*W*

*W*0

*qs*

*ha*

*qd*

*q*

*qy*

*hp*

*h*

*qb*

∆*x*

*x*

*qr*

*h*0

*z*0

*z*

∆*z*

Fig. 2. Definition sketch for channel infilling model

The transport rate *q *per unit length of channel near the updrift side of the channel can be

divided into a bedload transport rate *q*b, a rate of suspended material deposited into the

channel *q*d , and a rate *q*s of suspended material passing over the channel. For the situation

of a coastal inlet, for the portion of channel crossing the surf zone, the transport rate per

unit channel length can be estimated as the total transport rate *Q *multiplied by the ratio of

length of channel exposed to the longshore transport to the total width of the surf zone.

From Fig. 2 and above discussion, the transport rate per unit length of channel is

represented as:

*q *= *qb *+ *q*d + *q*s

(2)

The rate *q*c of material filling the channel is the sum of that entering and that resuspended

and leaving the channel:

*qc *= *q*b + *q*d - *q*r

(3)

The rate *q*y of material bypassing the channel is given by the sum of *q*s and the rate *q*r of

material resuspended from the channel:

*qy *= *q*s + *q*r

(4)

It is seen that *q *= *q*c + *q*y (= *q*b + *q*d + *q*s ) .

A closure assumption of the model is that the rate of material resuspended from the

channel bottom is proportional to the product of the depth of the channel (normalized by

the total channel depth) and the rate of deposition as,

Kraus and Larson

4