4.2. SHORT-WAVE HYDRODYNAMIC MODELS
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Finally, the directions of currents scaled and reproduced in a geometrically undistorted 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 Short-Wave Models
It was mentioned previously that short-wave models cannot be distorted
because this would alter the flow patterns in the model. This concept
is best illustrated by the phenomenon of wave refraction. Refraction of
water waves over bathymetry of varying depths can be calculated using
Snell’s Law, which was originally formulated for optics. Figure 4.3 from
Figure 4.3: Wave Refraction During Shoaling [from Johnson, et al. (1948)].
Johnson, et al. (1948) shows wave crests approaching a beach north of
Oceanside, California, as sketched from an aerial photograph. Wave orthogonals perpendicular to the wave crests have been drawn on the figure.
The relationship5 between two water depths is given as
5 The following derivation comes from Dalrymple (1985).