Edge waves or low frequency gravity motion waves are water waves that are trapped at the shoreline by refraction. It is produce by the variability of wave energy reaching shore. An edge-wave is a low frequency wave attached to the beach. The edge waves have periods of a minute, a long-shore wave-length of around a kilometer, and amplitude that decays exponentially offshore as shown in figure 1 (Cutchin and Smith, 1973).While they were originally considered to be a curiosity, these waves play a significant role in near shore hydrodynamics. (Eckart C., 1951).
The edge waves are modeled by creating incident waves that approach perpendicular to the direction of the constructed shoreline. The numerical modeling of edge waves was first described by Stokes equation in 1946.
Shear Wave is also known as the voticity wave. The stability of a steady alongshore current V(x) to small perturbations using a linear vorticity equation based on the shallow water equations and the rigid-lid approximation. They showed that in the region of strong seaward shear (d|V|/dx < 0), instabilities develop in the form of alongshore propagating velocity oscillations (shear waves). Ratios between variances of shear wave velocities and associated pressure fluctuations scale roughly as
pressure variance R, is 1 (i.e., equi-partitioning of kinetic and potential energy) independent of the mode mix. For shear waves , R = O(gh/V2), that is, 1 for natural alongshore currents with typically small Froude numbers (e.g., Oltman-Shay et al. 1989). Hence, can be used to estimate the contributions of gravity waves and shear waves to the infragravity band. If the gravity and shear wave velocity fluctuations are assumed to be statistically independent, then the fraction of the infragravity velocity variance contributed by shear waves is approximately given by = 1 1/R.(17).
The effects of Shear and Edge Wave in the Environment
The shape of the land under sea determines the strength and direction of the wave toward the coastline, while above ground it determines the run-up. Since the generation of a wave is defined by transferance of energy, or force in simple mathematical terms, the decrease in sea floor depth has the proportional effect of focusing and speeding up the movement of the wave. Thus a wave generated from a large, deep body of water will produce larger waves than those produced from a shallower body of water.
As shown by Adams & Lewis, (1979) offshore coastline has a modifying effect on the wave shape as it breaks on land. The most destructive waves are where the force of the wave is focused as it breaks on l