θb = arcsin 2π sin θo

(11)

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

(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=0.77*c*f K, where *K *= transport rate

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

(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 *q*l across the profile and assuming that the tip of the groin is located

Larson, Kraus, and Hanson

6

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