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JONSWAP

The JONSWAP spectra in the wave-frequency domain
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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.

JONSWAP Gnnw

JONSWAP Gnnw Calculator

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 doubleJONSWAP_Gnnw( double w double wp double alpha = 0.0081 double gamma = 3.3 double beta = 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
• 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
• 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 can be estimated using the subsequent two functions.

For a range of typical north sea conditions (where α =0.0081 and =0.5), but with varying peak enhancements the JONSWAP spectra has the form

Standards

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

Parameters

 w wave-frequency (2 π/s) wp the peak wave frequency (2 π/s) alpha The intensity of the Spectra. Default value = 0.0081 gamma Peak enhancement factor. Default value = 3.3 beta A shape factor (Rarely changed). Default value = 1.25
Source Code

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JONSWAP Wp

 doubleJONSWAP_wp( double wind double length )
The peak of the JONSWAP spectrum is empirically define by where
• is the wind speed at 10m above the sea surface
• is the fetch length

Standards

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

Parameters

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

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JONSWAP Alpha

 doubleJONSWAP_alpha( double wind double length )
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
• is the wind speed at 10m above the sea surface
• 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

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

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JONSWAP Gnnk

JONSWAP Gnnk Calculator

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 doubleJONSWAP_Gnnk( double k double wp double depth = 0 double alpha = 0.0081 double gamma = 3.3 double beta = 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 =0.5), but with varying peak enhancements the JONSWAP spectra has the following form in wave-number:

Parameters

 k Wave-number (2 π/m) wp The peak wave frequency depth The water depth. Default value=0 (infinite depth) alpha The intensity of the spectra. Default value = 0.01 gamma The peak enhancement factor. Default value = 3.3 beta A shape factor (Rarely changed). Default value = 1.25
Source Code

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