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# ewwdir

## 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:
 gravity returns the constant acceleration of gravity w2k Translates from frequency to wave number error Display message and abort function. meshgrid X and Y arrays for 3-D plots.
This function is called by:
 dirsp2chitwo gives parameters in non-central CHI-TWO process for directional Stokes waves.

## 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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