Coastal Engineering Technical Note IV-17
March 1999
Wave Breaking on an Opposing Current
by Jane McKee Smith
PURPOSE: The Coastal Engineering Technical Note (CETN) herein provides a method to
estimate wave breaking on an opposing current, such as at coastal inlet entrances.
PROBLEM: Waves propagating into a tidal inlet will shoal and break because of changes in
water depth, focusing by shoals, and interactions with an opposing (ebb) current. On an ebb
current, waves steepen because their height increases and length decreases. The wave steepening
can intensify wave breaking, causing a navigation hazard and inducing a wave-driven current and
sediment transport. Most wave-breaking criteria are based on a maximum ratio of wave height to
water depth. But, in regions where waves break because of steepening on an ebb current, the
height-to-depth criterion may significantly underestimate wave breaking and overestimate wave
height.
CETN IV-9 (Smith 1997) describes the process of wave-current interaction in one dimension and
gives the equations for calculating wave-height transformation on an ebb (opposing) or flood
(following) current. Extending the discussion in CETN IV-9, the present CETN provides
guidance on estimating wave breaking that may occur as waves transform on an opposing current.
Before the method for calculating breaking is described, the governing equation, wave-action
conservation, is reviewed (see also CETN IV-9), and wave shoaling on a current is discussed.
CONSERVATION OF WAVE ACTION: Wave height in the presence of a current is governed
by the conservation of wave action (Jonsson 1990, and others). The one-dimensional
conservation of wave action equation is given by:
(
) =
E Cgr + U
D
(1)
x
ωr
ωr
where
x
= horizontal coordinate direction (assumed to be the direction of wave
propagation)
E = wave energy (energy is proportional to wave height squared)
Cgr = group velocity relative to current
U = current velocity
1
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