(1) In this section, the scientific principles governing the transformation of waves from deep water to

shallow will be presented in sufficient detail to highlight critical assumptions and simplifications.

Unfortunately, the problem is so complex that detailed computations require use of complicated numerical

models whose background and implementation are beyond the scope of the Coastal Engineering Manual.

This chapter provides the principles of wave transformation, a simplified approach, and an introduction to

three numerical models used by the Corps of Engineers.

(2) Processes that can affect a wave as it propagates from deep into shallow water include:

(a) Refraction.

(b) Shoaling.

(c) Diffraction.

(d) Dissipation due to friction.

(e) Dissipation due to percolation.

(f) Breaking.

(g) Additional growth due to the wind.

(h) Wave-current interaction.

(i) Wave-wave interactions

The first three effects are *propagation *effects because they result from convergence or divergence of waves

caused by the shape of the bottom topography, which influences the direction of wave travel and causes wave

energy to be concentrated or spread out. Diffraction also occurs due to structures that interrupt wave

propagation. The second three effects are *sink *mechanisms because they remove energy from the wave field

through dissipation. The wind is a *source *mechanism because it represents the addition of wave energy if

wind is present. The presence of a large-scale current field can affect wave propagation and dissipation.

Wave-wave interactions result from nonlinear coupling of wave components and result in transfer of energy

from some waves to others. The procedures presented will stop just seaward of the surf zone, which is treated

in Part II-4, "Surf Zone Hydrodynamics."

(1) The general problem of wave transformation will be introduced in terms of the concept of directional

wave spectra discussed in Part II-1 and II-2. Adopting the notation of Part II-2, consider a directional

spectrum *E(x,y,t,f,θ) *where *f,θ *represents a particular frequency-direction component, *x,y *represents a location

in geographic space, and *t *represents time. The waves are propagating over a region with varying water

depths with no current. Water level will not be time-dependent in the following analyses. Structures are not

considered. The general equation used to estimate wave transformation is the radiative transfer equation

introduced in Part II-2.

M*E*(*x*,*y*,*t*,*f*,θ)

% L @ [*C*g(*x*,*y*,*f*) *E*(*x*,*y*,*t*,*f*,θ)] ' *S*w % *S*n % *S*D % *S*F % *S*P

(II-3-1)

M*t*

II-3-4

Estimation of Nearshore Waves

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