hb
θb = arcsin 2π sin θo
(11)
Lo
Longshore Sediment Transport
A newly derived formula (Larson and Bayram 2002) for the total longshore sediment
transport rate was implemented in Cascade, in which it is possible to include currents
generated by tide and wind. In the derivation of this formula, it was assumed that
suspended sediment mobilized by breaking waves is the dominant mode of transport. A
certain ratio of the incident wave energy flux provides the work for maintaining a steady-
state concentration in the surf zone. The product between the concentration and the
longshore current (from waves, wind, and tide) yields the transport rate Q as,
ε
Q=
FV
(12)
(ρs - ρ)(1 - a) gw
where F = wave energy flux directed toward shore, V = surf-zone average longshore
current velocity, ε = empirical coefficient, ρs (ρ)= sediment (water) density, a the porosity,
and w = sediment fall speed. Values on ε must be established through calibration against
data, but an alternative method is to compare the new formula with the CERC formula.
Larson and Bayram (2002) made such a comparison, employing the mean longshore
current in the surf zone based on the alongshore momentum equation with linearized
friction and F from linear wave theory. An equilibrium beach profile was assumed, using
the relationship between the shape parameter A and w from Kriebel et al. (1991). For small
angles at breaking, the transport coefficient is given by ε=0.77cf K, where K = transport rate
Bypassing of Jetties
To determine the bypassing at jetties (or groins), a model is needed to calculate the cross-
shore distribution of the longshore transport rate updrift the jetty. Such a model was
implemented in Cascade based on a sediment transport formula originally developed by
Larson and Hanson (1996). This formula was derived under similar assumptions as the total
longshore sediment transport formula previously discussed. However, because the local
transport is needed, the concentration profile becomes a function of the local wave energy
εc
ql =
VP
(13)
(ρs - ρ)(1 - a) gw
where V = local longshore current velocity, and εc - transport coefficient. The simplest
approach to determine how much of the sediment that may bypass a groin or jetty is to
assume that all sediment transported seaward of the groin tip is bypassed, whereas the
transport shoreward of the tip is blocked.
To compute V and P, the random wave transformation model by Larson (1995) was
employed, although a more simplified description of the energy dissipation due to breaking
was used. Integrating ql across the profile and assuming that the tip of the groin is located
Larson, Kraus, and Hanson
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