Development of a Method for numerical Calculation of Wave Refraction

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Development of a Method for numerical Calculation of Wave Refraction

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Harrison, Wyman / Wilson, W. Stanley

Steps in wave-ray construction are as follows: 1. Select wave periods and approach angles for each series of rays to be constructed. 2. Prepare a grid of depth values for the area of investigation. 3. Use a computer program to obtain a table of water depths and related wave velocities for each wave period selected in (1). 4. Make a grid of wave-velocity values for each wave period selected in (1), for the area of investigation, using a second computer program which takes as input the depth grid of (2) and the appropriate depth-velocity table of (3). 5. Derive, using a third computer program, matrices for use in the linear interpolation scheme of the computer program of (6). 6. Calculate, for each wave period specified in (1), the points along a wave ray using a computer program which takes for input: a. The appropriate velocity grid of (4). b. The matrices of (5). c. The origin points and approach angles of (1) for given wave rays. A linear-interpolation scheme (using the least-squares method) is used in determination of wave velocity at a given point along a ray. Ray curvature is then calculated at this point and an iteration procedure is solved to obtain the position of the next point. The ray terminates at the shore or grid border. An example of usage of the programs is presented in which 52 rays for waves of 4- and 6-second period, from six different deep-water origin points, are brought into the Atlantic shoreline of the City of Virginia Beach, Virginia. The procedure outlined is in the developmental stage, and suggestions for improvements are given that should offer a quick, accurate, and objective method of constructing wave rays.