JONSWAP Spectrum for Fetch-limited Seas Calculator

✖Dimensionless Scaling Parameter is used in the JONSWAP spectrum for fetch-limited seas.ⓘ Dimensionless Scaling Parameter [α]			+10% -10%
✖Wave Frequency is the number of waves that pass a fixed point in a given amount of time.ⓘ Wave Frequency [f]			+10% -10%
✖Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time.ⓘ Frequency at Spectral Peak [f_p]			+10% -10%
✖Peak Enhancement Factor refers to a ratio used to quantify the increase in force or load experienced by a structure during extreme events, such as storms or earthquakes.ⓘ Peak Enhancement Factor [γ]			+10% -10%
✖Standard Deviation is a statistical measure used to quantify the amount of variation or dispersion of a set of data points from the mean (average).ⓘ Standard Deviation [σ]			+10% -10%

✖Frequency Energy Spectrum refers to a representation of the distribution of energy across different frequencies within a system or environment.ⓘ JONSWAP Spectrum for Fetch-limited Seas [E_f]

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Formula

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JONSWAP Spectrum for Fetch-limited Seas

Formula

`"E"_{"f"} = (("α"*"[g]"^2)/((2*pi)^4*"f"^5))*(exp(-1.25*("f"/"f"_{"p"})^-4)*"γ")^exp(-(("f"/"f"_{"p"})-1)^2/(2*"σ"^2))`

Example

`"2.9E^-22"=(("0.1538"*"[g]"^2)/((2*pi)^4*("8kHz")^5))*(exp(-1.25*("8kHz"/"0.013162kHz")^-4)*"5")^exp(-(("8kHz"/"0.013162kHz")-1)^2/(2*("1.33")^2))`

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JONSWAP Spectrum for Fetch-limited Seas Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2))
E_f = ((α*[g]^2)/((2*pi)^4*f^5))*(exp(-1.25*(f/f_p)^-4)*γ)^exp(-((f/f_p)-1)^2/(2*σ^2))
This formula uses 2 Constants, 1 Functions, 6 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 refers to a representation of the distribution of energy across different frequencies within a system or environment.
Dimensionless Scaling Parameter - Dimensionless Scaling Parameter is used in the JONSWAP spectrum for fetch-limited seas.
Wave Frequency - (Measured in Hertz) - Wave Frequency is the number of waves that pass a fixed point in a given amount of time.
Frequency at Spectral Peak - (Measured in Hertz) - Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time.
Peak Enhancement Factor - Peak Enhancement Factor refers to a ratio used to quantify the increase in force or load experienced by a structure during extreme events, such as storms or earthquakes.
Standard Deviation - Standard Deviation is a statistical measure used to quantify the amount of variation or dispersion of a set of data points from the mean (average).

STEP 1: Convert Input(s) to Base Unit

Dimensionless Scaling Parameter: 0.1538 --> No Conversion Required
Wave Frequency: 8 Kilohertz --> 8000 Hertz (Check conversion here)
Frequency at Spectral Peak: 0.013162 Kilohertz --> 13.162 Hertz (Check conversion here)
Peak Enhancement Factor: 5 --> No Conversion Required
Standard Deviation: 1.33 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_f = ((α*[g]^2)/((2*pi)^4*f^5))*(exp(-1.25*(f/f_p)^-4)*γ)^exp(-((f/f_p)-1)^2/(2*σ^2)) --> ((0.1538*[g]^2)/((2*pi)^4*8000^5))*(exp(-1.25*(8000/13.162)^-4)*5)^exp(-((8000/13.162)-1)^2/(2*1.33^2))

Evaluating ... ...

E_f = 2.89619819293977E-22

STEP 3: Convert Result to Output's Unit

2.89619819293977E-22 --> No Conversion Required

FINAL ANSWER

2.89619819293977E-22 ≈ 2.9E-22 <-- Frequency Energy Spectrum

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Parametric Spectrum Models » JONSWAP Spectrum for Fetch-limited Seas

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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JONSWAP Spectrum for Fetch-limited Seas

Go Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2))

Frequency of Spectral Peak

Go Frequency at Spectral Peak = ([g]*18.8*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.33)/(2*pi*Wind Speed at Height of 10 m)

Frequency of Spectral Peak Given Wind Speed

Go Frequency at Spectral Peak = ([g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5))/(2*pi*Wind Speed at Height of 10 m)

Wind Speed given Maximum Controlling Parameter for Angular Distribution

Go Wind Speed at Height of 10 m = [g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5)/(2*pi*Frequency at Spectral Peak)

Maximum Controlling Parameter for Angular Distribution

Go Controlling Parameter for the Angular Distribution = 11.5*((2*pi*Frequency at Spectral Peak*Wind Speed at Height of 10 m)/[g])^-2.5

Wind Speed at Elevation 10m above Sea Surface given Scaling Parameter

Go Wind Speed at Height of 10 m = ((Fetch Length*[g])/(Dimensionless Scaling Parameter/0.076)^(-1/0.22))^0.5

Fetch Length given Scaling Parameter

Go Fetch Length = (Wind Speed at Height of 10 m^2*((Dimensionless Scaling Parameter/0.076)^-(1/0.22)))/[g]

Scaling Parameter

Go Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22

Dimensionless Time

Go Dimensionless Time = ([g]*Time for Dimensionless Parameter Calculation)/Friction Velocity

Significant Wave Height given Significant Wave Height of Lower and Higher frequency Components

Go Significant Wave Height = sqrt(Significant Wave Height 1^2+Significant Wave Height 2^2)

Significant Wave Height of Higher Frequency Component

Go Significant Wave Height 2 = sqrt(Significant Wave Height^2-Significant Wave Height 1^2)

Significant Wave Height of Lower Frequency Component

Go Significant Wave Height 1 = sqrt(Significant Wave Height^2-Significant Wave Height 2^2)

Fetch Length given Frequency at Spectral Peak

Go Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2

Frequency at Spectral Peak

Go Frequency at Spectral Peak = 3.5*(([g]^2*Fetch Length)/Wind Speed at Height of 10 m^3)^-0.33

Shape Factor for Higher Frequency Component

Go Shape Factor for Higher Frequency Component = 1.82*exp(-0.027*Significant Wave Height)

Wind Speed at Elevation 10m above Sea Surface given Frequency at Spectral Peak

Go Wind Speed = ((Fetch Length*[g]^2)/(Frequency at Spectral Peak/3.5)^-(1/0.33))^(1/3)

Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water

Go Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5

Weighing Factor for Angular Frequency greater than One

Go Weighing Factor for Angular Frequency = 1-0.5*(2-Coast Wave Angular Frequency)^2

Weighing Factor for Angular Frequency Lesser than or Equal to One

Go Weighing Factor = 0.5*Wave Angular Frequency^2

JONSWAP Spectrum for Fetch-limited Seas Formula

What is JONSWAP Spectrum?

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.

How to Calculate JONSWAP Spectrum for Fetch-limited Seas?

JONSWAP Spectrum for Fetch-limited Seas calculator uses Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)) to calculate the Frequency Energy Spectrum, The JONSWAP Spectrum for Fetch-limited Seas is defined as a Situation in which wave energy (or wave height) is limited by the size of the wave generation area (fetch). Frequency Energy Spectrum is denoted by E_f symbol.

How to calculate JONSWAP Spectrum for Fetch-limited Seas using this online calculator? To use this online calculator for JONSWAP Spectrum for Fetch-limited Seas, enter Dimensionless Scaling Parameter (α), Wave Frequency (f), Frequency at Spectral Peak (f_p), Peak Enhancement Factor (γ) & Standard Deviation (σ) and hit the calculate button. Here is how the JONSWAP Spectrum for Fetch-limited Seas calculation can be explained with given input values -> 2.9E-22 = ((0.1538*[g]^2)/((2*pi)^4*8000^5))*(exp(-1.25*(8000/13.162)^-4)*5)^exp(-((8000/13.162)-1)^2/(2*1.33^2)).

FAQ

What is JONSWAP Spectrum for Fetch-limited Seas?

The JONSWAP Spectrum for Fetch-limited Seas is defined as a Situation in which wave energy (or wave height) is limited by the size of the wave generation area (fetch) and is represented as E_f = ((α*[g]^2)/((2*pi)^4*f^5))*(exp(-1.25*(f/f_p)^-4)*γ)^exp(-((f/f_p)-1)^2/(2*σ^2)) or Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)). Dimensionless Scaling Parameter is used in the JONSWAP spectrum for fetch-limited seas, Wave Frequency is the number of waves that pass a fixed point in a given amount of time, Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time, Peak Enhancement Factor refers to a ratio used to quantify the increase in force or load experienced by a structure during extreme events, such as storms or earthquakes & Standard Deviation is a statistical measure used to quantify the amount of variation or dispersion of a set of data points from the mean (average).

How to calculate JONSWAP Spectrum for Fetch-limited Seas?

The JONSWAP Spectrum for Fetch-limited Seas is defined as a Situation in which wave energy (or wave height) is limited by the size of the wave generation area (fetch) is calculated using Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)). To calculate JONSWAP Spectrum for Fetch-limited Seas, you need Dimensionless Scaling Parameter (α), Wave Frequency (f), Frequency at Spectral Peak (f_p), Peak Enhancement Factor (γ) & Standard Deviation (σ). With our tool, you need to enter the respective value for Dimensionless Scaling Parameter, Wave Frequency, Frequency at Spectral Peak, Peak Enhancement Factor & Standard Deviation 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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