2π/year. Then, if the initial position of the spit at *t = *0 is located at *x *= 0, the

solution of Eq. 1 for the location of the tip of the spit, denoted as *x*S, is

F

I

G

J

1

H

K

sin(*σt *)

(3)

2*σ*

Eq. 3 shows that spit elongation is directly proportional to the longshore

sediment transport rate and to elapsed time, as modified by the fluctuating rate, and

inversely proportional to spit width and depth of active movement. It is feasible that

,

The elongation rate of the time-dependent term in Eq. 3 depends inversely on the

angular frequency. This means that, for the same amplitude of transport *Q*′2 , a

/

higher-frequency motion will damp more quickly and be less-perceptible than a

5 m, and *W = *100 m. In addition, suppose that two sinusoidal forcings occur with

respective angular frequencies of 2π/(1 year) and 2π/(1 month) and equal amplitude

/

distance. Fig. 2 shows the linear growth of the spit as produced by the mean

transport rate and the growth as modified by the two terms. The response of the spit

to the monthly change in transport rate is barely perceptible despite having the same

amplitude as the annual fluctuation.

For reference in interpreting the mean longshore transport rate, it can be shown

that for *N *equi-spaced measurements of the rate, the net longshore transport rate

=

200

Unrestricted Spit Growth

Constant Longshore

Transport Rate

150

100

Annual and monthly

variation about constant

transport rate

50

0

0.0

0.2

0.4

0.6

0.8

1.0

Elapsed Time, year

Fig. 2. Unrestricted spit elongation, constant and with time variation in transport.

Kraus

5