Bryan R. Pearce

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 the contribution of M2 tidal amplification to the Holocene rise of mean high water in the Gulf of Maine and the Bay of Fundy

Abstract Increase in the M2 (principal lunar semi-diurnal) component of the tidal range is an important contributor to the postglacial rise of the high-tide level in the Gulf of Maine and the Bay of Fundy in addition to relative sea-level rise. The increase occurred as the shape of this semi-enclosed embayment changed with sea-level rise and its natural period approached resonance with the M2 tide. A three-dimensional tide model (3DENS) predicts the following M2 tidal ranges averaged for the Gulf of Maine/Bay of Fundy as a percentage of the present range: 54–59% at 7000 yrs B.P., 73% at 5000 yrs B.P., 78% at 4000 yrs B.P., 85% at 3000 yrs B.P., 94% at 2000 yrs B.P., and 98% at 1000 yrs B.P. With a predicted sea-level rise of 0.15–0.90 m by the year 2100, M2 tidal range may increase 0.3–1.9%.

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...

A C++ implementation of an individual/landscape model

Abstract Dynamic models of biological systems are diverse, but have components in common. The description of a system may involve multiple databases which change and interact (individuals, populations, the landscape). A clock is required to advance the system description through time. In addition, the generation of random variates from different probability distributions, interpolation of values from tabular data, and the collection of statistics on system components may be required. All of these tasks can be effectively achieved through object oriented programming (OOP). The C++ programming language is the object oriented language utilized in the implementation described. Object oriented programming can be utilized to facilitate the organization and development of dynamic models of biological systems. A C++ hierarchy of classes describing objects in the system can start at the level of machine processing. A binary object can use individual bits of memory to represent binary data. Computer memory requirements can be minimized by using a linked list class to place objects in a list whose composition and size vary as the program executes. The C++ feature of runtime linking can connect a general base class with the data required for a specific application. These machine oriented classes can then be inherited into an individual animal class with binary data (male/female, diseased/nondiseased) and a population class which is a linked list of individuals. The binary arithmetic and memory pointers involved in these base classes can be completely transparent to the user of the individual and population classes which are described in biological rather than machine terms. OOP can facilitate the development of a description of the individual, population, landscape and their interactions. A landscape object can be described by a grid of rectangular cells linked on four sides to adjoining cells by memory pointers. These memory pointers to adjoining cells can be utilized to describe flows and movement of objects over the grid. This base class grid description can be inherited into a derived habitat class with additional data. The location or coordinates of objects located on the grid can be utilized to access the data for the cell in which it is located. Since grids describing landscapes can be large and heterogeneous, GIS can be utilized for grid initialization and for analysis of spatial data in the simulation output. A simulation clock is required to advance the description of the objects in the system and their interactions through time. A base clock class advances time in specified increments, or between events, or in specified increments until an event occurs. Events can be either scheduled long term or triggered by a change in the system and stored in an event queue by using the same base linked list class used to describe populations. The type of events which occur in a system are specified in a derived clock class which is accessed by the base clock class when the program executes through run-time linking. An example application is developed to describe winter kill of deer. Analysis of the simulation output in a GIS showed simple rules for individual animal behavior affected the pattern of landscape usage through time. Source code and documentation are available.

Mariculture siting : a GIS description of intertidal areas

Variations in habitat parameters greatly affect the physiological state and the growth of bivalves. To achieve success in shellfish mariculture, environmental parameters favorable to the cultured species must be determined and then characteristics of potential grow-out sites evaluated. An intertidal bay in Eastern Maine was described in a GIS (geographical information system), which incorporated infrared aerial photographs and maps of bottom types, topography and bathymetry. Data layers included elevations from both nautical charts and GPS measurements made in the bay. From the elevation data, a series of programs was developed to generate a triangulated irregular network and a grid of elevations. A numerical flow model used the elevation grid to simulate a time series of tidal current vectors and free surface elevations. Gridded data from the numerical model were imported into the GIS and displayed as false color images of elevations, maximum current velocities and tidally averaged current velocities. Current vectors were layered over aerial photos showing sediment transport in the water. The GIS can be queried to identify sites for mariculture. A sample query identified sites for shellfish grow-out.

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.

Currents in Penobscot Bay, Maine

A three-dimensional numerical model is applied to Penobscot Bay, a complicated estuarine system on Maines Atlantic coast. The estuary classification varies from stratified to well-mixed depending upon season and distance from the ocean. Bathymetry and topography are complex. Because an extensive data set exists for Penobscot Bay, testing and verification of the model is attempted here in spite of the bays physical complications. NOS/NOAA collected data for two consecutive summers (1969 and 1970) at over 100 stations using moored sets of current meters. Observation periods ranged from 3 days to 3 months. The model has been updated and run including the density gradients in the bay. Calculated currents are the same order as the residual currents measured in the bay or about 2 km/day.

The Effect of Surface Contamination on the Drift Velocity of Water Waves

This paper presents a study on the effect of surface contamination on the damping of progressive waves and on the second order Eulerian drift. The results are shown to subsume those obtained by Phillips in the limiting case of an inextensible film. The quasi-steady states are examined.

Storm Generated Waves in the Gulf of Maine

A project to generate wave height information for the Gulf of Maine is discussed. A model is described which calculates synoptic wind speeds for northeast storms. Numerical hindcast models are also discussed. A parametric type wave model was used with a set of the 22 strongest northeast storms from a 32 year record. The highest wave height at each grid point for each storm was used to generate the extreme statistics. The results are presented.