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# getjonswappeakedness

## PURPOSE

Peakedness factor Gamma given Hm0 and Tp for JONSWAP

## SYNOPSIS

gam = getjonswappeakedness(Hm0,Tp)

## DESCRIPTION

``` GETJONSWAPPEAKEDNESS Peakedness factor Gamma given Hm0 and Tp for JONSWAP

CALL: Gamma =  getJonswapPeakedness(Hm0,Tp);

Hm0   = significant wave height [m].
Tp    = peak period [s]
gamma = Peakedness parameter of the JONSWAP spectrum

GETJONSWAPPEAKEDNESS relate GAMMA to Hm0 and Tp.
A standard value for GAMMA is 3.3. However, a more correct approach is
to relate GAMMA to Hm0 and Tp:
D = 0.036-0.0056*Tp/sqrt(Hm0);
gamma = exp(3.484*(1-0.1975*D*Tp^4/(Hm0^2)));
This parameterization is based on qualitative considerations of deep water
wave data from the North Sea, see Torsethaugen et. al. (1984)
Here GAMMA is limited to 1..7.

NOTE: The size of GAMMA is the common size of Hm0 and Tp.

Example
Hm0 = linspace(1,20);
Tp = Hm0;
[T,H] = meshgrid(Tp,Hm0);
gam = getjonswappeakedness(H,T);
contourf(Tp,Hm0,gam,1:7),fcolorbar(1:7)

Hm0 = 1:10;
Tp  = linspace(2,16);
[T,H] = meshgrid(Tp,Hm0);
gam =  getjonswappeakedness(H,T);
plot(Tp,gam)
xlabel('Tp [s]')
ylabel('Peakedness parameter')

## CROSS-REFERENCE INFORMATION

This function calls:
 comnsize Check if all input arguments are either scalar or of common size. error Display message and abort function.
This function is called by:
 jhnlwparfun Wave height, Hd, distribution parameters for Stokes waves with Jonswap spectrum. jhscdf Joint (Scf,Hd) CDF for linear waves with a JONSWAP spectrum. jhsnlcdf Joint (Scf,Hd) CDF for non-linear waves with JONSWAP spectrum. jhsnlpdf Joint (Scf,Hd) PDF for nonlinear waves with a JONSWAP spectra. jhsnlpdf2 Joint (Scf,Hd) PDF for non-linear waves with a JONSWAP spectra. jhspdf Joint (Scf,Hd) PDF for linear waves with JONSWAP spectra. jhspdf2 Joint (Scf,Hd) PDF for linear waves with a JONSWAP spectrum. jhvcdf Joint (Vcf,Hd) CDF for linear waves with JONSWAP spectrum. jhvnlcdf Joint (Vcf,Hd) CDF for non-linear waves with JONSWAP spectrum. jhvnlpdf Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. jhvnlpdf2 Joint (Vcf,Hd) PDF for non-linear waves with a JONSWAP spectrum. jhvpdf Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. jhvpdf2 Joint (Vcf,Hd) PDF for linear waves with a JONSWAP spectrum. jhwparfun Wave height, Hd, distribution parameters for Jonswap spectrum. jonswap Calculates (and plots) a JONSWAP spectral density

## SOURCE CODE

```001 function gam = getjonswappeakedness(Hm0,Tp)
002 %GETJONSWAPPEAKEDNESS Peakedness factor Gamma given Hm0 and Tp for JONSWAP
003 %
004 %  CALL: Gamma =  getJonswapPeakedness(Hm0,Tp);
005 %
006 % Hm0   = significant wave height [m].
007 % Tp    = peak period [s]
008 % gamma = Peakedness parameter of the JONSWAP spectrum
009 %
010 %  GETJONSWAPPEAKEDNESS relate GAMMA to Hm0 and Tp.
011 %  A standard value for GAMMA is 3.3. However, a more correct approach is
012 %  to relate GAMMA to Hm0 and Tp:
013 %        D = 0.036-0.0056*Tp/sqrt(Hm0);
014 %        gamma = exp(3.484*(1-0.1975*D*Tp^4/(Hm0^2)));
015 %  This parameterization is based on qualitative considerations of deep water
016 %  wave data from the North Sea, see Torsethaugen et. al. (1984)
017 %  Here GAMMA is limited to 1..7.
018 %
019 %  NOTE: The size of GAMMA is the common size of Hm0 and Tp.
020 %
021 % Example
022 % Hm0 = linspace(1,20);
023 % Tp = Hm0;
024 % [T,H] = meshgrid(Tp,Hm0);
025 % gam = getjonswappeakedness(H,T);
026 % contourf(Tp,Hm0,gam,1:7),fcolorbar(1:7)
027 %
028 % Hm0 = 1:10;
029 % Tp  = linspace(2,16);
030 % [T,H] = meshgrid(Tp,Hm0);
031 % gam =  getjonswappeakedness(H,T);
032 % plot(Tp,gam)
033 % xlabel('Tp [s]')
034 % ylabel('Peakedness parameter')
035 %
037
038 % Tested on matlab 6.1
039 %History
040 % revised pab 13april2004
041 % -made sure gamma is 1 if Tp/sqrt(Hm0) > 5.1429
042 % by pab 11Jan2004
043
044   error(nargchk(2,2,nargin))
045   [errorcode,Hm0,Tp] = comnsize(Hm0,Tp);
046   if errorcode > 0
047     error('Requires non-scalar arguments to match in size.');
048   end
049   x   = Tp./sqrt(Hm0);
050
051   gam = ones(size(x));
052
053   k1 = find(x<=5.14285714285714);
054   if any(k1), %limiting gamma to [1 7]
055     D       = 0.036-0.0056*x(k1); % approx 5.061*Hm0^2/Tp^4*(1-0.287*log(gam));
056     gam(k1) = min(exp(3.484*( 1-0.1975*D.*x(k1).^4 ) ),7); % gamma
057   end
058   return```

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

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