. The directional analysis of ocean waves : an introductory discussion. Ocean waves. S' (Jl,m,fo) = (zero where i? + m^ i' K^ a power density >_ 0 for 9? + H = K^^. S'(£,m,fQ) thus defines power density at f = f^ for wave energy over 0 < 6 < Ztt. Figure 3 illustrates this case in wave number space. S(ji, m, fj S'(X,, m,, fj. r + m^ = Kf FIGURE 3. DIRECTIONAL WAVE SPECTRUM AT A FIXED FREQUENCY, f We want to estimate the shape of S'(Jl,m,fQ) above the circle l^ + m'' K in a directional wave train analysis. Remember, the S'(Jl,m,f ) above is restricted to f >_ 0 and is, in fact, equal
. The directional analysis of ocean waves : an introductory discussion. Ocean waves. S' (Jl,m,fo) = (zero where i? + m^ i' K^ a power density >_ 0 for 9? + H = K^^. S'(£,m,fQ) thus defines power density at f = f^ for wave energy over 0 < 6 < Ztt. Figure 3 illustrates this case in wave number space. S(ji, m, fj S'(X,, m,, fj. r + m^ = Kf FIGURE 3. DIRECTIONAL WAVE SPECTRUM AT A FIXED FREQUENCY, f We want to estimate the shape of S'(Jl,m,fQ) above the circle l^ + m'' K in a directional wave train analysis. Remember, the S'(Jl,m,f ) above is restricted to f >_ 0 and is, in fact, equal to where if ri(x,y,t) is to be real. () Let us see how S' (£,m,f) might be found: we have said that Ti(x,y,t) can be assumed to be a stationary Gaussian process. One char- acteristic of such a process is that for fixed values (xq, y^, t^) qf_ -the_pro£ess_ipdicas»_j5_Cx^i. y^.t^) is random^y with a Gaussian distribution; ?rek(>l(*..y*.0].)= jj:^^ e*^^^ i 1. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Bennett, Carl M; Naval Coastal Systems Laboratory (U. S. ). Panama City, Fla. : Naval Coastal Systems Laboratory
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