have been superseded by the numerical methods discussed in Part II, Section 3-5. Refraction and shoaling

analyses typically try to specify the wave height and direction along a ray.

(2) Figure II-3-4 provides idealized plots of wave rays for several typical types of bathymetry. Simple

parallel contours tend to reduce the energy of waves inshore if they approach at an angle. Shoals tend to

focus rays onto the shoals and spread energy out to either side. Canyons tend to focus energy to either side

and reduce energy over the head of the canyon. The amount of reduction or amplification will depend not

only on bathymetry, but on the initial angle of approach and period of the waves. For natural sea states that

have energy spread over a range of frequencies and directions, reduction and amplification are also dependent

upon the directional spread of energy (Vincent and Briggs 1989).

(3) Refraction and shoaling have been derived and treated widely. The following presentation follows

that of Dean and Dalrymple (1991) very closely. Other explanations are provided in Ippen (1966), the *Shore*

(1) First, the equation for specifying how wave angle changes along the ray is developed, followed by

the equation for wave height. The derivation is only for parallel and straight contours with no currents

present. The x-component of the coordinate system will be taken to be orthogonal to the shoreline; the y-

coordinate is taken to be shore-parallel. The straight and shore-parallel contours assumption will imply that

any derivative in the y-direction is zero because *dh/dy *is zero.

Estimation of Nearshore Waves

II-3-7

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