122
CHAPTER 4. HYDRODYNAMIC MODELS
Forming the prototype-to-model scale ratio of Eqn. 4.78 gives the approximate scaling relation
(AWcurr.„, =
‘
(4-79)
where the subscript “max” has been dropped and the subscript “current
has been added to represent long waves and currents.
Substituting the Froude similitude expressions for the velocity and depth
scales gives the requirement
(^.U„„l = Ar7(JVi)3/4(^.)1/4
(4.80)
which is somewhat different than Eqn. 4.76 found for short-wave shear stress
scale. However, if the model bottom roughness is in geometric similitude
with the prototype bottom roughness, then the shear stress scales for both
waves and currents are the same as the Froude stress scale. Thus, we can
state
The rough turbulent boundary layer formed by unidirectional currents and long-wave (tidal) motions reproduced in short-wave models will be in similitude provided the bottom roughness scale is the same as the
geometric length scale.
Combined Currents and Short Waves (Offshore Model)
Ideally, the physical model bottom roughness scale would be the same as
the length scale; however, there are situations when this is difficult to accomplish. The most common occurrence of the model bottom being relatively rougher than called for by Froude scaling is when movable bed model
sediments are not geometrically reduced from the prototype10.
In many coastal sediment problem areas, geometric reduction of sediments by the
model length scale would result in cohesive model sediments.
1 he formation of sand ripples produces a different roughness, and this needs to be
considered when preparing a fixed-bed model to simulate hydrodynamic motion over
sandy bottoms.
Over flat mobile beds, roughness is determined by grain size11. If the
model grain size is larger than is should be, then N^t < Nl which means
To ) waves < (^rjcurrent < nl
In words, shear stresses in the model are larger than they should be, and
this scale effect is more pronounced for waves than for currents.
CHAPTER 4. HYDRODYNAMIC MODELS
Forming the prototype-to-model scale ratio of Eqn. 4.78 gives the approximate scaling relation
(AWcurr.„, =
‘
(4-79)
where the subscript “max” has been dropped and the subscript “current
has been added to represent long waves and currents.
Substituting the Froude similitude expressions for the velocity and depth
scales gives the requirement
(^.U„„l = Ar7(JVi)3/4(^.)1/4
(4.80)
which is somewhat different than Eqn. 4.76 found for short-wave shear stress
scale. However, if the model bottom roughness is in geometric similitude
with the prototype bottom roughness, then the shear stress scales for both
waves and currents are the same as the Froude stress scale. Thus, we can
state
The rough turbulent boundary layer formed by unidirectional currents and long-wave (tidal) motions reproduced in short-wave models will be in similitude provided the bottom roughness scale is the same as the
geometric length scale.
Combined Currents and Short Waves (Offshore Model)
Ideally, the physical model bottom roughness scale would be the same as
the length scale; however, there are situations when this is difficult to accomplish. The most common occurrence of the model bottom being relatively rougher than called for by Froude scaling is when movable bed model
sediments are not geometrically reduced from the prototype10.
In many coastal sediment problem areas, geometric reduction of sediments by the
model length scale would result in cohesive model sediments.
1 he formation of sand ripples produces a different roughness, and this needs to be
considered when preparing a fixed-bed model to simulate hydrodynamic motion over
sandy bottoms.
Over flat mobile beds, roughness is determined by grain size11. If the
model grain size is larger than is should be, then N^t < Nl which means
To ) waves < (^rjcurrent < nl
In words, shear stresses in the model are larger than they should be, and
this scale effect is more pronounced for waves than for currents.