Breslin, Savitsky, and Tsakonas 



The Effect of Shift of Wave Measurement on Reference Points 



Suppose that a wave system is moving from left to right in the direction of 

 positive X or ^ and one has by measurement a knowledge of the waves as a 

 function of time at x = <f and z = and asks what the fluid motion is at some 



^ o 



point X = <f and z = -^ "downwind" so ^ > ^^. The answer can be secured by 

 regarding the fluid as one following the linear system concept that at any dis- 

 crete frequency: 



output = input X unit frequency response function 



and thence to deduce an impulsive response function which is then convoluted 

 with the known wave record. 



However, a much more direct approach is to utilize the foregoing formulas 

 for heave response by regarding the body to be shrunk to a point and thus indis- 

 tinguishable from a fluid element. The heave frequency response function of the 

 ship- sea system contracts to 



$, = e 



and the vertical fluid motion at ^, i in terms of the surface motion r]{t;^^,0) is 



ZwCt;^-0 = J t7(t;^^,0) K„(t-T; ^-^„, O dr (52) 



- 00 



where the wave-induced impulsive response function is given by 



CO ^^l"l(^-^o) _^ 



(53) 



This integral can be expressed (as shown in Appendix A) by 



where 



R^ indicates that only the real part is to be retained, 



z = i -i(^-^,), 



Erfc is the complementary error function (which is tabulated for complex 

 arguments). 



(The plus sign is applied for positive time u and the minus for negative u.) 



474 



