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

✖Constant B often refers to the significant wave height. Significant wave height is defined as the average of the highest one-third of waves in a wave record.ⓘ Constant B [b]			+10% -10%
✖Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).ⓘ Wave Angular Frequency [ω]			+10% -10%

✖Phillip's Equilibrium Range of Spectrum is the range of wave frequencies for which the rate of energy input from the wind matches the rate of dissipation due to wave breaking.ⓘ Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water [E_ω]

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Formula

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

Formula

`"E"_{"ω"} = "b"*"[g]"^2*"ω"^-5`

Example

`"0.00105"="0.1"*"[g]"^2*("6.2rad/s")^-5`

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

STEP 0: Pre-Calculation Summary

Formula Used

Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5
E_ω = b*[g]^2*ω^-5
This formula uses 1 Constants, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Phillip's Equilibrium Range of Spectrum - Phillip's Equilibrium Range of Spectrum is the range of wave frequencies for which the rate of energy input from the wind matches the rate of dissipation due to wave breaking.
Constant B - Constant B often refers to the significant wave height. Significant wave height is defined as the average of the highest one-third of waves in a wave record.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).

STEP 1: Convert Input(s) to Base Unit

Constant B: 0.1 --> No Conversion Required
Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_ω = b*[g]^2*ω^-5 --> 0.1*[g]^2*6.2^-5

Evaluating ... ...

E_ω = 0.00104974279780533

STEP 3: Convert Result to Output's Unit

0.00104974279780533 --> No Conversion Required

FINAL ANSWER

0.00104974279780533 ≈ 0.00105 <-- Phillip's Equilibrium Range of Spectrum

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Parametric Spectrum Models » Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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National Institute of Technology (NIT), Warangal

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< 18 Parametric Spectrum Models Calculators

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 Lesser than or Equal to One

Go Weighing Factor = 0.5*Wave Angular Frequency^2

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

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

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.

How to Calculate Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water?

Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water calculator uses Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5 to calculate the Phillip's Equilibrium Range of Spectrum, The Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water formula is defined as the energy distribution of ocean waves in a fully developed sea state in deep water. Phillip's Equilibrium Range of Spectrum is denoted by E_ω symbol.

How to calculate Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water using this online calculator? To use this online calculator for Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water, enter Constant B (b) & Wave Angular Frequency (ω) and hit the calculate button. Here is how the Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water calculation can be explained with given input values -> 0.00105 = 0.1*[g]^2*6.2^-5.

FAQ

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

The Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water formula is defined as the energy distribution of ocean waves in a fully developed sea state in deep water and is represented as E_ω = b*[g]^2*ω^-5 or Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5. Constant B often refers to the significant wave height. Significant wave height is defined as the average of the highest one-third of waves in a wave record & Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).

How to calculate Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water?

The Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water formula is defined as the energy distribution of ocean waves in a fully developed sea state in deep water is calculated using Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5. To calculate Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water, you need Constant B (b) & Wave Angular Frequency (ω). With our tool, you need to enter the respective value for Constant B & Wave Angular Frequency 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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