3.3. HYDRAULIC SIMILITUDE
79
Kinematic Scales. In Eqn. 3.36,
is the same as the horizontal length scale,
Nx', Nh is the same as the vertical length scale, N z\ and the wave period scale, Nt,
is the same as the time scale, Nt. Making these substitutions and rearranging gives
the distorted long wave time scale in terms of the horizontal and vertical scales, i.e.,
The distorted long wave horizontal velocity scale ratio is found as
Nx
Nx
/KT KT
Nu =
= ~'~Nx
= V N9NZ
The horizontal acceleration scale ratio in a distorted long wave model is given as
„ _Nu _ VMgNz _ NaNz
a ~ Nt
~ Nx
y/NgNz
Finally, the distorted long wave horizontal discharge scale ratio is found by noting
the cross-sectional area scale is NzNx, so the volume scale is TVz(Nx)2, and
Nq = Nz(^'x? = Wz^-)2. = JVx(JV,)1/2(JVz)3/2
The above example illustrates that distorted models can be useful in
coastal engineering. However, the distorted model designed to the above
guidance (Eqn. 3.36 or 3.38) is only useful for problems related to long wave
action.