After the destruction of the Deepwater Horizon drilling platform during the spring of 2010, the northern Gulf of Mexico was threatened by an oil spill from the Macondo well. Emergency responders were concerned about oil transport in the nearshore, where it threatened immediately the fishing waters and coastline from Louisiana to Florida. In this region, oil movement was influenced by a continental shelf with varying width, the protruding Mississippi River delta, the marshes and bayou of southern Louisiana, and the shallow sounds and barrier islands that protect the coastline. Transport forecasts require physics-based computational models and high-resolution meshes that represent the circulation in deep water, on the continental shelf, and within the complex nearshore environment.
This work applies the coupled SWAN+ADCIRC model on a high-resolution computational mesh to simulate the current velocity field on the continental shelf, nearshore and marsh areas during the time that oil was visible on the surface of the Gulf. The SWAN+ADCIRC simulations account for the influence of tides, riverine discharge, winds and wind-driven waves. A highly-efficient Lagrangian particle transport model is employed to simulate the surface trajectories of the oil. The transport model accounts for dispersion and advection by wind and currents. Transport is evaluated using two week-long sequences of satellite images. During both periods, the SWAN+ADCIRC current fields alone appeared to be more successful moving the oil than when direct wind forcing was included. In addition, hypothetical oil transport is considered during two hurricane scenarios. Had a hurricane significantly impacted the areas, depending on its track, oil would have moved farther into the marshes of southern Louisiana or farther along the shelf toward Texas than actually occurred during the spill.
JC Dietrich, CJ Trahan, MT Howard, JG Fleming, RJ Weaver, S Tanaka, L Yu, RA Luettich Jr, CN Dawson, JJ Westerink, G Wells, A Lu, K Vega, A Kubach, KM Dresback, RL Kolar, C Kaiser, RR Twilley (2012). “Surface Trajectories of Oil Transport along the Northern Coastline of the Gulf of Mexico.” Continental Shelf Research, 41(1), 17-47, DOI:10.1016/j.csr.2012.03.015.
On large geographic scales, ocean waves are represented in a spectral sense via the action balance equation, which propagates action density through both geographic and spectral space. In this paper, a new computational spectral wave model is developed by using discontinuous Galerkin (DG) methods in both geographic and spectral space. DG methods allow for the use of unstructured geographic meshes and higher-order approximations for action propagation in both geographic and spectral space, which we show leads to increased accuracy. This DG spectral wave propagation model is verified and validated through comparisons to manufactured and analytic solutions as well as to the Simulating WAves Nearshore (SWAN) model. Coupled wave/circulation models are needed for many applications including for the interaction between waves and currents during daily wind and tide driven flows. We loosely couple the newDGspectralwavemodel to the DG Shallow Water Equation Model (DG-SWEM), an existing DG circulation model. In addition to formulating the DG method for the coupled wave/circulation model, we derive an a priori error estimate. Preliminary numerical results of the DG coupled wave/circulation model are presented with comparisons to DG-SWEM coupled tightly to SWAN.
This paper investigates model response sensitivities to mesh resolution, topographical details, bottom friction formulations, the interaction of wind waves and circulation, and nonlinear advection on tidal and hurricane surge and wave processes at the basin, shelf, wetland, and coastal channel scales within the Gulf of Mexico. Tides in the Gulf of Mexico are modestly energetic processes, whereas hurricane surge and waves are highly energetic. The unstructured-mesh, coupled wind-wave and circulation modeling system, SWAN+ADCIRC, is implemented to generate modeled tidal harmonic constituents and hurricane waves and surge for a Hurricane Ike (2008) hindcast. In the open ocean, mesh resolution requirements are less stringent in achieving accurate tidal signals or matching hurricane surge and wave responses; however, coarser resolution or the absence of intertidal zones decreases accuracy along protected nearshore and inland coastal areas due to improper conveyance and/or lateral attenuation. Bottom friction formulations are shown to have little impact on tidal signal accuracy, but hurricane surge is much more sensitive, especially in shelf waters, where development of a strong shore-parallel current is essential to the development of Ike’s geostrophic setup. The spatial and temporal contributions of wave radiation stress gradients and nonlinear advection were charted for Ike. Nonlinear advection improves model performance by capturing an additional 10–20 cm of geostrophic setup and increasing resonant cross-shelf waves by 30–40 cm. Wave radiation stress gradients improve performance at coastal stations by adding an extra 20–40 cm to water levels.
Hurricane Ike (2008) made landfall near Galveston, Texas, as a moderate intensity storm. Its large wind field in conjunction with the Louisiana-Texas coastline’s broad shelf and large scale concave geometry generated waves and surge that impacted over 1000 km of coastline. Ike’s complex and varied wave and surge response physics included: the capture of surge by the protruding Mississippi River Delta; the strong influence of wave radiation stress gradients on the Delta adjacent to the shelf break; the development of strong wind driven shore-parallel currents and the associated geostrophic setup; the forced early rise of water in coastal bays and lakes facilitating inland surge penetration; the propagation of a free wave along the southern Texas shelf; shore-normal peak wind-driven surge; and resonant and reflected long waves across a wide continental shelf. Preexisting and rapidly deployed instrumentation provided the most comprehensive hurricane response data of any previous hurricane. More than 94 wave parameter time histories, 523 water level time histories, and 206 high water marks were collected throughout the Gulf in deep water, along the nearshore, and up to 65 km inland. Ike’s highly varied physics were simulated using SWAN+ADCIRC, a tightly coupled wave and circulation model, on SL18TX33, a new unstructured mesh of the Gulf of Mexico, Caribbean Sea, and western Atlantic Ocean with high resolution of the Gulf’s coastal floodplain from Alabama to the Texas-Mexico border. A comprehensive validation was made of the model’s ability to capture the varied physics in the system.
As phase-averaged spectral wave models continue to grow in sophistication, they are applied more frequently throughout the ocean, from the generation of waves in deep water to their dissipation in the nearshore. Mesh spacings are varied within the computational domain, either through the use of nested, structured meshes or a single, unstructured mesh. This approach is economical, but it can cause accuracy errors in regions where the input parameters are under-resolved. For instance, in regions with a coarse representation of bathymetry, refraction can focus excessive wave energy at a single mesh vertex, causing the computed solution to become non-physical. Limiters based on the Courant–Friedrichs–Lewy (CFL) criteria are proposed for the spectral propagation (refraction and frequency shifting) velocities in SWAN. These limiters are not required for model stability, but they improve accuracy by reducing local errors that would otherwise spread throughout the computational domain. As demonstrated on test cases in deep and shallow water, these limiters prevent the excessive directional turning and frequency shifting of wave energy and control the largest errors in under-resolved regions.
The Lower Mississippi River protrudes into the Gulf of Mexico, and manmade levees line only the west bank for 55 km of the Lower Plaquemines section. Historically, sustained easterly winds from hurricanes have directed surge across Breton Sound, into the Mississippi River and against its west bank levee, allowing for surge to build and then propagate efficiently upriver and thus increase water levels past New Orleans. This case study applies a new and extensively validated basin- to channel-scale, high-resolution, unstructured-mesh ADvanced CIRCulation model to simulate a suite of historical and hypothetical storms under low to high river discharges. The results show that during hurricanes, (1) total water levels in the lower river south of Pointe à La Hache are only weakly dependent on river flow, and easterly wind-driven storm surge is generated on top of existing ambient strongly flow-dependent river stages, so the surge that propagates upriver reduces with increasing river flow; (2) natural levees and adjacent wetlands on the east and west banks in the Lower Plaquemines capture storm surge in the river, although not as effectively as the manmade levees on the west bank; and (3) the lowering of manmade levees along this Lower Plaquemines river section to their natural state, to allow storm surge to partially pass across the Mississippi River, will decrease storm surge upriver by 1 to 2 m between Pointe à La Hache and New Orleans, independent of river flow.
Hurricanes in southeastern Louisiana develop significant surges within the lower Mississippi River. Storms with strong sustained easterly winds push water into shallow Breton Sound, overtop the river’s east bank south of Pointe à la Hache, Louisiana, penetrate into the river, and are confined by levees on the west bank. The main channel’s width and depth allow surge to propagate rapidly and efficiently up river. This work refines the high-resolution, unstructured mesh, wave current Simulating Waves Nearshore + Advanced Circulation (SWAN+ADCIRC) SL16 model to simulate river flow and hurricane-driven surge within the Mississippi River. A river velocity regime–based variation in bottom friction and a temporally variable riverine flow-driven radiation boundary condition are essential to accurately model these processes for high and/or time-varying flows. The coupled modeling system is validated for riverine flow stage relationships, flow distributions within the distributary systems, tides, and Hurricane Gustav (2008) riverine surges.
Coupling wave and circulation models is vital in order to define shelf, nearshore and inland hydrodynamics during a hurricane. The intricacies of the inland floodplain domain, level of required mesh resolution and physics make these complex computations very cycle-intensive. Nonetheless, fast wall-clock times are important, especially when forecasting an incoming hurricane.