. X AiLollg'^ o A2ujllg^ + A^u^llg^ 1 1 1 1 1 6 10 12 Figure : Evolution of the solution for a shallow water wave pletely independently of the other windows. In this case, the parameters of the LFI solution are: primary window width of 2s (tq = ,), with a sixth order potential function (J = 6), seven samples on the pressure record, and seven water surface nodes (/ = A' = 7), resulting in 21 equations in 16 unknowns in each window. The window width of two seconds is one fifth of the period of the wave, and is a reasonable length of time to extend the locally steady approximation. Evo
. X AiLollg'^ o A2ujllg^ + A^u^llg^ 1 1 1 1 1 6 10 12 Figure : Evolution of the solution for a shallow water wave pletely independently of the other windows. In this case, the parameters of the LFI solution are: primary window width of 2s (tq = ,), with a sixth order potential function (J = 6), seven samples on the pressure record, and seven water surface nodes (/ = A' = 7), resulting in 21 equations in 16 unknowns in each window. The window width of two seconds is one fifth of the period of the wave, and is a reasonable length of time to extend the locally steady approximation. Evolution of the Solution Fig. shows the evolution of the solution as the window is moved along the wave. The top figure shows the non-dimensional values of the local fundamental wave number, k, and the local fundamental frequency, ui. The importance of the local nature of the solution is apparent in this figure, as the solution varies substantially from window to window. The wave number and frequency both increase to maximum magnitude near the crest (4 < tu), < 7), and have lower values in the trough region (near tu^ = 3 and tu^ = 9). This pattern suggests that the kinematics in the crest region are similar to those of a much higher frequency lower
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