ERDC/CHL CETN-IV-25
June 2000
MEAN WATER LEVEL: The mean water level η (setup and setdown) is determined from the
cross-shore momentum equation:
dη
dS
ρgd
= - xx - CDρa W W cos ϕ
(25)
dx
dx
2
1
C
1
gr (cos 2 α + 1) -
= ρgH
S xx
(26)
2
8
Cr
For random waves, Sxx and Sxy are determined as averages for the selected number of waves in
the Monte-Carlo simulation before they are inserted in the momentum equations. The cross-
shore mean current does not enter Equation 25 and is assumed only to modify the wave
transformation.
EXAMPLES:
Example 1: Wave transformation at an inlet entrance. Smith et al. (1998) measured
wave breaking on a current at an idealized inlet in the laboratory. A 1:50 scale model of an inlet
was constructed in a 46-m-wide by 99-m-long concrete basin with 0.6-m-high walls. The
parallel jetties at the inlet had a spacing of 3.66 m and extended 5.5 m offshore. A seaward
flowing (ebb) current Uc was generated between the jetties that diffused as it propagated
offshore. The experimental conditions constituted permutations of the following parameter
values: mean spectral wave height in deep water Hmo = 3.7 and 5.5 cm, spectral peak period Tp =
0.7 and 1.4 sec, wave direction perpendicular to the jetties, and Uc = 0, 12, and 24 cm/sec. Wave
height and current were measured at several gauges around the inlet with the main objectives to
study wave breaking and determining the decay in wave height on the current.
Here, two cases are discussed to illustrate the performance of NMLong-CW, in particular for the
algorithm developed to calculate wave breaking on a current. These simulations were partly
carried out to validate the generalization of Equation 8 (calculation of the energy dissipation on a
current). It was found that the standard value of Γ= 0.4 overall provided reasonable results,
although this value should be confirmed by further simulations against other data sets. The cases
discussed here encompassed Case 5 (Hmo = 4.1 cm, Tp = 1.4 sec, Uc = 13 cm/sec) and Case 11
(Hmo = 3.9 cm, Tp = 0.83 sec, Uc = 24 cm/sec) from Smith et al. (1998) illustrating the results for
both the weaker and stronger current cases. Wave height transformation was calculated by
Monte-Carlo simulation with a Rayleigh distribution specified in the offshore. The actual
simulated time series of waves at each location was input in the present cases to compute the
significant wave height, which was assumed to be equal to Hmo. Figures 3a and 3b display the
calculated significant wave height for Cases 5 and 11, respectively, together with the measured
wave heights. Viewing Figure 3 together with other cases not shown here, the agreement
between calculations and measurements is regarded as satisfactory.
8
Previous Page
