EM 1110-2-1100 (Part II)
30 Apr 02
(2) Although multidimensional, this equation is fundamentally simple. Term A represents the temporal
rate of change of the spectrum, term B represents the propagation of wave energy, term C represents inputs
from the wind, term D represents the redistribution of wave energy between different wave components that
arise from nonlinearities of the waves, term E represents dissipation due to breaking, term F represents losses
due to bottom friction, and term G represents losses due to percolation. Many different algebraic forms have
been suggested for the various Si; three references that provide examples are WAMDI (1988), Sobey and
Young (1986), and Young (1988). Since they are complicated and cannot be used in manual computations,
their algebraic form is not provided here. More detailed discussion of spectral wave mechanics may be found
in Leblond and Mysak (1978), Hasselmann (1962, 1963a, 1963b), Hasselmann et al. (1973), Barnett (1968),
Phillips (1977), Resio (1981), WAMDI (1988), and in Parts II-1 and II-2.
(3) Surface wave motions produce a velocity field that extends to some depth in the water column. This
depth for a deepwater wave is L/2 where L is the deepwater wave length. If the water depth is less than L/2,
the motion extends to the bottom. In cases where the wave motion interacts with the bottom, several physical
changes occur as shown in Part II-1: the celerity C and group velocity Cg are changed, as is the wavelength.
If the waves are propagating in a region in which the depths are variable (and sufficiently shallow so that
the wave interacts with the bottom), the changes in wave speed change the direction of wave travel
and change the amplitude of the wave (refraction and shoaling). If the patterns of wave propagation
lead to strong focusing of waves, wave energy may be radiated away from the convergence by diffraction
(Penny and Price 1944; Berkhoff 1972). The interaction of the wave with the bottom produces a boundary
layer, which will result in the loss of wave energy to the bed due to bottom friction (Term F) resulting from
bottom materials and bed forms (Bagnold 1946). If the bed is reasonably porous, the pressure field associated
with the passing wave can induce flow into and out of the bed (Bretschneider and Reid 1953), resulting in
energy losses due to percolation (Term G). If the bed is muddy or visco-elastic other losses may occur
(Forristall and Reece 1985). Typically, only one of the bottom loss mechanisms is dominant at one locality
although in a large, complicated area a variety of bottom types may exist with differing mechanisms
important at different sites along the path of wave travel. However, the bottom-loss terms are often not
applied because inadequate information is available on bottom-material composition to allow their proper use.
(4) Wind input, interwave transfers, and breaking follow the principles outlined in Part II-2, though
modified due to depth effects. Of the three, wave breaking is most affected by depth. If shoals exist,
depth-induced breaking may be significant even though it is outside of the surf zone. Surf zone wave
breaking is treated in Part II-4. The effect of sporadic breaking of large waves on shoals or other depth-
related features outside the surf zone is not negligible in high sea states. Even in deep water, waves break
through whitecapping or oversteepening due to superposition of large waves. The interaction of waves and
an underlying current can result in refraction of the waves and wave breaking (Jonsson 1978; Peregrine
c. Types of wave transformation.
(1) Three classic cases of wave transformation describe most situations found in coastal engineering:
(a) A large storm generates deepwater waves that propagate across shallower water while the waves
continue to grow due to wind.
(b) A large storm generates winds in an area remote from the site of interest and as waves cross shallower
water with negligible wind, they propagate to the site as swell.
(c) Wind blows over an area of shallow water generating waves that grow so large as to interact with the
bottom (no propagation of waves from deeper water into the site).
Estimation of Nearshore Waves