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Title: The limit of applicability of linear wave refraction theory in a convergence zone
Authors: Texas A & M University
Whalin, Robert W. (Robert Warren)
Keywords: Linear wave refraction theory
Submarine topography
Water waves
Wave propagation
Wave refraction
Wave motion
Publisher: Hydraulics Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Research report (U.S. Army Engineer Waterways Experiment Station) ; H-71-3.
Description: Research Report
Abstract: Reported here is an experimental investigation to assess the limits of applicability of linear wave refraction theory in a convergence zone. One bottom topography with parallel circular contours symmetric about the center of the tank was utilized and three wave periods (1, 2, and 3 sec) were tested along with three wave heights for each period. All tests were conducted for nonbreaking waves. Data were obtained at 100 locations within the model basin for each condition tested. The data were analyzed on the basic assumption that the total energy was equally partitioned between potential energy and kinetic energy. The basic computation performed was to calculate the potential energy transmitted per unit width over one wave period. Measurements of the reflected energy from the underwater topographic variations indicated that such reflections were negligible. This was verified by computations utilizing the long wave theory as well as a theory not requiring the long wave assumption. The theoretical computations indicated that the reflection coefficient was between 0.002 and 0.01 for the 3-sec waves, while the measured data indicated that it was within the scatter of the data (less than 0.02). A computation of the viscous dissipation of energy at the bottom indicated an amplitude attenuation of approximately 3 percent during propagation over the entire length of the measurement area. The experimental data indicated an amplitude attenuation of less than 5 percent due to the combined effects of reflection and bottom friction. Linear refraction theory indicated that cusped caustics should occur on either side of the centerline of the tank for each wave period. It was vividly illustrated that a significant amount of energy was involved in diffraction along the wave crest; in some cases, over 80 percent of the total energy was diffracted into the shadow zone across the caustic. The necessity of developing a theory to include the stepwise computation of diffraction processes simultaneously with the computation of wave refraction is now evident, particularly in cases where strong convergence of wave orthogonals occurs. The nonlinear transfer of energy from lower to higher frequency components during propagation over the topography in the test basin was investigated by carrying out a harmonic analysis of the wave form over one wave period. As expected, the nonlinear effects increased as the period increased and increased as the wave height increased (for a given wave period). For the smallest period tested (1 sec), nonlinear effects were negligible; however, in the case of the largest wave period and largest wave height, only 20 percent of the energy remained in the fundamental frequency component at the end of the measurement area. Furthermore the higher frequency components ranged from being completely coupled to the fundamental frequency (for the 1- sec wave) to almost completely uncoupled (for the 3-sec waves) as ascertained from the phase relations over the propagation path. It was evident that in some circumstances the consideration of nonlinear effects becomes extremely important.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Research Report

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