Elsevier

Marine Pollution Bulletin

Volume 140, March 2019, Pages 374-387
Marine Pollution Bulletin

Tidal eddies at a narrow channel inlet in operational oil spill models

https://doi.org/10.1016/j.marpolbul.2019.01.051Get rights and content

Highlights

  • The modeled eddy characteristics at the Galveston Bay inlet are well presented at the grid size of ∼140 m.

  • The model validated against observed channel velocities does not guarantee the correct prediction of tidal eddies.

  • The subgrid ELT models are required to represent Lagrangian transport effect of eddies in a coarse-grid model.

Abstract

In operational oil spill modeling, hydrodynamic models often employ a coarse-resolution grid for computational efficiency. However, this practical grid resolution poorly resolves small-scale flow features, such as starting jet vortices (tidal eddies) that are common at the inlet of bar-built estuaries with narrow inlet channels, particularly where channel dredging and jetties have been employed to aid ship traffic. These eddies influence Lagrangian transport paths and hence the fate of an oil spill potentially entering or leaving an estuary. This research quantifies the effect of tidal eddies on the mixing process and effects at model scales relevant to the operational prediction of oil spills, using the Galveston Bay entrance channel as a study site. Model grid sensitivity was analyzed, yielding an adequate eddy solution at the horizontal grid size of ∼140 m. It is demonstrated that the SUNTANS model at a practical operational grid resolution (∼400 m) captures neither the eddies nor their effects on particle movement, despite showing a satisfactory prediction of net transport through the inlet. The need for subgrid eddy modeling is discussed, and an empirical approach is proposed that can improve oil spill predictions at operational grid resolution scales when results from a high-resolution model are available.

Introduction

A narrow channel connecting a bar-built bay to the coastal ocean can cause the generation of a complex set of tidal eddies over a tidal cycle that affect the net transport through the channel (Whilden et al., 2014). These tidal eddies have spatial scales similar to the channel width and can be difficult to correctly capture in a computational model (Zhao et al., 2006). Herein, we examine the effects of grid resolution on the representation of tidal eddies and modeled Lagrangian transport for the Galveston Bay ship channel in Texas, USA. We demonstrate that a coarse-grid model that validates against velocity field data does not produce the correct scales of eddies or the correct particle transport affected by eddies. We discuss the need for subgrid-scale eddy models to represent the effects of unresolved eddies on surface (oil spill) Lagrangian transport, and we propose an empirical approach to subgrid modeling that can be used in coarse-grid models where high-resolution hydrodynamic model results are available for calibration.

Tidal eddies, also referred to as starting-jet vortices, are created as a result of flow separation near the tip of headlands or jetties when water is pushed through the tidal inlet. The tidal currents through the narrow channel generate pairs of vortices across the channel as lateral advection transfers the energy from the starting jet to the vortices. Eddies have a variety of possible behaviors, including being pulled back into the channel on the flood tide, detaching and moving down coast, or detaching and blocking the channel. As the eddies move offshore they interact with the shelf physics, such as an along-coast flow. Each behavior has different consequences for the net exchange of material between the bay and offshore waters over a tidal cycle. The advection strength through the channel affects eddying behaviors, with eddy length scales of 1–10 km (Signell and Geyer, 1991). The generation and propagation of tidal eddies have been observed and studied in extensive research using experimental methods in laboratories (Bryant et al., 2012, del Roure et al., 2009, Hutschenreuter et al., 2018), field particle experiments (Whilden et al., 2014) and numerical approaches (Signell and Geyer, 1991). Hydrodynamic models have been used to simulate the development of such eddies in the complex geometries of estuaries (e.g. Zhao et al., 2006, Yang and Wang, 2013).

The tidal eddies associated with the complex hydrodynamics at an inlet will influence the local transport of passive tracers, e.g., sediment, nutrients, larvae, and oil spills. Any Lagrangian particles trapped in an eddy will generally be transported with the eddy until the eddy is dissipated (Socolofsky and Jirka, 2004). Thus, if a model does not correctly create and advect the tidal eddies the modeled fate of transported Lagrangian particles will be in error. As a further complication, particle diffusion is also enhanced by the straining behavior of an eddy (Signell and Geyer, 1991), which implies that particle diffusion models need to include eddy effects. Although the commonly-observed eddies are those generated on an ebb tide, similar eddies can be generated within a bay on a flood tide. The creation, persistence, and transport of eddies on either end of a channel entrance will affect the residence time of spilled oil in a channel, determining whether a spill rapidly moves outward, inward, or merely oscillates with the tide.

Unfortunately, resolving tidal vortices requires a three-dimensional high-resolution model with sufficient vertical layers and a small time step to resolve the local complex topography, e.g. man-dredged shipping channel that yields a critical depth gradient. For example, a horizontal resolution of ∼100 m and 20 vertical layers were employed to resolve the Houston Ship Channel, which requires a 2 s time step (Rayson et al., 2015). Although such high-resolution models can be implemented on research supercomputers, they simply are not practical for operational models requiring routine access by emergency management personnel in the event of an oil spill. At practical coarse-grid resolution required for response modeling (e.g., 400 m), such models typically cannot accurately capture tidal eddies, which results in error and uncertainty in the predicted flux through a narrow channel (Andrejev et al., 2011). We provide further evidence of the importance of resolving eddies in Sections 3.2 and 3.3, which show that the poorly resolved eddies produced by the coarse-grid model underestimate the net Lagrangian flux from the bay to the ocean coast.

Where resolving physics in a hydrodynamic model is impractical, we seek some form of subgrid-scale theory or empiricism to account for the missing effects. Unfortunately, the present state of theory for vortices (van Heijst and Clercx, 2009) does not provide an understanding of eddy evolution that could be used to develop a subgrid vortex model from first principles. Indeed, the literature (prior to the present work) lacks sufficient quantitative detail on eddy behaviors to propose even an empirically-based model of unresolved eddy effects. Developing a comprehensive theory for subgrid-scale modeling of tidal vortices is a major challenge — herein, we take a step forward by examining the scales and practical effects of 3D eddies on the 2D surface signature and transport that is critical to predicting oil spills on the water surface. We examine the fine grid resolution scales required for a typical ship channel to adequately capture the eddies and then we demonstrate the effects of failing to capture the eddies at coarse grid resolution. Further, we propose and test an example of an empirical subgrid model that improves the ability of a coarse-resolution model to capture some of the effects of tidal eddies on transport.

From a practical viewpoint, our research question is: what does it take to capture the particle transport by eddies out of a bay mouth for an operational-scale model? In the Methods section, we first provide a brief overview of the study site and an existing model of Galveston Bay (Section 2.1), which has been previously presented in detail by Rayson et al. (2015). A new grid sensitivity analysis technique for eddies is developed in Section 2.2, and quantitative methods for evaluating eddy effects on Lagrangian transport are provided in Section 2.3. The Results 3 section shows that a wide range of grid resolutions can provide reasonable agreement with limited field data (Section 3.1), and yet the eddy behavior is only represented accurately with fine grid resolution (Section 3.2). In Section 3.3, we show that simulated particle distributions are significantly different when the eddies are resolved versus when they are not. In the Discussion section ( Section 4), we analyze the significance of the failure of a coarse-resolution model to represent eddy effects. Further, we propose and test an approach for developing an empirical subgrid-scale model using high-resolution model results. This empirical model should be considered preliminary as we do not have field experiments to evaluate the model. We discuss this empirical approach with a goal of stimulating further experiments and theory development that provides a more robust basis for subgrid modeling of starting-jet vortices.

Section snippets

Study site and numerical model

The greater Houston area and Galveston Bay, Texas (USA) are home to major petrochemical and oil industries as well as container shipping and barge traffic along the Gulf Intracoastal Water Way (Fig. 1). Ship traffic creates risks for collisions and oil spills, with roughly 4000 reported oil spills in this area from 1998 to 2009 (Lester and Gonzalez, 2011). A notable recent example is the Texas City “Y” spill, which occurred on March 22, 2014 with over 168,000 gallons of oil released in

Tidal currents

The tidal currents of the reduced-domain models (R400, R200, R140 and R80) can be compared with the available NOAA velocity measurement at the Galveston Bay entrance as shown in Fig. 4; the corresponding values for the index of agreement (I) from Eq. (10) are 0.87, 0.87, 0.87 and 0.85, respectively. All the models, including the coarsest grid R400, show good agreement with the observations in terms of velocity amplitude and direction. Thus, based on standard approaches to model confirmation the

The need for an Eddy Lagrangian Transport model

The results indicate the coarse grid size of ∼400 m is sufficient to model the large-scale channel currents at the inlet to Galveston Bay, but model agreement with measured currents does not guarantee the correct prediction of smaller-scale physics (e.g., tidal eddies) and particle motions that affect the net Lagrangian transport. The predicted eddy on the R400 grid is more dissipative, which results in underestimating the effects of eddy trapping and mixing on Lagrangian particles. The most

Conclusion

This research investigated the influence of model grid resolution and a new tidal-eddy model on Lagrangian particle transport at the narrow entrance of a bar-built estuary. We demonstrated an approach to upscale the eddy effects into an operational-scale coarse-grid models for oil spill modeling. The new Eddy Lagrangian Transport (ELT) improves the agreement between Lagrangian transport computed on fine-grid and coarse-grid models.

The horizontal grid sensitivity for an unstructured hydrodynamic

Acknowledgments

The authors are indebted to Matt Rayson and Oliver Fringer for their work in setting up and validating the Galveston Bay SUNTANS model and prior work of Xianlong Hou in developing the HyosPy system. The work presented in this paper is based totally or in part upon work supported by the Research and Development program of the Texas General Land Office Oil Spill Prevention and Response Division under Grant No. 18-133-000-A674.

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