainty tend to either enter neighboring clusters or deviate from all predicted outcomes.

Effects of strongly eddying oceans on multidecadal climate variability in the Community Earth System Model

Climate variability on multidecadal time scales appears to be organized in pronounced patterns with clear expressions in sea surface temperature, such as the Atlantic Multidecadal Variability and the Pacific Decadal Oscillation. These patterns are now well studied both in observations and global climate models and are important in the attribution of climate change. Results from CMIP5 models have indicated large biases in these patterns with consequences for ocean heat storage variability and eventually the global mean surface temperature. In this paper, we use two multi-century Community Earth System Model simulations at coarse (1°) and fine (0.1°) ocean model horizontal grid spacing to study the effects of the representation of mesoscale ocean flows on major patterns of multidecadal variability. We find that resolving mesoscale ocean flows both improves the characteristics of the modes of variability with respect to observations and increases the amplitude of the heat content variability in the individual ocean basins. The effect on the global mean surface temperature is relatively minor.

Numerical Prediction of the Behavior of CO2 Bubbles Leaked from Seafloor and Their Convection and Diffusion near Southeastern Coast of Korea

Among various carbon capture and storage technologies to mitigate global warming and ocean acidification due to greenhouse gases, ocean geological storage is considered the most feasible for Korea due to insufficient inland space to store CO2. However, the risk of CO2 leakage and the behavior and environmental effects of the leaked CO2 need to be assessed for its successful implementation. Therefore, the behavior of CO2 bubbles/droplets dissolving into the surrounding seawater and the diffusion of dissolved CO2 by ocean flows should be accurately predicted. However, finding corresponding research has been difficult in Korea. Herein, the behavior and convection-diffusion of CO2 that was assumed to have leaked from the seafloor near the southeastern coast of Korea were numerically predicted using a multi-scale ocean model for the first time. In the simulation region, one of the pilot projects of CO2 ocean geological storage had started but has been temporarily halted. In the ocean model, hydrostatic approximation and the Eulerian–Lagrangian two-phase model were applied for meso- and small-scale regions, respectively. Parameters for the simulations were the leakage rate and the initial diameter of CO2. Results revealed that all leaked and rising CO2 bubbles were dissolved into the seawater before reaching the free surface; further, the change in the partial pressure of CO2 did not exceed 500 ppm during 30 days of leakage for all cases.