Properties of the Energy Transport for Plane-Parallel Polychromatic Surface Gravity Waves in Waters of Arbitrary Depth


It's well known that the energy transport of ocean waves propagates with the group velocity and that the energy decreases exponentially with depth. Expanding this theory, we have a tendency to will derive expressions for the energy transport as a perform of depth and the entire instantaneous transport's development over time for waves in waters of finite depth. Solutions to the Laplace equation are found for plane-parallel polychromatic waves with linearized boundary conditions. A time series of wave elevation collected at Uppsala University's wave energy analysis test site is chosen to present the results. Solutions for waters of each infinite and arbitrary depths are presented and compared. The solutions are convolution-sort integrals with the wave elevation where we have found efficient ways that to calculate the kernels. The difference in cluster velocity between finite depth and infinite depth and its impact on the energy transport is clearly seen in the results. The use of the deep-water approximation provides a too low energy transport within the time averaged plus in the full instantaneous energy transport. We tend to further show that the entire instantaneous energy transport can truly have a direction that's opposite to the direction of the waves as observed from a reference frame fastened to the seabed.

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