# JONSWAP

The JONSWAP spectra in the wave-frequency domain

Controller:
## Dependents

## Interface

C++

HTML

## 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_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

## 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

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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)

**JONSWAP_wp**(above) to obtain w_{p}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

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

Source code is available when you buy a Commercial licence.

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