Malcolm L. Spaulding

A Vertically Averaged Circulation Model Using Boundary-Fitted Coordinates

Abstract A two-dimensional vertically averaged circulation model using boundary-fitted coordinates has been developed for predicting sea level and currants in estuarine and shelf waters. The basic idea of the approach is to use a set of coupled quasi-linear elliptic transformation equations to map the physical domain to a corresponding transformed plane such that all boundaries are coincident with coordinate lines and the transformed mesh is rectangular. The hydrodynamic equations are then solved by a multi-operation finite difference technique in the rectangular mesh transformed grid. Comparisons of the circulation model predictions for tidally forced flows in a wedge section with both flat and quadratic bottom topography, and in a flat channel with exponential variation in width, were in excellent agreement with corresponding analytic solutions. Simulation of steady-state wind-induced setup in a closed basin formed using elliptic cylindrical coordinates also was in excellent agreement with the analytic ...

Numerical simulations of the tidal- and wind-driven circulation in Narragansett Bay

Abstract A three-dimensional numerical hydrodynamic model was used to study the tides and certain aspects of the wind-forced flow in Narragansett Bay. The governing equations are solved using the Galerkin-spectral method in the vertical and explicit finite differences in the horizontal and time. A split-mode formulation is used to minimize computational time. Simulations of the M 2 tide gave average errors of less than 2% in amplitude and 2° in phase when compared with observations at 12 tidal-height stations within the Bay. An investigation of the Bays response to steady, spatially uniform wind forcing indicated that the non-linear interaction between the tidal and wind induced motions strongly affected the predicted steady state current pattern. Calculation of the steady-state wind-induced transports showed that a significant exchange exists between the West Passage, East Passage and Sakonnet River. The dependence of the exchange on the wind magnitude and direction and on the choice of vertical eddy viscosity was investigated. A comparison between modeled results and measurements of current at three locations in the Bay indicated that the model is capable of reproducing some of the features of the wind-induced flow.

Flushing times for the Providence River based on tracer experiments

The flushing time of the Providence River was estimated using three different data sets and three different methodologies. Dye concentrations were measured following instantaneous dye releases during wet weather experiments performed by the Narragansett Bay Project between October 1988 and June 1989. These data were analyzed to obtain flushing time estimates. Salinity measurements collected during the Sinbadd (Sampling In Narragansett Bay All During the Day) cruises, Spray (Sampling the Providence River All Year) cruises and wet weather experiments were used with the fraction of fresh water method and box model to calculate flushing time. The Sinbadd cruises performed 4 seasonal surveys at 22 stations in Narragansett Bay during 1986 to obtain a view of the whole Narragansett Bay with respect to the concentrations of nutrients and trace metals. The Spray cruises collected data in the Providence River at 10 stations to determine the relationship of nutrients and trace metals concentrations in the Seekonk and Providence rivers as a function of point source inputs. Based on the flushing time estimates, an exponential relationship between freshwater inflow and flushing time was developed (correlation coefficient of 0.826). The flushing time ranged from 0.8 d at high (90 m3 m−1) freshwater inflows to 4.4 d at low (20 m3 s−1) freshwater inflows. The average flushing time of the Providence River was estimated as 2.5 d for the mean freshwater inflow of 42.3 m3 s−1.

Numerical simulation of wind-driven flow through the Bering Strait

Abstract A two-dimensional, vertically averaged hydrodynamic model has bean applied to predict the wind-forced circulation in the Bering and Chukchi seas. A simulation of the steady state flows ind...

A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems

In the present study, an existing two-dimensional boundary-fitted model [J. Hydraul. Eng.-ASCE 122 (9) (1996) 512] is used to study the effect of grid non-orthogonality on the solution of shallow water equations using boundary-fitted grids. The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and aspect ratio. The truncation errors of the finite difference approximations used in the solution of the governing equations are shown to be dependent on the grid angle and the aspect ratio. The coefficient of the truncation error was shown to increase, with the decrease in the grid angle. The RMS errors in model predicted surface elevations and velocities for the case of seiching in a rectangular basin are found to increase gradually, as the grid resolution decreases from 174 to 80 grid-points per wavelength or as the grid angle decreases from 90° to 50° and increases rather sharply for a grid angle of 30° at grid resolutions less than 80 gridpoints per wavelength. The model predicted surface elevations for the case of tidal forcing in a rectangular basin are found to be insensitive to the grid angle at grid resolutions higher than 600 gridpoints per wavelength. The RMS error in the model predicted velocities is found to increase gradually as the grid angle decreases from 90° to 30° or as the grid resolution decreases from 1400 gridpoints per wavelength to 400 gridpoints per wavelength and increases sharply as the grid resolution decreases from 400 to 150 gridpoints per wavelength. Two-dimensional depth averaged hydrodynamic modeling of tidal circulation in Narragansett Bay, using three different boundary-fitted grids showed that the model predicted surface elevations are insensitive to the grid angle at grid resolutions as low as 200 gridpoints per wavelength. However, the model predicted velocities were found to increase as the grid resolution decreases from 600 to 200 gridpoints per wavelength. We conclude from this study that grid angle and grid resolution affects the accuracy of the model predicted currents and the numerical dispersion increases with the decrease in grid angle or grid resolution and these are in agreement with that reached by Sankaranarayanan and Spaulding [Dispersion and Stability Analyses of Shallow Water Equations in Boundary-fitted Coordinates, Department of Ocean Engineering, University of Rhode Island, 2001, p. 33] through a Fourier analysis of the discretized equations in boundary-fitted coordinates.

WQMAP: An integrated three-dimensional hydrodynamic and water quality model system for estuarine and coastal applications

WQMAP is an integrated system for modeling the circulation and water quality of estuarine and coastal waters. The system includes a suite of integrated environmental models including a boundary conforming grid generation model, a three hydrodynamic model, and a suite of pollutant transport and fate models (single and multiple constituent and WASP5 eutrophication kinetics). All operate on a boundary conforming grid system and are supported by an embedded geographic information system and environmental data management tools. WQMAP is configured for operation on a Pentium personal computer and features a Windows based user interface. The interface employs point and click and pull down menu operation. Color graphics and animations are used to display model predictions. The system is structured to facilitate application to any geographic area. As an illustration of its capability WQMAP was applied to predict the three-dimensional circulation and thermal dynamics for Mt. Hope Bay, RI, located on the eastern side of Narragansett Bay. The area receives fresh water input from the Taunton River and a thermal discharge from a 1600 MW coal and oil fired power plant located at Brayton Point, along the north shore of the bay. Model predictions were performed for the month of August 1997 and compared to time series at three stations in the vicinity of the power plant discharge. Measurements of currents, temperature, and salinity were made near the surface and the bottom at each of the three stations. Model predictions (currents, temperature, and salinity) were in good agreement with available data using relative error, root mean square error, linear regression analysis, and error coefficient of variation as quantitative evaluation criteria. Model predictions showed that circulation in the bay is generally dominated by the tide, except in the lower reaches of the Taunton River where density induced, two layer flow becomes important. The thermal structure of the bay is dominated by the power plant discharge in the northwestern section of the bay and otherwise by natural atmospheric heating and cooling. Thermal stratification near the power plant is principally dependent on the discharge plume. It is strongest and most wide spread on ebb tide along the central axis of the plume and weaker during flood tide when the plume is confined to the near shore area.

Application of three-dimensional oil spill model (WOSM/OILMAP) to Hindcast the Braer spill

Abstract A state-of-the-art, three-dimensional oil spill model (WOSM/OILMAP) was applied to hindcast the transport and fate of the Braer oil spill, which occurred off the southern coast of Shetland Island in January 1993. The model included advection, spreading, evaporation, emulsification, entrainment, oil-shoreline interaction, and subsurface transport. Tidal and winter residual flow data necessary as input to the model were derived from prior hydrodynamic modeling studies of the area. Wind data were obtained from observations at the Sumburgh Airport for the time period of interest. Model predictions of the surface and subsurface oil paths, shoreline oiling, and subsurface oil distributions are generally in reasonable agreement with available observations. The simulations clearly show the importance of entrainment, subsurface transport, and resurfacing of oil and accurate representations of the current field in the vicinity of the grounding site and to the south of Shetland Island in accurately hindcasting the spill.

A Model of the Tidally Induced Residual Circulation in the Gulf of Maine and Georges Bank

Abstract A three-dimensional nonlinear numerical hydrodynamic model using Legendre polynomials to represent the vertical structure of the horizontal currents has been used to study the tidally induced residual flows in the Gulf of Maine–Georges Bank study region using a 6.25 km square grid. Tidal elevations in terms of the M2 phase and amplitude along the open boundaries are specified using Schwiderskis deep ocean tidal model. The model predicts strong clockwise circulation gyres around Georges Bank and Nantucket Shoals with a weak gyre around Browns Bank. Strong inflow to the Gulf of Maine is predicted near the Southwestern tip of Nova Scotia. These results are in good agreement with recent model predictions of Greenberg.

Development of a unified oil droplet size distribution model with application to surface breaking waves and subsea blowout releases considering dispersant effects

An oil droplet size model was developed for a variety of turbulent conditions based on non-dimensional analysis of disruptive and restorative forces, which is applicable to oil droplet formation under both surface breaking-wave and subsurface-blowout conditions, with or without dispersant application. This new model was calibrated and successfully validated with droplet size data obtained from controlled laboratory studies of dispersant-treated and non-treated oil in subsea dispersant tank tests and field surveys, including the Deep Spill experimental release and the Deepwater Horizon blowout oil spill. This model is an advancement over prior models, as it explicitly addresses the effects of the dispersed phase viscosity, resulting from dispersant application and constrains the maximum stable droplet size based on Rayleigh-Taylor instability that is invoked for a release from a large aperture.

State of the art review and future directions in oil spill modeling

A review of the state of the art in oil spill modeling, focused on the period from 2000 to present is provided. The review begins with an overview of the current structure of spill models and some lessons learned from model development and application and then provides guiding principles that govern the development of the current generation of spill models. A review of the basic structure of spill models, and new developments in specific transport and fate processes; including surface and subsurface transport, spreading, evaporation, dissolution, entrainment and oil droplet size distributions, emulsification, degradation, and sediment oil interaction are presented. The paper concludes with thoughts on future directions in the field with a primary focus on advancements in handling interactions between Lagrangian elements.