EM 1110-2-1100 (Part II)
30 Apr 02
II-3-2. Principles of Wave Transformation
a. Introduction.
(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."
b. Wave transformation equation.
(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.
ME(x,y,t,f,θ)
% L @ [Cg(x,y,f) E(x,y,t,f,θ)] ' Sw % Sn % SD % SF % SP
(II-3-1)
Mt
A
B
C
D
E
F
G
II-3-4
Estimation of Nearshore Waves
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