EM 1110-2-1100 (Part II)
31 July 2003
1
ηs ' ηb %
hb
(II-4-24)
8
1%
2
3γb
g. The first term in Equation II-4-24 is setdown at the break point and the second term is setup across
of 0.8, &s . 0.15 db. Note that, for higher breaking waves, db will be greater and thus setup will be greater.
the surf zone. The setup increases linearly through the surf zone for a plane beach. For a breaker depth index
η
Equation II-4-24 gives setup at the still-water shoreline; to calculate maximum setup and position of the mean
shoreline, the point of intersection between the setup and beach slope must be found. This can be done by
trial and error, or, for a plane beach, estimated as
ηs
∆x '
dη
tanβ &
dx
(II-4-25)
dη
∆x
ηmax ' η s %
dx
where ∆x is the shoreward displacement of the shoreline and &max is the setup at the mean shoreline.
η
h. Wave setup and the variation of setup with distance on irregular (non-planar) beach profiles can be
calculated based on Equations II-4-21 and II-4-22 (e.g., McDougal and Hudspeth 1983, Larson and Kraus
1991). NMLONG calculates mean water level across the nearshore under the assumptions previously
discussed.
i. Setup for irregular waves should be calculated from decay of the wave height parameter Hrms. Wave
setup produced by irregular waves is somewhat different than that produced by regular waves (Equation II-4-
22) because long waves with periods of 30 sec to several minutes, called infragravity waves, may produce
a slowly varying mean water level. See Part II-4-5 for discussion of magnitude and generation of infragravity
waves. Figures II-4-8 and II-4-9 show irregular wave setup, nondimensionalized by Hrmso, for plane slopes
of 1/100 and 1/30, respectively. Setup in these figures is calculated from the decay of Hrms given by the
irregular wave application of the Dally, Dean, and Dalrymple (1985) wave decay model (see Figure II-4-4).
Nondimensional wave setup increases with decreasing deepwater wave steepness. Note that beach slope is
predicted to have a relatively small influence on setup for irregular waves.
II-4-4. Wave Runup on Beaches
Runup is the maximum elevation of wave uprush above still-water level (Figure II-4-11). Wave uprush
consists of two components: superelevation of the mean water level due to wave action (setup) and fluctua-
tions about that mean (swash). Runup, R, is defined in Figure II-4-12 as a local maximum or peak in the
instantaneous water elevation, η, at the shoreline. The upper limit of runup is an important parameter for
determining the active portion of the beach profile.
At present, theoretical approaches for calculating runup on beaches are not viable for coastal design.
Difficulties inherent in runup prediction include nonlinear wave transformation, wave reflection, three-
dimensional effects (bathymetry, infragravity waves), porosity, roughness, permeability, and groundwater
elevation. Wave runup on structures is discussed in Chapter VI-2.
II-4-14
Surf Zone Hydrodynamics
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