Vijay G. Panchang

SOLUTION OF THE MILD-SLOPE WAVE PROBLEM BY ITERATION

Iterative solution procedures for solving the complete mild-slope wave (combined refractiondiffraction) equation are developed. Existing models for investigating wave refraction-diffraction in coastal areas have one of two main problems: (i) Some of the physics is lost as they resort to approximate solutions (e.g. parabolic approximations). Thus they are inappropriate in many situations. (ii) If all of the physics is to be incorporated, the problem defies computer solution except for extremely small domains (approximately 10 wavelengths), chiefly because the matrix equation associated with numerical discretization of the complete problem does not normally lend itself to solution by iteration. This paper describes the construction of iterative models that overcome both problems. First, a modified equation with an identical solution but which lends itself to iterative procedures is formulated, and the conjugate gradient method is used. A second, more rapidly converging algorithm is obtained by preconditioning. It is shown that the algorithms can be conveniently implemented on regions much larger than those handled by conventional models, without compromising the physics of the equation. Further, they can be efficiently run in either the linear or nonlinear mode. Comparisons of model results with laboratory data and other numerical and analytical solutions are found to be excellent for several cases. The procedures thus enable the engineer to expand the scope of the mild-slope equation. As an example, an experiment is performed to demonstrate the sensitivity of the wavefield to the location of a breakwater in a region with complex bathymetry.

Modeling hydrodynamics and aquaculture waste transport in coastal maine

Net-pen aquaculture results in the introduction of excess fish food and fecal matter in coastal waters. These wastes may modify the benthic environment. Mathematical models are developed in this study to simulate tidal and wind-driven currents, waves, and the resulting dispersion of fish food and fecal matter in coastal Maine, a region where limited modelling studies have been performed. Cobscook Bay and Toothacher Bay in Maine are studied in detail through the use of mathematical models and field data. We find that a systematic, site-specific, step-by-step modeling strategy involving the use of numerical models to simulate the overall hydrodynamic environment in combination with a waste-particle transport model can be an extremely powerful method of determining a priori whether aquaculture operations will cause high rates of net-pen waste accumulation at a particular site.

Estimation of extreme wave heights using GEOSAT measurements

Satellite technology has yielded a large database of global ocean wave heights which may be used for engineering applications. However, the sampling protocol used by the satellite leads to some difficulties in making use of these data for practical applications. These difficulties and techniques to estimate extreme wave heights using satellite measurements are discussed. Significant wave heights for a 50-year return period are estimated using GEOSAT measurements for several regions around North America. Techniques described here may be used for estimation of wave heights associated with any specified return interval in regions where buoy data are not readily available.

Comparison of Two- and Three-Dimensional Model Simulation of the Effect of a Tidal Barrier on the Gulf of Maine Tides

Abstract Two-dimensional and three-dimensional tide models were used to simulate the M2 tide in the Gulf of Maine. Model estimates of changes to the tide caused by a tidal barrier in the upper Bay of Fundy were made and compared. Tidal amplitudes in the presence of a barrier increased 30–50 cm for both models, corroborating the results of previous studies by Greenberg and by Duff. The three-dimensional model uniformly produced postbarrier elevations of 3.5 cm less than the two-dimensional model in the Gulf of Maine. A comparison of model amplitudes and velocities with data for the existing M2 tide is provided for both models. Total frictional dissipation is also calculated for each model and compared. Finally, the postbarrier amplitudes as predicted by each model are compared. Root-mean-square errors of M2 tidal amplitude and phase at 45 locations in the Gulf of Maine were 7.9 cm and 6° for the two-dimensional model and 5.7 cm and 7° for the three-dimensional model. Both models predicted essentially ident...

Simulation of wave breaking effects in two-dimensional elliptic harbor wave models

A technique is developed for including the effects of dissipation due to wave breaking in two-dimensional elliptic models based on the mild-slope wave equation. This involves exploration of convergence properties pertaining to iteration due to presence of the nonlinear wave breaking parameter in the governing equations as well as new boundary conditions that include wave-breaking effects. Five wave-breaking formulations are examined in conjunction with the resulting model, which is applied to tests involving a sloping beach, a bar-trough bottom configuration, shore-connected and shore-parallel breakwaters on a sloping beach, and two real-world cases. Model results show that three of the formulations, when used within the context of the modeling scheme presented here, provide excellent results compared to data.

Wave Prediction Models For Coastal Engineering Application

Publisher Summary This chapter provides a review of some state-of-the-art nearshore wave models that can be used for practical prediction in engineering studies. The chapter describes modeling philosophy, strengths, and limitations of models based on the steady state energy equation and the steady and unsteady state mass and momentum equations. Coastal engineering projects such as those dealing with wave agitation in harbors, beach protection, maintenance of navigational channels, studies of shoreline evolution, etc. typically require a detailed knowledge of the wave field in the project area. Mathematical models of wave propagation attempt to simulate the various mechanisms that induce the transformation of waves. This chapter reviews some wave models that strive to provide an acceptable mix of simplification, sophistication, and convenience of application from the standpoint of practical engineering. The purpose of this chapter is to briefly describe the overall philosophy, methodology, advantages, difficulties, and some applications of each modeling strategy. The chapter describes two kinds of wave models commonly used for coastal engineering applications: models based on the conservation of energy and models based on the conservation of mass and momentum. Both types of models can, by some rigorous or approximate method, incorporate many of the mechanisms mentioned in this chapter. Concluding remarks address some general difficulties that a practicing engineer is likely to encounter while using numerical wave models.

Improved coastal boundary condition for surface water waves

Surface water waves in coastal waters are commonly modeled using the mild slope equation. One of the parameters in the coastal boundary condition for this equation is the direction at which waves approach a coast. Three published methods of estimating this direction are examined, and it is demonstrated that the wave fields obtained using these estimates deviate significantly from the corresponding analytic solution. A new method of estimating the direction of approaching waves is presented and it is shown that this method correctly reproduces the analytic solution. The ability of these methods to simulate waves in a rectangular harbor is examined.

On the determination of three-parameter Weibull MLE's

The determination of maximum likelihood estimators for the three–parameter Weibull model is usually considered a nontrivial problem, because of the nonlinear likelihood equations. Despite the availability of a large number of algorithms that tackle this problem, there is considerable dissatisfaction among practitioners, who report an inability to conveniently determine the desired MLEs (e.g. Adatia and Chan, 1985; Sinha and Sloan, 1988). We therefore review several existing algorithms for obtaining these estimators and investigate the causes of failure and some computational difficulties associated with these procedures. We find that a simple procedure outlined by Lawless (1982) is the only one that is guaranteed to yield parameter estimates that maximize the likelihood function for any sample. We describe this procedure in detail with modifications to improve its efficiency. The method is based on first principles and requires less computational effort than most other schemes. Several examples from the ...

Outgoing Boundary Conditions for Finite-Difference Elliptic Water-Wave Models

Two-dimensional elliptic water-wave models based on the mild-slope equation find wide application in engineering and other studies. Model results are often adversely influenced by approximate treatment of the open boundary condition. A method to incorporate the exact radiation condition at infinity in finite-difference models is therefore developed. Since directly matching the solutions within the computational domain to those outside is too stringent a requirement, the new method is based on minimizing the overall discrepancy between the solutions along the open boundary. This relaxation permits the development of a suitable solution method, which is tested against analytical solutions for two situations. Satisfactory results are obtained with no artificial reflection of wave energy from the open boundary, even when it is placed very close to the scatterer.

HINDCAST ESTIMATES OF EXTREME WAVE CONDITIONS IN THE GULF OF MAINE

The Gulf of Maine is a region lacking in wave data that can be used for engineering and research purposes. Extreme wave statistics for this area are therefore computed in this paper by numerical hindcasting. A representative sample of twenty-two strong extratropical northeast storms from the period 1942–1976 was selected, and wave heights were computed with a hybrid parametric wave model. The highest wave height at each point in the Gulf of Maine model grid for each storm was used to calculate 50 and 100-year return period wave heights. It is concluded that as a first-order estimate, any major engineering effort in the Gulf of Maine will have to reckon with significant wave heights as high as 13 metres for a 1% chance of occurrence. These results agree extremely well with other estimates based on shipboard observations.