EXAMPLE PROBLEM II-4-3

FIND:

Maximum and significant runup.

GIVEN:

A plane beach having a 1 on 80 slope, and normally incident waves with deepwater height of 4.0

m and period of 9 sec.

SOLUTION:

Calculation of runup requires determining deepwater wavelength

and, from Equation II-4-1, the surf similarity parameter

Maximum runup is calculated from Equation II-4-28

Significant runup is calculated from Equation II-4-31

Maximum runup is 1.2 m and significant runup is 0.86 m.

of the surf zone energy. These motions are termed *infragravity waves*. Swash at wind wave frequencies

(period of 1-20 sec) dominates on reflective beaches (steep beach slopes, typically with plunging or surging

breakers), and infragravity frequency swash dominates on dissipative beaches (gentle beach slopes, typically

with spilling breakers) (see Wright and Short (1984) for description of dissipative versus reflective beach

types).

waves. Bounded long waves are generated by gradients in radiation stress found in wave groups, causing a

lowering of the mean water level under high waves and a raising under low waves (Longuet-Higgins and

Stewart 1962). The bounded wave travels at the group speed of the wind waves, hence is bound to the wave

group. Edge waves are freely propagating long waves which reflect from the shoreline and are trapped along

shore by refraction. Long waves may be progressive or stand along the shore. Edge waves travel alongshore

with an antinode at the shoreline, and the amplitude decays exponentially offshore. Leaky waves are also

freely propagating long waves or standing waves, but they reflect from the shoreline to deep water and are

not trapped by the bathymetry. Proposed generation mechanisms for the freely propagating long waves

include time-varying break point of groupy waves (Symonds, Huntley, and Bowen 1982), release of bounded

waves through wave breaking (Longuet-Higgins and Stewart 1964), and nonlinear wave-wave interactions

(Gallagher 1971).

Surf Zone Hydrodynamics

II-4-19

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