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JONSWAP

The JONSWAP spectra in the wave-frequency domain
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Dependents

Info

Interface

C++

Overview

The JONSWAP (Joint North Sea Wave Project) spectra is an empirical relationship that defines the distribution of energy with frequency within the ocean.

The JONSWAP spectrum is effectively a fetch-limited version of the Pierson-Moskowitz spectrum, except that the wave spectrum is never fully developed and may continue to develop due to non-linear wave-wave interactions for a very long time. Therefore in the JONSWAP spectrum, waves continues to grow with distance (or time) as specified by the α (alpha) term, and the peak in the spectrum is more pronounced, as specified by the γ (gamma) term. Hasselmann (1966) found the latter to be particularly important as it lead to enhanced non-linear interactions.

References

JONSWAP Gnnw

 
doubleJONSWAP_Gnnwdoublew
doublewp
doublealpha = 0.0081
doublegamma = 3.3
doublebeta = 1.25 )
The JONSWAP (Joint North Sea Wave Project) spectra is an empirical relationship that defines the distribution of energy with frequency within the ocean.

The underlying equation is: where
  • \displaystyle a=\exp \left [-\frac{(\omega - \omega_p)^2}{2 w_p^2 \sigma^2} \right ]
  • \displaystyle \sigma = \begin{cases} 0.07 & \text{ if } \omega\leq \omega_p  \\ 0.09 & \text{ if } \omega>\omega_p \end{cases}
  • \displaystyle \beta = \frac{5}{4}
  • α is a constant that relates to the wind speed and fetch length, see below. Typical values in the northern north sea are in the range of 0.0081 to 0.01
  • ω is the wave frequency
  • \omega_p is the peak wave-frequency

Most problems is the literature are expressed in the above form. However if a particular wind speed and fetch length are known, then α and \omega_p can be estimated using the subsequent two functions.

For a range of typical north sea conditions (where α =0.0081 and \omega_p=2 \pi/12.4=0.5), but with varying peak enhancements the JONSWAP spectra has the form
There is an error with your graph parameters for JONSWAP_Gnnw with options w=0:1.5 wp=0.5 alpha=0.0081 gamma=1:3.3:4

Error Message:Function JONSWAP_Gnnw failed. Ensure that: Invalid C++

Standards

This function conforms to British Standards (BS 6349-1:2000), 24 July 2003.

Parameters

wwave-frequency (2 π/s)
wpthe peak wave frequency (2 π/s)
alphaThe intensity of the Spectra. Default value = 0.0081
gammaPeak enhancement factor. Default value = 3.3
betaA shape factor (Rarely changed). Default value = 1.25
Source Code

Source code is available when you buy a Commercial licence.

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JONSWAP Wp

 
doubleJONSWAP_wpdoublewind
doublelength )
The peak of the JONSWAP spectrum is empirically define by where
  • U_W is the wind speed at 10m above the sea surface
  • L_F is the fetch length

Standards

This function conforms to British Standards (BS 6349-1:2000), 24 July 2003.

Parameters

windThe wind speed 10m above the sea surface. [m/s]
lengthThe fetch length. [m]
Source Code

Source code is available when you buy a Commercial licence.

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JONSWAP Alpha

 
doubleJONSWAP_alphadoublewind
doublelength )
The overall energy within the JONSWAP spectrum is controlled by the α constant and is related to wind speed and the peak frequency by: where
  • U_W is the wind speed at 10m above the sea surface
  • \omega_p is the peak frequency calculated using equation (2)

This function uses JONSWAP_wp (above) to obtain wp for a given fetch length and wind speed.

Parameters

windThe wind speed 10m above the sea surface. [m/s]
lengthThe fetch length. [m]
Source Code

Source code is available when you buy a Commercial licence.

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JONSWAP Gnnk

 
doubleJONSWAP_Gnnkdoublek
doublewp
doubledepth = 0
doublealpha = 0.0081
doublegamma = 3.3
doublebeta = 1.25 )
Uses the description of the JONSWAP spectra described in frequency to obtain the distribution in wave-number using the 1st order dispersion relationship give in dispersion.

This conversion is thus

where in deep water and in shallow water

For a range of north sea conditions (where α =0.0081 and \omega_p=2 \pi/12.4=0.5), but with varying peak enhancements the JONSWAP spectra has the following form in wave-number:
There is an error with your graph parameters for JONSWAP_Gnnk with options k=0:0.1 wp=0.5 alpha=0.0081 gamma=1:3.3:4 depth=0

Error Message:Function JONSWAP_Gnnk failed. Ensure that: Invalid C++

Parameters

kWave-number (2 π/m)
wpThe peak wave frequency
depthThe water depth. Default value=0 (infinite depth)
alphaThe intensity of the spectra. Default value = 0.01
gammaThe peak enhancement factor. Default value = 3.3
betaA shape factor (Rarely changed). Default value = 1.25
Source Code

Source code is available when you buy a Commercial licence.

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