found that growth of the platform preceded formation of the spit. Here, the term

"spit" will represent both the subaerial ridge and platform, unless otherwise stated.

a

**(a) Cross -**

*Qout*

*Qin*

**section view**

*B*

**∇**

**∆***x*

*D*

*DC*

*x*

*Qin*

*Qout*

**∆***x*

**(b) Plan view**

*W*

Fig. 1. Definition sketch for analytical model of spit elongation.

Viewing Fig. 1, in time interval ∆*t*, the volume change ∆V equals *WD*∆*x*, for

which the depth of active motion is *D *= *B *+ *D*C (sum of the berm elevation and the

depth of closure); and ∆*x *is the increment of change in length of the spit in time ∆*t*.

By assumption, the volume change is equal to the volume entering minus that

leaving during the time interval, i.e., ∆*t*(*Q*in *Q*out). In the limit, the sand

conservation equation becomes

b

g

*dx*

1

=

*Qin *- *Q*out

(1)

*dt WD*

Solutions of the Eq. (1) are determined after specifying an initial condition,

boundary condition and functional forms for the transport rates and other parameters,

as appropriate. We now consider four examples of increasing complexity.

**Example 1: Unrestricted Spit Growth**

If a spit can elongate without restriction over the period under consideration, then

*Qout *= 0 (no sediment leaves or enters the spit from the distal end). Consider

*Q*′

*Qin *= *Q *+

cos(σ*t *)

(2)

2

where *Q *= time-mean longshore sediment transport rate; *Q*′ = amplitude of a

/2