Spectral Energy Density or Classical Moskowitz Spectrum Calculator

✖Dimensionless Constant are numbers having no units attached and having a numerical value that is independent of whatever system of units may be used.ⓘ Dimensionless Constant [λ]			+10% -10%
✖Coriolis Frequency also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate Ω of the Earth multiplied by the sine of the latitude φ.ⓘ Coriolis Frequency [f]			+10% -10%
✖Limiting Frequency for a fully developed Wave Spectrum assumed to be a function fully of wind speed.ⓘ Limiting Frequency [f_u]			+10% -10%

✖Spectral Energy Density is independent of wind speed and saturated region of spectral energy density is assumed to exist in some region from spectral peak to frequencies sufficiently high.ⓘ Spectral Energy Density or Classical Moskowitz Spectrum [E_(f)]

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Formula

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Spectral Energy Density or Classical Moskowitz Spectrum

Formula

`"E"_{"(f)"} = (("λ"*("[g]"^2)*("f"^-5))/(2*pi)^4)*exp(0.74*("f"/"f"_{"u"})^-4)`

Example

`"0.003085"=(("1.6"*("[g]"^2)*(("2")^-5))/(2*pi)^4)*exp(0.74*("2"/"0.0001")^-4)`

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Spectral Energy Density or Classical Moskowitz Spectrum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spectral Energy Density = ((Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4)*exp(0.74*(Coriolis Frequency/Limiting Frequency)^-4)
E_(f) = ((λ*([g]^2)*(f^-5))/(2*pi)^4)*exp(0.74*(f/f_u)^-4)
This formula uses 2 Constants, 1 Functions, 4 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

Spectral Energy Density - Spectral Energy Density is independent of wind speed and saturated region of spectral energy density is assumed to exist in some region from spectral peak to frequencies sufficiently high.
Dimensionless Constant - Dimensionless Constant are numbers having no units attached and having a numerical value that is independent of whatever system of units may be used.
Coriolis Frequency - Coriolis Frequency also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate Ω of the Earth multiplied by the sine of the latitude φ.
Limiting Frequency - Limiting Frequency for a fully developed Wave Spectrum assumed to be a function fully of wind speed.

STEP 1: Convert Input(s) to Base Unit

Dimensionless Constant: 1.6 --> No Conversion Required
Coriolis Frequency: 2 --> No Conversion Required
Limiting Frequency: 0.0001 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_(f) = ((λ*([g]^2)*(f^-5))/(2*pi)^4)*exp(0.74*(f/f_u)^-4) --> ((1.6*([g]^2)*(2^-5))/(2*pi)^4)*exp(0.74*(2/0.0001)^-4)

Evaluating ... ...

E_(f) = 0.00308526080579487

STEP 3: Convert Result to Output's Unit

0.00308526080579487 --> No Conversion Required

FINAL ANSWER

0.00308526080579487 ≈ 0.003085 <-- Spectral Energy Density

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

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NSS College of Engineering (NSSCE), Palakkad

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< 9 Wave Hindcasting and Forecasting Calculators

Spectral Energy Density or Classical Moskowitz Spectrum

Go Spectral Energy Density = ((Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4)*exp(0.74*(Coriolis Frequency/Limiting Frequency)^-4)

Straight-Line Distance over which Wind Blows

Go Straight Line Distance over which Wind Blows = (Friction Velocity^2/[g])*5.23*10^-3*([g]*Wind Duration/Friction Velocity)^(3/2)

Wind Speed given Time required for Waves crossing Fetch under Wind Velocity

Go Wind Speed = ((77.23*Straight Line Distance over which Wind Blows^0.67)/(Time required for Waves crossing Fetch*[g]^0.33))^(1/0.34)

Straight-Line Distance given Time required for Waves Crossing Fetch under Wind Velocity

Go Straight Line Distance over which Wind Blows = ((Time required for Waves crossing Fetch*Wind Speed^0.34*[g]^0.33)/77.23)^(1/0.67)

Time required for Waves Crossing Fetch under Wind Velocity to become Fetch Limited

Go Time required for Waves crossing Fetch = 77.23*(Straight Line Distance over which Wind Blows^0.67/(Wind Speed^0.34*[g]^0.33))

Spectral Energy Density

Go Spectral Energy Density = (Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4

Water Depth for given Limiting Wave Period

Go Water Depth from Bed = [g]*(Limiting Wave Period/9.78)^(1/0.5)

Limiting Wave Period

Go Limiting Wave Period = 9.78*((Water Depth from Bed/[g])^0.5)

Drag Coefficient for Wind Speed at 10m Elevation

Go Drag Coefficient = 0.001*(1.1+(0.035*Wind Speed at Height of 10 m))

Spectral Energy Density or Classical Moskowitz Spectrum Formula

What is Coriolis Frequency?

The Coriolis frequency ƒ, also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate Ω of the Earth multiplied by the sine of the latitude φ.

How to Calculate Spectral Energy Density or Classical Moskowitz Spectrum?

Spectral Energy Density or Classical Moskowitz Spectrum calculator uses Spectral Energy Density = ((Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4)*exp(0.74*(Coriolis Frequency/Limiting Frequency)^-4) to calculate the Spectral Energy Density, The Spectral Energy Density or Classical Moskowitz Spectrum formula is defined as a parameter describing how the energy of a signal or a time series is distributed with frequency such that Limiting Frequency for a fully developed Wave Spectrum is assumed to be a function fully of wind speed. Spectral Energy Density is denoted by E_(f) symbol.

How to calculate Spectral Energy Density or Classical Moskowitz Spectrum using this online calculator? To use this online calculator for Spectral Energy Density or Classical Moskowitz Spectrum, enter Dimensionless Constant (λ), Coriolis Frequency (f) & Limiting Frequency (f_u) and hit the calculate button. Here is how the Spectral Energy Density or Classical Moskowitz Spectrum calculation can be explained with given input values -> 0.003085 = ((1.6*([g]^2)*(2^-5))/(2*pi)^4)*exp(0.74*(2/0.0001)^-4).

FAQ

What is Spectral Energy Density or Classical Moskowitz Spectrum?

The Spectral Energy Density or Classical Moskowitz Spectrum formula is defined as a parameter describing how the energy of a signal or a time series is distributed with frequency such that Limiting Frequency for a fully developed Wave Spectrum is assumed to be a function fully of wind speed and is represented as E_(f) = ((λ*([g]^2)*(f^-5))/(2*pi)^4)*exp(0.74*(f/f_u)^-4) or Spectral Energy Density = ((Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4)*exp(0.74*(Coriolis Frequency/Limiting Frequency)^-4). Dimensionless Constant are numbers having no units attached and having a numerical value that is independent of whatever system of units may be used, Coriolis Frequency also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate Ω of the Earth multiplied by the sine of the latitude φ & Limiting Frequency for a fully developed Wave Spectrum assumed to be a function fully of wind speed.

How to calculate Spectral Energy Density or Classical Moskowitz Spectrum?

The Spectral Energy Density or Classical Moskowitz Spectrum formula is defined as a parameter describing how the energy of a signal or a time series is distributed with frequency such that Limiting Frequency for a fully developed Wave Spectrum is assumed to be a function fully of wind speed is calculated using Spectral Energy Density = ((Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4)*exp(0.74*(Coriolis Frequency/Limiting Frequency)^-4). To calculate Spectral Energy Density or Classical Moskowitz Spectrum, you need Dimensionless Constant (λ), Coriolis Frequency (f) & Limiting Frequency (f_u). With our tool, you need to enter the respective value for Dimensionless Constant, Coriolis Frequency & Limiting Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Spectral Energy Density?

In this formula, Spectral Energy Density uses Dimensionless Constant, Coriolis Frequency & Limiting Frequency. We can use 1 other way(s) to calculate the same, which is/are as follows -

Spectral Energy Density = (Dimensionless Constant*([g]^2)*(Coriolis Frequency^-5))/(2*pi)^4

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