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ewwdir

PURPOSE ^

Computes values of the quadratic transfer function E, for quadratic sea

SYNOPSIS ^

[out]=ewwdir(omega,theta,omegat,thetat,h);

DESCRIPTION ^

  EWWDIR Computes values of the quadratic transfer function E, for quadratic sea  
  
   CALL:  [Eww]= ewwdir(w,th,wt,tht,h); 
    
      Eww  = a matrix with the quadratic transfer function E(w,th,wt,tht).  
      w,wt = two equally long vectors with angular frequencies. 
      w,wt = two equally long vectors with angular frequencies. 
      h    = water depth (default 5000 [m]). 
  
    Function uses w2k and is used in  dirsp2chitwo

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [out]=ewwdir(omega,theta,omegat,thetat,h); 
002 % EWWDIR Computes values of the quadratic transfer function E, for quadratic sea  
003 % 
004 %  CALL:  [Eww]= ewwdir(w,th,wt,tht,h); 
005 %   
006 %     Eww  = a matrix with the quadratic transfer function E(w,th,wt,tht).  
007 %     w,wt = two equally long vectors with angular frequencies. 
008 %     w,wt = two equally long vectors with angular frequencies. 
009 %     h    = water depth (default 5000 [m]). 
010 % 
011 %   Function uses w2k and is used in  dirsp2chitwo 
012  
013 % 
014 %---------------------------------------------------------------------- 
015 % References: Marc Prevosto "Statistics of wave crests from second 
016 % order irregular wave 3D models" 
017 % 
018 % Reduces to E(w,wt) from Eq.(6) in R. Butler, U. Machado, I. Rychlik (2002)  
019 % if th, tht are constant - longcrested sea eww.m. 
020 % By I.R 22.10.04 
021  
022 g=gravity; 
023 eps0=0.000001; 
024 if ((length(omega)~=length(omegat))|(length(theta)~=length(thetat))|(length(thetat)~=length(omegat))) 
025    error('error in input to eww_new')     
026 end 
027  
028 if nargin<5 | h<=0 
029   h=5000; 
030 end 
031  
032 [w wt]=meshgrid(omega,omegat); 
033 [th tht]=meshgrid(theta,thetat); 
034 wpl=w+wt; 
035  
036  
037 ind=find(abs(w.*wt)<eps0); 
038 ind1=find(abs(wpl)<eps0); 
039 wpl(ind)=1; 
040 w(ind)=1; 
041 wt(ind)=1; 
042       
043    kw=w2k(w,[],h,g); 
044    kwx=kw.*cos(th);   kwy=kw.*sin(th); 
045    kwt=w2k(wt,[],h,g); 
046    kwtx=kwt.*cos(tht);   kwty=kwt.*sin(tht); 
047    kk=sqrt((kwx+kwtx).^2+(kwy+kwty).^2); kkh=g*kk.*tanh(kk*h); 
048    Dkwkwt=(2*wpl.*(g^2*((kwx.*kwtx)+(kwy.*kwty))-(w.*wt).^2)+g^2*((kw.^2.*wt)+(kwt.^2.*w))-wt.*w.*(wt.^3+w.^3))... 
049    ./(2*w.*wt.*(wpl.^2-kkh)); 
050    Dkwkwt(ind1)=0.; 
051    out=(1/2/g)*(-g^2*((kwx.*kwtx)+(kwy.*kwty))./(w.*wt)+w.^2+wt.^2+w.*wt+2*wpl.*Dkwkwt); 
052    out(ind)=0; 
053

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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