131 



Directional Trend A first estimate for the directional trend of the wave field is 

 computed from the gradients of the dynamic pressure. A set of complex direction 

 vectors are computed: 



7t ■ fdpd.m\ fdpd.m . .dpd,m\ ,^.-.. 



V^ = sign (^-^J (^-^ + r^^) (6.11) 



The spatial gradients are estimated from finite difference approximation from the 

 measured pressures, and the time gradient is computed from a fitted smoothing spline 

 (de Boor 1978) of the estimated dynamic pressure at the center of the array. 



For the single wave method, the estimated propagation direction is the orientation 

 of the mean of the complex direction vectors: 



^ = angle f^f^:^„j (6.12) 



For the two wave method, the two dominant propagation directions are defined 

 as the angles of the means of the sets of direction vectors within n greater than and 

 less than the mean direction: 



/ 1 ^' \ 



6i = angle — — 2_] Dm 1 where: < angle(^m) < + rr 



/ 1 ^2 \ 



&2 = angle [ — — Y^ Dm ) where: — n < angle(^m) < ^ 



V^2 V / 



(6.13) 



Frequency The frequency is computed from the second derivative of the pressure 

 at the center of the arrav. 



1 d^pd,c,m ^g_^4^ 



Pd,c,m df^ 



where g'^;"'"' is computed from the same smoothed spline used above. For the two 

 wave method, it is assumed that the bimodal sea is the result of reflection, so that 

 the same frequency is used as the first estimate for both waves. 



Wave Numbers The wave numbers are estimated from the linear dispersion rela- 

 tion. 



(a; — KnUnY — gK-a tanh. Knh, kx,n = Kn cosdn, ky^n = A'„ sin ^„ (6.15) 



