6.4. SUSPENSION-DOMINATED MODELS
315
Uma]: ~ maximum horizontal component of the orbital
water particle velocity near the bed
- incipient motion critical velocity of the sediment
cu - sediment fall speed
High values of the parameter implied movement by suspension (turbulencedominated), and low values corresponded to bedload-dominated conditions.
Le Méhauté (1970) proposed a similar parameter, given as Umaxl
Xie (1981) suggested that the value of the parameter given by Eqn. 6.156
should be the same in the model as in the prototype, but he noted that
this would be difficult at times because of the dependence of both I/ * and
w on grain size.
The scaling criterion that is derived from maintaining similarity of Xie’s
parameter in a geometrically undistorted Froude model requires that:
(6.157)
Hughes and Fowler (1990a) rearranged Eqn. 6.157 and expressed it in
terms of scale ratios as
N. NUm., = Na
(6.158)
where
(6.159)
Noting that Numax = Nl/Nt in a geometrically undistorted Froude model,
Eqn. 6.158 becomes
N * Nl = NwNt
(6.160)
or
N„ = N *
when the Froude time scale is substituted into Eqn. 6.160.
In essence, the scaling guidance given by Eqns. 6.161 and 6.159 is a
more generalized version of Dean’s modeling guidance determined from the
fall speed parameter (Eqn. 6.155). Equation 6.161 agrees with that given
by Eqn. 6.155 if the scale ratio TV * is equal to unity.
315
Uma]: ~ maximum horizontal component of the orbital
water particle velocity near the bed
- incipient motion critical velocity of the sediment
cu - sediment fall speed
High values of the parameter implied movement by suspension (turbulencedominated), and low values corresponded to bedload-dominated conditions.
Le Méhauté (1970) proposed a similar parameter, given as Umaxl
Xie (1981) suggested that the value of the parameter given by Eqn. 6.156
should be the same in the model as in the prototype, but he noted that
this would be difficult at times because of the dependence of both I/ * and
w on grain size.
The scaling criterion that is derived from maintaining similarity of Xie’s
parameter in a geometrically undistorted Froude model requires that:
(6.157)
Hughes and Fowler (1990a) rearranged Eqn. 6.157 and expressed it in
terms of scale ratios as
N. NUm., = Na
(6.158)
where
(6.159)
Noting that Numax = Nl/Nt in a geometrically undistorted Froude model,
Eqn. 6.158 becomes
N * Nl = NwNt
(6.160)
or
N„ = N *
when the Froude time scale is substituted into Eqn. 6.160.
In essence, the scaling guidance given by Eqns. 6.161 and 6.159 is a
more generalized version of Dean’s modeling guidance determined from the
fall speed parameter (Eqn. 6.155). Equation 6.161 agrees with that given
by Eqn. 6.155 if the scale ratio TV * is equal to unity.