Shoreline Profile of the Stokes-Mode Edge Waves
WASHINGTON UNIV SEATTLE DEPT OF CIVIL ENGINEERING
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Based on the assumptions of inviscid and incompressible fluid, irrotational flow, and infinitesimal wave amplitude, Stokes 1846 found a solution to the water-wave problem with a uniformly sloping impermeable boundary beach. The solution, often termed the Stokes-mode edge wave, can be written in terms of velocity potential, phi, as a certain formula where A is the amplitude of wave runup distance along the beach surface, omega is the wave angular frequency, k is the wave number in the longshore direction, beta is the beach slope from the horizontal, and the coordinates x,y,z point to the alongshore, offshore, and vertically upward directions, respectively. Equation 1 indicates that the edge waves propagate parallel to the shoreline, y0, and decays exponentially offshore with an e-folding distance of K cos b to the -1 power.
- Physical and Dynamic Oceanography