6.3. BEDLOAD-DOMINATED TRANSPORT MODELS
261
The first requirement of the LWM is found by solving NR* = 1 for v *
and substituting into the Np. = 1 to get
NltN^ = NpN^
(6.43)
Assuming that water is the model fluid (Np = N» = 1) the above requirement reduces to
=
(6.44)
The relative length scale ratio is nothing more than
= yr
(6.45)
11 d
The LWM shear velocity scale was found to be Nv* = (Nd)'1' , however,
it is not possible to determine a relationship for the Lightweight Model
relative fall speed scale until a specific lightweight sediment has been chosen.
Lightweight Model Shear Stress and Current Scales
The Lightweight Model sediment shear stress sediment scale can be derived
from the requirement, Nr* — 1 with the definition Nv* = y/NTb/Np, i.e.,
N N2
Nrb =
(6.46)
Assuming water as the model fluid (Np — N^ = 1), Eqn. 6.46 becomes
Nrt = (M,)’2
(6.47)
In order for the hydrodynamic bottom shear stresses to be in correct
proportion with the shear necessary to move sediment, the wave and current
shear stresses must have the same scale as the sediment shear stresses.
Equating the short-wave bottom shear stress (Eqn. 6.14) with the sediment
shear stress (Eqn. 6.47) gives
N, (Nl)'14 (Nt. )3/4 = (Nd)~2
(6.48)
Assuming a flat bottom so that Nk, = Nd and taking Ny = 1, Eqn. 6.48
reduces to
Nd = (7VL)"1/n
(6.49)
thus fixing the relative length scale to N\/d — (A^r)12^11, the sediment
immersed specific weight scale to AT7i = (TV^,)3^11, the shear velocity scale
to Nv* = (A^)1/11, and the shear stress scale to NTb = (A^)2/11.