Equilibrium Form of PM Spectrum for Fully-Developed Seas Calculator

✖Wave Frequency is the number of waves that pass a fixed point in a given amount of time.ⓘ Wave Frequency [f]			+10% -10%
✖Wind Speed is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature.ⓘ Wind Speed [U]			+10% -10%

✖Frequency Energy Spectrum or wave energy spectral density or Spectral Energy Density.ⓘ Equilibrium Form of PM Spectrum for Fully-Developed Seas [E_f]

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Formula

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Equilibrium Form of PM Spectrum for Fully-Developed Seas

Formula

`"E"_{"f"} = ((0.0081*"[g]"^2)/((2*pi)^4*"f"^5))*exp(-0.24*((2*pi*"U"*"f")/"[g]")^-4)`

Example

`"1.5E^-8"=((0.0081*"[g]"^2)/((2*pi)^4*("8kHz")^5))*exp(-0.24*((2*pi*"4m/s"*"8kHz")/"[g]")^-4)`

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Equilibrium Form of PM Spectrum for Fully-Developed Seas Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4)
E_f = ((0.0081*[g]^2)/((2*pi)^4*f^5))*exp(-0.24*((2*pi*U*f)/[g])^-4)
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Frequency Energy Spectrum - Frequency Energy Spectrum or wave energy spectral density or Spectral Energy Density.
Wave Frequency - (Measured in Kilohertz) - Wave Frequency is the number of waves that pass a fixed point in a given amount of time.
Wind Speed - (Measured in Meter per Second) - Wind Speed is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature.

STEP 1: Convert Input(s) to Base Unit

Wave Frequency: 8 Kilohertz --> 8 Kilohertz No Conversion Required
Wind Speed: 4 Meter per Second --> 4 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_f = ((0.0081*[g]^2)/((2*pi)^4*f^5))*exp(-0.24*((2*pi*U*f)/[g])^-4) --> ((0.0081*[g]^2)/((2*pi)^4*8^5))*exp(-0.24*((2*pi*4*8)/[g])^-4)

Evaluating ... ...

E_f = 1.52530386864411E-08

STEP 3: Convert Result to Output's Unit

1.52530386864411E-08 --> No Conversion Required

FINAL ANSWER

1.52530386864411E-08 ≈ 1.5E-8 <-- Frequency Energy Spectrum

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Period Distribution and Wave Spectrum » Equilibrium Form of PM Spectrum for Fully-Developed Seas

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Coorg Institute of Technology (CIT), Coorg

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< 12 Wave Period Distribution and Wave Spectrum Calculators

Equilibrium Form of PM Spectrum for Fully-Developed Seas

Go Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4)

Most Probable Maximum Wave Period

Go Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2))

Probability Density of Wave Period

Go Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4)

Wave Component Amplitude

Go Wave Amplitude = sqrt(0.5*sqrt(Coefficient of Wave Component Amplitude^2+Coefficient of Wave Component Amplitude bn^2))

Spectral Bandwidth

Go Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))

Spectral Width

Go Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1)

Mean Zero-upcrossing Period

Go Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2)

Relative Phase given coefficients

Go Relative Phase = atanh(Coefficient of Wave Component Amplitude bn/Coefficient of Wave Component Amplitude)

Mean Crest Period

Go Wave Crest Period = 2*pi*(Moment of Wave Spectrum 2/Moment of Wave Spectrum 4)

Mean Wave Period

Go Wave Period = 2*pi*(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1)

Normal Distribution with Wave Period

Go Wave Period = Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1

Maximum Wave Period

Go Maximum Wave Period = Coefficient Eckman*Mean Wave Period

Equilibrium Form of PM Spectrum for Fully-Developed Seas Formula

Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4)
E_f = ((0.0081*[g]^2)/((2*pi)^4*f^5))*exp(-0.24*((2*pi*U*f)/[g])^-4)

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

What is the definition of wave spectrum?

Wave Spectrum is a concept used to describe the distribution of energy among waves of different period. Wave speed increases with wave length, so distant storms may be detected by the increase of energy in long period waves.

How to Calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas?

Equilibrium Form of PM Spectrum for Fully-Developed Seas calculator uses Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4) to calculate the Frequency Energy Spectrum, The Equilibrium form of PM Spectrum for fully-developed seas is expressed in terms of wave frequency and wind speed . PM spectrum describes a fully developed sea with one parameter, the wind speed, and assumes that both the fetch and duration are infinite. Frequency Energy Spectrum is denoted by E_f symbol.

How to calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas using this online calculator? To use this online calculator for Equilibrium Form of PM Spectrum for Fully-Developed Seas, enter Wave Frequency (f) & Wind Speed (U) and hit the calculate button. Here is how the Equilibrium Form of PM Spectrum for Fully-Developed Seas calculation can be explained with given input values -> 1.5E-8 = ((0.0081*[g]^2)/((2*pi)^4*8000^5))*exp(-0.24*((2*pi*4*8000)/[g])^-4).

FAQ

What is Equilibrium Form of PM Spectrum for Fully-Developed Seas?

The Equilibrium form of PM Spectrum for fully-developed seas is expressed in terms of wave frequency and wind speed . PM spectrum describes a fully developed sea with one parameter, the wind speed, and assumes that both the fetch and duration are infinite and is represented as E_f = ((0.0081*[g]^2)/((2*pi)^4*f^5))*exp(-0.24*((2*pi*U*f)/[g])^-4) or Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4). Wave Frequency is the number of waves that pass a fixed point in a given amount of time & Wind Speed is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature.

How to calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas?

The Equilibrium form of PM Spectrum for fully-developed seas is expressed in terms of wave frequency and wind speed . PM spectrum describes a fully developed sea with one parameter, the wind speed, and assumes that both the fetch and duration are infinite is calculated using Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4). To calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas, you need Wave Frequency (f) & Wind Speed (U). With our tool, you need to enter the respective value for Wave Frequency & Wind Speed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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