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# phi1

## PURPOSE

factor for transforming spectra to finite water depth spectra

ph=phi1(w,h)

## DESCRIPTION

``` PHI1 factor for transforming spectra to finite water depth spectra

CALL: tr = phi1(w,h)

tr = vector of transformation factors
w = angular frequency
h = water depth

Example: Transform a JONSWAP spectrum to a spectrum for waterdepth = 30 m
S = jonswap;
S1=S; S1.S=S1.S.*phi1(S1.w,30);```

## CROSS-REFERENCE INFORMATION

This function calls:
 gravity returns the constant acceleration of gravity w2k Translates from frequency to wave number
This function is called by:
 Chapter2 % CHAPTER2 Modelling random loads and stochastic waves

## SOURCE CODE

```001 function ph=phi1(w,h)
002 %PHI1 factor for transforming spectra to finite water depth spectra
003 %
004 % CALL: tr = phi1(w,h)
005 %
006 %    tr = vector of transformation factors
007 %     w = angular frequency
008 %     h = water depth
009 %
010 % Example: Transform a JONSWAP spectrum to a spectrum for waterdepth = 30 m
011 %   S = jonswap;
012 %   S1=S; S1.S=S1.S.*phi1(S1.w,30);
013
014 % Reference
015 % Buows, E., Gunther, H., Rosenthal, W. and Vincent, C.L. (1985)
016 % 'Similarity of the wind wave spectrum in finite depth water: 1 spectral form.'
017 %  J. Geophys. Res., Vol 90, No. C1, pp 975-986
018
019 % Tested on: Matlab 5.2
020 % History:
021 % by pab 16.02.2000
022 g=gravity;
023 if h==inf, % special case infinite water depth
024   ph=ones(size(w));
025   return
026 end
027 ph=zeros(size(w));
028
029 k1=w2k(w,0,inf);
030 dw1=2*w/g; % dw/dk|h=inf
031 k2=w2k(w,0,h);
032
033 dw2=ph;
034 ix=find(k1~=0);
035
036 dw2(ix)=dw1(ix)./(tanh(k2(ix)*h)+k2(ix)*h./cosh(k2(ix)*h).^2); % % dw/dk|h=h0
037 ph(ix)=(k1(ix)./k2(ix)).^3.*dw2(ix)./dw1(ix);```

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

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