influence the penetration of wave energy into the wave lee? of an island ares 

 (i) refraction by underwater topography, (il) refraction by currents, (iii) 

 diffraction, (iv) variability in direction of wave travel. These factor's rnny 

 be closely related. 



Refraction by underwater topography . The distribution of refracted wave energy 

 in the lee of an island is critically dependent upon the bottom slope. When 

 the wave approaches the shore, its velocity will be reduced due to the decreas- 

 ing depth of the water; and when the crests reach the beach they tend to become 

 parallel to the shoreline, regardless of their direction of approach from deep 

 water. The waves "wheel" around and b re alt nearly at right angles to the beach. 



In Run 13 (Figure 3c) a transparent cone-shaped island was introduced, with 

 uniformly sloping beaches extending above the water level. The slope of the 

 beach was lsl£ (see data in Table I). One can see clearly the refraction of 

 the waves on the beach: the widening of the crest-lines in the pictures 

 indicates the increase in wave heights toward the shore due to the convergence 

 of energy along the crest. 



Re fraction by currents . The wave characteristics such as steepness, length and 

 direction of travel will be changed when waves encounter currents, (i) The 

 steepnesses of waves meeting opposing currents increases, and when the current 

 is strong enough the waves might break, (ii) The wave steepnesses will be 

 reduced by a current in direction of the wave travel, (iii) When waves meet 

 a current at an angle, directional changes occur in wave travel. 



In these idealized ripple-tank studies no currents were present. The usual 

 semi-permanent currents around islands is not significant because of low current 

 velocities involved. However, tidal currents around the islands may be strong 

 enough to cause important refraction effects. 



Diffraction of waves around the islands . Wave energy is also propagated into 

 the lee of an island by diffraction, as well as by refraction. The effect of 

 such diffraction was estimated by Putmam and Arthur (Ref. 2). They utilized 

 the theory of diffraction of waves by a semiwinfinite plane barrier in water 

 of uniform depth as introduced by Penny and Price (Ref. 9). This theory does 

 not apply for small islands, but the results appear to be useful in the case of 

 large islands (many wave lengths in diameter). This is illustrated by compar- 

 ing the results of runs 15> to 2£ (Figs. 3f and 3g) where a wave-train is 

 interrupted by a cylinder with the axes perpendicular to the water surface and 

 with the cylinder diameter varying from 0.09 L to 6.5 L. It appears that very 

 small cylinders have almost no effect upon the wave train (Run l5» D = 0.09 L)» 

 For the cylinders with D = 0.8 L the effect of the cylinder was apparent to a 

 distance of approximately 3 wave lengths in the lee of the cylinder. This 

 distance increased with increasing cylinder diameter, until at D » 3»1 I» 

 (Run 23, Figure 3g) nearly circular waves passed around the cylinder without 

 interference effects in the lee. This phenomenon takes a relatively definite 

 configuration at a distance of approximately D - 6 L. Hence, it appears that 

 the theory of diffraction of waves around a semi-infinite breakwater tip might 

 be used for islands larger than 6 wave lengths (which compared with diffraction 

 at a breakwater gap) . However, more experiments are necessary before more 

 definite conclusions can be stated. 



Variability in direction of wave travel . The extent of the sheltered region in 

 the lee of an island depends largely upon the variability in direction of travel 

 of the incident waves, larger variability means an increase in wave intensity 

 in the sheltered area. 



10 



