142
CHAPTER 4. HYDRODYNAMIC MODELS
Ny = Ng Nz
(4.110)
Additionally, correct reproduction of time variations in nonsteady flows
requires similitude of the Strouhal number {Condition 2, Eqn. 4.106), which
when combined with Condition 1 leads to the time scale for current variations,
N-t — ,
■ =
(4.111)
which is the same as the time scale for wave period (Eqn. 4.107).
We again recognize that our usual inability to satisfy the Reynolds criterion (given by Condition 5) means that similitude of combined horizontal
currents and long waves is restricted to the region of the flow field that is
considered to be inviscid. Current-induced boundary layers will not be in
similitude if viscous forces are significant or if boundary roughness is not
correctly scaled. Similitude requirements for boundary layers and shear
stresses for long waves are discussed shortly.
Finally, the directions of horizontal currents scaled and reproduced in
a geometrically distorted long-wave physical model must be same as in the
prototype in order have the correct influence on the waves (and vice versa).
Refraction and Diffraction in Long-Wave Models
Refraction and diffraction in un distorted long-wave models will accurately
portray the prototype situation, the same as undistorted short-wave models.
But unlike distorted short-wave models,
Geometrically distorted long-wave models will also reproduce refraction and diffraction accurately so long as
the long-waves obey the shallow water approximation.
(Hudson, et al. 1979).
The requirement for refraction developed from Snell’s Law was derived
earlier in general form for short-wave models, and it is given by Eqns. 4.28
and 4.29. For waves that conform to the shallow water linear wave approximation, wavelength is given as
C=^=y/^h
(4.112)
where T is wave period, L is wavelength, h is depth, and g is gravity. From
this approximation it is seen that long waves travel at the same speed,
irrespective of wave period.
CHAPTER 4. HYDRODYNAMIC MODELS
Ny = Ng Nz
(4.110)
Additionally, correct reproduction of time variations in nonsteady flows
requires similitude of the Strouhal number {Condition 2, Eqn. 4.106), which
when combined with Condition 1 leads to the time scale for current variations,
N-t — ,
■ =
(4.111)
which is the same as the time scale for wave period (Eqn. 4.107).
We again recognize that our usual inability to satisfy the Reynolds criterion (given by Condition 5) means that similitude of combined horizontal
currents and long waves is restricted to the region of the flow field that is
considered to be inviscid. Current-induced boundary layers will not be in
similitude if viscous forces are significant or if boundary roughness is not
correctly scaled. Similitude requirements for boundary layers and shear
stresses for long waves are discussed shortly.
Finally, the directions of horizontal currents scaled and reproduced in
a geometrically distorted long-wave physical model must be same as in the
prototype in order have the correct influence on the waves (and vice versa).
Refraction and Diffraction in Long-Wave Models
Refraction and diffraction in un distorted long-wave models will accurately
portray the prototype situation, the same as undistorted short-wave models.
But unlike distorted short-wave models,
Geometrically distorted long-wave models will also reproduce refraction and diffraction accurately so long as
the long-waves obey the shallow water approximation.
(Hudson, et al. 1979).
The requirement for refraction developed from Snell’s Law was derived
earlier in general form for short-wave models, and it is given by Eqns. 4.28
and 4.29. For waves that conform to the shallow water linear wave approximation, wavelength is given as
C=^=y/^h
(4.112)
where T is wave period, L is wavelength, h is depth, and g is gravity. From
this approximation it is seen that long waves travel at the same speed,
irrespective of wave period.