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P. Wang et al. / Coastal Engineering 46 (2002) 175211
A reasonable estimate of the time-averaged longshore sediment flux was obtained from the product of time-averaged
profiles of longshore current and sediment concentration. Accurate estimates of time-averaged cross-shore sediment flux,
however, could not be obtained from the product of time-averaged current and concentration.
D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Surf-zone sediment transport; Surf-zone hydrodynamics; Sediment suspension; Longshore sediment transport; Cross-shore sediment
transport; Physical modeling; Sediment flux
surf-zone current and sediment concentration for the
1. Introduction
determination of sediment flux, ux,y and c are often
Sediment concentration along with fluid velocity
partitioned as (e.g., Osborne and Greenwood, 1993;
determines sediment flux. A general form for comput-
Grasmeijer and Van Rijn, 1999; Thornton et al., 1996)
ing sediment flux is given as
ux;y ux;y ux;ylow ux;yhigh
3
~
~
Fx;yx; y; z; t ux;yx; y; z; t cx; y; z; t
1
c c clow chigh
4
~
~
where F is sediment flux per unit area; u is current
velocity; c is sediment concentration; t is time; and x,
where u and c are the time-averaged velocity and
y, and z are cross-shore, longshore, and vertical
sediment concentration, respectively. u and c are
~
~
oscillatory components of velocity and concentration.
represents cross-shore or longshore current, respec-
The subscripts high and low indicate high (e.g., wind
tively. Variations in the longshore direction are typi-
wave) and low (e.g., infragravity) frequency compo-
cally much less than those in the cross-shore and
nents. The time-averaged sediment flux is then deter-
vertical directions and are, therefore, often neglected,
mined as
reducing Eq. (1) to
Fx;y ux;yc ux;yc ux;ylowclowux;yhighchigh
5
~
~
~
~
Fx;yx; z; t ux;yx; z; t cx; z; t
2
The second and third terms on the right-hand side are
Due to the dynamic nature of the surf zone, simul-
poorly understood and often neglected or simplified in
taneously determining the fluid velocity and sediment
sediment transport modeling. An improved under-
concentration with adequate temporal and spatial res-
standing of the temporal variations of surf-zone
olutions is difficult. Less detailed approaches, typi-
hydrodynamics and sediment concentration is essen-
cally empirical ones, are commonly used to determine
tial to improve our capability of predicting sediment
a temporally averaged and spatially integrated sedi-
flux. To obtain a transport rate across an area of
ment transport rate. For example, the broadly used
interest, e.g., longshore transport rate across the surf
CERC formula assumes that the total rate of longshore
zone, it is necessary to integrate the point sediment
sediment transport in the surf zone is proportional to
flux (Eq. (5)) over space, which requires knowledge
longshore energy flux at the main breaker line
of spatial variation. One of the goals of this paper is to
document the temporal and spatial variations of surf-
is specified in the CERC formula and the spatial scale
zone current and sediment concentration over a large
spans the entire surf zone. The cross-shore sediment
laboratory beach.
transport rate per unit width of beach is often deter-
The analyses presented here are based on data
mined from time-varying beach profile changes with
collected in the recently established Large-scale Sedi-
temporal scales of up to months or even years (Dean,
ment Transport Facility, LSTF (Hamilton et al., 2001;
1977; Dean and Zheng, 1994; Zheng and Dean, 1997).
Hamilton and Ebersole, 2001; Wang et al., 2002; Wang
In order to examine the influences of the compli-
and Kraus, in press). Two unidirectional long-crested
cated temporal variations and phase coupling of the
irregular wave conditions, with one resulting in pre-
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