V. MODEL SCALE EFFECTS 



1 . Causes of Physical Model Scale Effects . 



Wave energy dissipation and resulting reduction of wave height produced by 

 a breakwater are due to a combination of laminar and turbulent energy loss as 

 well as wave modification. Little information is available on scale effects 

 of wave transmission by overtopping, but scale effects are probably small. 

 This is illustrated by Saville (1963) who tested wave transmission by over- 

 topping for similar breakwaters that differed by a scale of 10. There was 

 little systematic difference between the results of tests run at the two scales, 

 with the small-scale tests being slightly conservative. 



Wave transmission through permeable breakwaters is controlled primarily by 

 laminar and turbulent energy loss of flow through the structure (Wilson and 

 Cross, 1972; Keulegan, 1973; Madsen and White, 1976). In the protoytpe the 

 wave height reduction is due largely to turbulent effects, but in a model 

 laminar and turbulent losses may be important so that a moduli underpredicts 

 the coefficient of transmission through a breakwater. The size of the scale 

 effect is a complex function of model design, water depth, and wave height and 

 period. 



2 . Interpreting and Applying Laboratory Results to Prototype Conditions . 



The recommended method of estimating scale effects of transmission through 

 permeable breakwaters is to use the computer program MADSEN to predict transmis- 

 sion coefficients for the model and prototype. The physical model correction 

 factor, CF, is defined as the expected coefficient of wave transmission 

 through the structure in the prototype divided by the coefficient of wave trans- 

 mission through the structure at the model scale. CF is determined by first 

 running the program MADSEN with prototype conditions to determine Ky^ (MADSEN 

 prototype) . The program is then rion at the model scale to determine Ky^ 

 (MADSEN scale model). CF is defined as 



Ky^ (MADSEN prototype) 



CF = (18) 



Ky^ (MADSEN scale model) 



The coefficient for wave transmission through the structure measured in the 

 physical scale model should then be multiplied by CF to estimate the prototype 

 coefficient. 



For example, assume that the laboratory breakwater tested by Sollitt and 

 Cross (1976) is a 1 on 10-scale Froude model of a prototype structure (Fig. 47) . 

 There was no transmission by overtopping. The program MADSEN was run at both 

 model and prototype scales and the results together with the physical model 

 measurements are shown in Figure 48. The MADSEN program output shows that the 

 physical model was probably underpredicting the prototype coefficient because 

 the scale model has proportionally more laminar energy loss than the prototype. 

 Even in this large 1 on 10-scale Froude physical model, the prototype Ky^ is 

 expected to be as much as 20 percent higher than in the scale model over the 

 range of conditions tested. 



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