4.2. SHORT-WAVE HYDRODYNAMIC MODELS
119
Laminar Boundary Layer
Because laminar and transitional boundary layers are a function of Reynolds
number, it is immediately recognized that
Shear stresses developed in laminar boundary layers
will not be scaled properly in the Froude model.
Actually, this is not too big a problem for coastal engineers because laminar
boundary layers rarely occur in coastal hydrodynamics in nature. However, there is the possibility that laminar boundary layers may develop
in the physical model when inappropriate, and the model engineer must
guard against such an occurrence. In fixed-bed short-wave models, artificial roughness elements can be added to assure the boundary layer is rough
turbulent.
If the need arises, laminar boundary layer experiments can be properly designed by scaling the flow characteristics using the Reynolds similitude criterion with the characteristic velocity and length being those of the
boundary layer and not the upper level flow.
Rough Turbulent Boundary Layer
Although Froude similitude fails to model viscous forces, the derivation
of similitude requirements from the equations of motion did indicate that
turbulent dissipative processes would be in similitude in a Froude-scaled,
geometrically undistorted model because viscosity is not a parameter in
the formulation of the Reynolds stress terms. Therefore, we should expect
that boundary layers in the fully turbulent (rough turbulent) range will be
dynamically similar between the prototype and models meeting the shortwave Froude model criteria.
Having correct correspondence between prototype and model turbulent
boundary layers can be an important aspect of some coastal hydrodynamic
short-wave models. For example, waves propagating for a distance over a
rough bed, such as a scour blanket made of stone, will be attenuated by
bottom turbulence more rapidly than if they were travelling over a smooth
bed. Similarly, shear stresses created by waves and currents flowing over
a mobile bed of sand have the potential of transporting the loose material. (See Chapter 6 for movable-bed modeling considerations.) In both
instances, model response depends on correct similitude of shear stresses
within the boundary layer.
Kamphuis (1973) derived scaling considerations for the rough turbulent boundary layer for short waves. Previous researchers had shown that
the friction factor, fw, is independent of Reynolds number in the rough
turbulent range and can be approximated as
119
Laminar Boundary Layer
Because laminar and transitional boundary layers are a function of Reynolds
number, it is immediately recognized that
Shear stresses developed in laminar boundary layers
will not be scaled properly in the Froude model.
Actually, this is not too big a problem for coastal engineers because laminar
boundary layers rarely occur in coastal hydrodynamics in nature. However, there is the possibility that laminar boundary layers may develop
in the physical model when inappropriate, and the model engineer must
guard against such an occurrence. In fixed-bed short-wave models, artificial roughness elements can be added to assure the boundary layer is rough
turbulent.
If the need arises, laminar boundary layer experiments can be properly designed by scaling the flow characteristics using the Reynolds similitude criterion with the characteristic velocity and length being those of the
boundary layer and not the upper level flow.
Rough Turbulent Boundary Layer
Although Froude similitude fails to model viscous forces, the derivation
of similitude requirements from the equations of motion did indicate that
turbulent dissipative processes would be in similitude in a Froude-scaled,
geometrically undistorted model because viscosity is not a parameter in
the formulation of the Reynolds stress terms. Therefore, we should expect
that boundary layers in the fully turbulent (rough turbulent) range will be
dynamically similar between the prototype and models meeting the shortwave Froude model criteria.
Having correct correspondence between prototype and model turbulent
boundary layers can be an important aspect of some coastal hydrodynamic
short-wave models. For example, waves propagating for a distance over a
rough bed, such as a scour blanket made of stone, will be attenuated by
bottom turbulence more rapidly than if they were travelling over a smooth
bed. Similarly, shear stresses created by waves and currents flowing over
a mobile bed of sand have the potential of transporting the loose material. (See Chapter 6 for movable-bed modeling considerations.) In both
instances, model response depends on correct similitude of shear stresses
within the boundary layer.
Kamphuis (1973) derived scaling considerations for the rough turbulent boundary layer for short waves. Previous researchers had shown that
the friction factor, fw, is independent of Reynolds number in the rough
turbulent range and can be approximated as