6.3. BEDLOAD-DOMINATED TRANSPORT MODELS
275
where
= 1.3 x IO"3
\ ^op
-5/4
1/4
sin3/5(2a6) (6.68)
Q
Hsb
P
T Jp
L op
mb
^50
ab
total longshore transport rate
breaking significant wave height
fluid density
peak period of the offshore wave spectrum
deepwater wavelength associated with the
peak period, Tp (linear wave theory)
beach slope
median grain size diameter
breaking wave angle
Provided Eqn. 6.68 correctly represents prototype and model transport
rate, then the prototype-to-mo del scale of total longshore transport can be
expressed as
Nq = Nt/2
scale effect
(6.69)
Q
where Np = 1 for water in the model, and use was made of the fact that
Nn,b — NLop = Nl and Nt =
for a geometrically undistorted model
with Froude-scaled hydrodynamics.
Kamphuis surmised that the actual longshore transport rate scale, as
given by Eqn. 6.69, differed from the theoretical Froude discharge scale
(^Froude = ^L/2) by the factor
Scale Effect = (Mnb)3/4 pm 1/4
Um
(6.70)
where Nmb is the prototype-to-model scale of beach slope. This scale factor
compensates for model scale effects when scaling model results to prototype
scale. For example, if the scale effect parameter is larger than unity, the
model transport rate is scaled to a prototype value that will be larger than
what would be given by the Froude discharge scale.
For model sediment larger than that required by geometric scaling, the
beach slope will tend to be steeper in the model which will force beach
slope scale, Nmb, to be less than one. The relatively larger model sediment