are given in terms of distance and velocity. Since horizontal motions are 

 highly constrained by mooring lines, the velocity criteria seem more useful 

 for present purposes (though they are stated to be applicable only for 

 fishing vessels, coasters, freighters, ferries, and Ro-Ro vessels). Velocity 

 criteria vary with size of ship, but they are as follows: 



it < 0.3-0.6 m /s 



(20) 



4. Damage at a wharf presumably occurs when forces (in mooring lines, 

 against fenders, against ship hull, etc.) are too great. Since force is equal 

 to mass times acceleration, it seems that an operational criterion based on 

 long wave accelerations would be most relevant to the physical problem. 



Intercomparison of existing criteria. It is useful to consider how consistent 

 the above four criteria are with each other. Slope, velocity, and acceleration 

 criteria can be inter-related by using equations for an idealized two-dimensional 

 standing wave. Velocity can be expressed as (Sorensen 1993) 



He . . 

 — sin kx sin at 

 d 



(21) 



where 



k = wave number, = 



2k 



x = horizontal coordinate 

 o~= frequency 

 t =time 

 Differentiating with respect to time gives an expression for acceleration, a 



du 

 ~dt 



He 



d 



2-kHc 

 Td 



a sin kx cos at 



sin fcc cos at 



(22) 





H 



— sin fcc cos at 

 T 



The term in parentheses is relatively constant (assuming that d is relatively 

 constant). The key variable is H/T. Thus it is clear that Wilson's slope criterion 



66 



Chapter 4 Numerical Model 



