60. Using the notation for scale ratios and noting that, in an undistorted Froude model, the scale for 

 the water velocity will be the same as the time scale. Equation 9 becomes 



or 



N^Nt = N^ (11) 



where 



(i-tfc) 



61. In essence, the scaling guidance given by Equation 10 is a more generalized version of the guidance 

 determined with the fall speed parameter (Equation 6). The scaling guidance given by Equation 10 agrees 

 with that given by Equation 6 if the scale ratio TV, is equal to unity. 



62. Examining Equation 12, there are two conditions by which A'^, could approach unity. The first is if 

 Umax ^ Ut in both the prototype and model. This would be representative of highly turbulent conditions, 

 such as exist in the surf zone during energetic wave conditions; and in the limit it corresponds somewhat to 

 the physical description given by Gourlay' and Dean (1973) for a suspended grain falling through the 

 water column under the influence of horizontal currents. 



63. The other conditions leading to unit value for N, is if the ratio Ut/Umax is kept similar between 

 prototype and model. Although there may be unique cases where this similarity could be maintained, in 

 general the investigator will be unable to satisfy both the fall speed scale and the grain size scale necessary 

 to meet this condition. Even if possible, the scaling would be valid for only one specific hydrodynamic 

 condition because Umax depends on wave period and wave height, whereas [/, is independent of wave 

 height. This would hamper investigations using irregular waves, as well as studies in which numerous 

 regular wave periods were of interest. The best achievable situation, if scaling according to the fall speed 

 parameter guidance (Equation 6), is that where velocity ratios (Ut/Umax) remain reasonably close in value 

 for the prototype grain size and the derived model grain size. 



64. The preceding discussion may help to explain why distorted model scaling guidance using bed 

 materials similar in size to the prototype perform well in the surf zone, but suffer in the comparisons for 

 the region seaward of breaking (Dette and Uliczka 1986, Fowler and Smith 1987). In the surf zone, Umax is 

 typically much larger than (/, , and the scale ratio A'^, will be approximately unity. Seaward of the wave 

 breaking zone, model sand grains having approximately the same mean diameter as the prototype sand will 

 undergo transition to a bed-load dominant transport mode in the model sooner than the equivalent 

 transition in the prototype, and the seaward migration of the sand will be less in the model than in the 

 prototype (for the case of net offshore transport conditions). 



^ Gourlay, op. cit. 



23 



