# Pierson Moskowitz

**Contents**

## Dependents

## Interface

## Overview

The Pierson-Moskowitz (PM) spectra is an empirical relationship that defines the distribution of energy with frequency within the ocean. Developed in 1964 the PM spectrum is one of the simplest descriptions for the energy distribution. It assumes that if the wind blows steadily for a long time over a large area, then the waves will eventually reach a point of equilibrium with the wind. This is known as a*fully developed*sea. Pierson and Moskowitz developed their spectrum from measurements in the North Atlantic during 1964, and presented the following relationship between energy distribution and wind: where

- is a numerical constant =0.0081
- is a numerical constant =0.74
*g*is gravity*Missing Equation End: $U_{19*.4}Missing Equation End: $ is the wind speed at 19.4m above the sea surface.

### References

- http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_04.htm
- Massel, S.R. 1996. Ocean Surface Waves: Their Physics and Predictions. Advanced Series on Coastal Engineering. 11. London

## Standards

- These functions conform to British Standards (BS 6349-1:2000), 24 July 2003.
- These functions conform to European ISO standards 19901-1:2005

## PM Gnnw U

doublePM_Gnnw_U( | double | w | |

double | U | ||

double | alpha` = 0.0081` | ||

double | beta` = 1.25` | ) |

### Parameters

w wave-frequency () U is the wind speed at 19.4m above the sea surface (m/s) alpha controls the intensity of the Spectra, the default value is beta controls the shape factor,

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## PM Gnnw Wp

doublePM_Gnnw_wp( | double | w | |

double | wp | ||

double | alpha` = 0.0081` | ||

double | beta` = 1.25` | ) |

### 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 beta A shape factor. Default value = 1.25

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## PM Gnnw Tp

doublePM_Gnnw_Tp( | double | w | |

double | Hs | ||

double | Tp | ) |

### Parameters

w wave-frequency (2 π/s) Hs significant wave height (m) Tp peak wave period (s)

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## PM Gnnw Tz

doublePM_Gnnw_Tz( | double | w | |

double | Hs | ||

double | Tz | ) |

### Parameters

w wave-frequency (2 π/s) Hs significant wave height (m) Tz zero crossing period (s)

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## PM Wind To Wp

doublePM_wind_to_wp( | double | wind | ) |

- is the wind speed at 19.5m above the sea surface

### Parameters

wind The wind speed 19.4m above the sea surface. [m/s]

### Returns

- peak wave frequency (rad/s)

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## PM Wind To Tp

doublePM_wind_to_Tp( | double | wind | ) |

### Parameters

wind The wind speed 19.4m above the sea surface. [m/s]

### Returns

- peak wave frequency (rad/s)

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## PM Tp To Alpha

doublePM_Tp_to_alpha( | double | Hs | |

double | Tp | ) |

- is the significant wave heights (m)
- is the peak wave period (s)

### Parameters

Hs significant wave height (m), i.e. . Tp peak wave period, i.e. .

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## PM Tz To Alpha

doublePM_Tz_to_alpha( | double | Hs | |

double | Tz | ) |

- is the significant wave heights (m)
- is the zero crossing wave period (s)

### Parameters

Hs significant wave height (m), i.e. . Tz peak wave period, i.e. .

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## PM Tz To Tp

doublePM_Tz_to_Tp( | double | Tz | ) |

- is the peak wave period (s)
- is the zero crossing wave period (s)

### Parameters

Tz zero crossing wave period, .

### Returns

- the peak wave period,

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## PM Gnnk Wp

doublePM_Gnnk_wp( | double | k | |

double | wp | ||

double | depth` = 0` | ||

double | alpha` = 0.0081` | ||

double | beta` = 1.25` | ) |

### 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 beta Default value = 1.25

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