140
CHAPTER 4. HYDRODYNAMIC MODELS
Chapter 3 discussed the difficulties in maintaining similarity of both Froude
and Reynolds numbers in the same model, and usually coastal models do
not fulfill the Reynolds criterion.
Finally, Condition 4 revealed that vertical viscous shear stresses will
only be in similitude when the long-wave model is geometrically undistorted, so we conclude that
Long-wave models maintain similitude of vertical viscous shear stresses only when the model is geometrically undistorted and the Reynolds criterion has been
met.
In summary, examination of similitude requirements resulting from the
vertically integrated fluid equations of motion for long waves reveals that
flow patterns and velocity distributions in long-wave hydrodynamic models
are essentially governed by inertia and gravity effects because similitude of
Froude number must be maintained between model and prototype. However, the assumption of negligible vertical fluid velocities and hydrostatic
pressure variation in the inviscid flow region allows relaxation of the model
requirements so that geometrically distorted models (horizontal scale different than the vertical scale) can be considered.
The turbulent shear stress terms were not included in the equations
of motion, and we do not anticipate any large scale turbulent dissipation
such as associated with wave breaking. Hence, we can expect a scale effect
to be associated with turbulent dissipation if it occurs in a geometrically
distorted15 long-wave model. Careful evaluation must be made of model
situations that involve a significant amount of turbulent energy dissipation.
Often it is possible to make an empirical correction to the model.
Note that undistorted long-wave models will maintain similitude of the turbulent
dissipation processes, because they follow the same scaling criteria as short-wave models.
As in short-wave models, the viscous shear stress terms result in the fact
that viscous forces can only be scaled correctly in a long-wave model when
the Reynolds scaling criterion is met. At the slower flow speeds in the longwave physical model, laminar boundary layers are more likely to occur at
locations where turbulent boundary layers occur in the prototype, and this
situation must be avoided in order to comply with the long-wave scaling
requirements. It is standard practice to add artificial boundary roughness
elements to some models in order to assure that fully rough conditions exist
in the model. The resulting turbulent boundary layer will not be in exact
similitude; however, it will generally be closer to representing what occurs
in the prototype than if a laminar boundary layer is allowed to occur.
CHAPTER 4. HYDRODYNAMIC MODELS
Chapter 3 discussed the difficulties in maintaining similarity of both Froude
and Reynolds numbers in the same model, and usually coastal models do
not fulfill the Reynolds criterion.
Finally, Condition 4 revealed that vertical viscous shear stresses will
only be in similitude when the long-wave model is geometrically undistorted, so we conclude that
Long-wave models maintain similitude of vertical viscous shear stresses only when the model is geometrically undistorted and the Reynolds criterion has been
met.
In summary, examination of similitude requirements resulting from the
vertically integrated fluid equations of motion for long waves reveals that
flow patterns and velocity distributions in long-wave hydrodynamic models
are essentially governed by inertia and gravity effects because similitude of
Froude number must be maintained between model and prototype. However, the assumption of negligible vertical fluid velocities and hydrostatic
pressure variation in the inviscid flow region allows relaxation of the model
requirements so that geometrically distorted models (horizontal scale different than the vertical scale) can be considered.
The turbulent shear stress terms were not included in the equations
of motion, and we do not anticipate any large scale turbulent dissipation
such as associated with wave breaking. Hence, we can expect a scale effect
to be associated with turbulent dissipation if it occurs in a geometrically
distorted15 long-wave model. Careful evaluation must be made of model
situations that involve a significant amount of turbulent energy dissipation.
Often it is possible to make an empirical correction to the model.
Note that undistorted long-wave models will maintain similitude of the turbulent
dissipation processes, because they follow the same scaling criteria as short-wave models.
As in short-wave models, the viscous shear stress terms result in the fact
that viscous forces can only be scaled correctly in a long-wave model when
the Reynolds scaling criterion is met. At the slower flow speeds in the longwave physical model, laminar boundary layers are more likely to occur at
locations where turbulent boundary layers occur in the prototype, and this
situation must be avoided in order to comply with the long-wave scaling
requirements. It is standard practice to add artificial boundary roughness
elements to some models in order to assure that fully rough conditions exist
in the model. The resulting turbulent boundary layer will not be in exact
similitude; however, it will generally be closer to representing what occurs
in the prototype than if a laminar boundary layer is allowed to occur.