6.4. SUSPENSION-DOMINATED MODELS
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where
dh
dq
dt
dx
(6.138)
h - water depth
t - time
x - horizontal coordinate in the onshore/offshore direction
q - volumetric sediment transport rate (per unit width)
in the x-direction
They performed an inspectional analysis of Eqn. 6.138 to get a nondimensional form of the equation shown below
dh
di
dq
dx
(6.139)
where the “hat” refers to nondimensional quantities, and
qt
- reference total sediment transport rate
tm
- reference morphologic time
X - characteristic horizontal length
Z - characteristic vertical length
Similitude of sediment conservation will be achieved if the value of the
nondimensional coefficient is the same in the model as in the prototype. In
terms of scale ratios this stipulation becomes
Ngt Ntm
NxNz
or
Nt
NxNz
NgT
(6.140)
Wang, et al. assumed that beach profile development in the surf zone
was dominated by suspended sediment transport, so the total transport
rate could be approximated by the suspended transport, which they gave
as
qt ~ q> = h U c
(6.141)
where U is the mean horizontal transport velocity and c is suspended
sediment concentration. Forming the prototype-to-model scale ratio of
Eqn. 6.141, noting that Ny — Nx/N? where Nr is the hydrodynamic
time scale, and substituting into Eqn. 6.140 gives