Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton Calculator

✖Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength.ⓘ Deep-Water Wavelength [λ_o]			+10% -10%
✖Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Coastal Mean Depth [d]			+10% -10%

✖Relative Height as a function of Wavelength refers to the ratio of wave height to wavelength.ⓘ Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton [Hmd]

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Formula

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Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton

Formula

`"Hmd" = (0.141063*("λ"_{"o"}/"d")+0.0095721*("λ"_{"o"}/"d")^2+0.0077829*("λ"_{"o"}/"d")^3)/(1+0.078834*("λ"_{"o"}/"d")+0.0317567*("λ"_{"o"}/"d")^2+0.0093407*("λ"_{"o"}/"d")^3)`

Example

`"0.098798"=(0.141063*("7m"/"10m")+0.0095721*("7m"/"10m")^2+0.0077829*("7m"/"10m")^3)/(1+0.078834*("7m"/"10m")+0.0317567*("7m"/"10m")^2+0.0093407*("7m"/"10m")^3)`

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Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton Solution

STEP 0: Pre-Calculation Summary

Formula Used

Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3)
Hmd = (0.141063*(λ_o/d)+0.0095721*(λ_o/d)^2+0.0077829*(λ_o/d)^3)/(1+0.078834*(λ_o/d)+0.0317567*(λ_o/d)^2+0.0093407*(λ_o/d)^3)
This formula uses 3 Variables

Variables Used

Relative Height as a function of Wavelength - Relative Height as a function of Wavelength refers to the ratio of wave height to wavelength.
Deep-Water Wavelength - (Measured in Meter) - Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength.
Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

STEP 1: Convert Input(s) to Base Unit

Deep-Water Wavelength: 7 Meter --> 7 Meter No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Hmd = (0.141063*(λ_o/d)+0.0095721*(λ_o/d)^2+0.0077829*(λ_o/d)^3)/(1+0.078834*(λ_o/d)+0.0317567*(λ_o/d)^2+0.0093407*(λ_o/d)^3) --> (0.141063*(7/10)+0.0095721*(7/10)^2+0.0077829*(7/10)^3)/(1+0.078834*(7/10)+0.0317567*(7/10)^2+0.0093407*(7/10)^3)

Evaluating ... ...

Hmd = 0.0987980050454994

STEP 3: Convert Result to Output's Unit

0.0987980050454994 --> No Conversion Required

FINAL ANSWER

0.0987980050454994 ≈ 0.098798 <-- Relative Height as a function of Wavelength

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Non-Linear Wave Theory » Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton

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Coorg Institute of Technology (CIT), Coorg

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Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton

Go Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3)

Mean Depth given Ursell Number

Go Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)

Wavelength given Ursell Number

Go Deep-Water Wavelength = ((Ursell Number*Coastal Mean Depth^3)/Wave Height for Surface Gravity Waves)^0.5

Wave Height given Ursell Number

Go Wave Height for Surface Gravity Waves = (Ursell Number*Coastal Mean Depth^3)/Deep-Water Wavelength^2

Ursell Number

Go Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3

Volume Flow Rate per unit Span Underneath Waves given Second Type of Mean Fluid Speed

Go Rate of Volume Flow = Coastal Mean Depth*(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)

Wave Speed given Second First Type of Mean Fluid Speed

Go Fluid Stream Velocity = Mean Horizontal Fluid Velocity+(Rate of Volume Flow/Coastal Mean Depth)

Mean Depth given Second Type of Mean Fluid Speed

Go Coastal Mean Depth = Rate of Volume Flow/(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)

Second Type of Mean Fluid Speed

Go Mean Horizontal Fluid Velocity = Fluid Stream Velocity-(Rate of Volume Flow/Coastal Mean Depth)

Wave Speed given First Type of Mean Fluid Speed

Go Wave Speed = Fluid Stream Velocity-Mean Horizontal Fluid Velocity

First Type of Mean Fluid Speed

Go Mean Horizontal Fluid Velocity = Fluid Stream Velocity-Wave Speed

Volume Flow Rate in Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Rate of Volume Flow = Wave Speed*Coastal Mean Depth

Mean Depth in Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Coastal Mean Depth = Rate of Volume Flow/Wave Speed

Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Wave Speed = Rate of Volume Flow/Coastal Mean Depth

Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton Formula

What are the Main Theories for Steady Waves?

There are two main theories for steady waves – Stokes theory, most suitable for waves which are not very long relative to the water depth; and Cnoidal theory, suitable for the other limit where the waves are much longer than the depth. In addition there is one important numerical method – the Fourier approximation method which solves the problem accurately, and is now widely used in ocean and coastal engineering.

How to Calculate Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton?

Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton calculator uses Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3) to calculate the Relative Height as a function of Wavelength, The Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton is defined as an empirical expression for the relative height of the highest wave Hm/d as a function of wavelength obtained by Fenton (1990). Relative Height as a function of Wavelength is denoted by Hmd symbol.

How to calculate Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton using this online calculator? To use this online calculator for Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton, enter Deep-Water Wavelength (λ_o) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton calculation can be explained with given input values -> 0.098798 = (0.141063*(7/10)+0.0095721*(7/10)^2+0.0077829*(7/10)^3)/(1+0.078834*(7/10)+0.0317567*(7/10)^2+0.0093407*(7/10)^3).

FAQ

What is Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton?

The Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton is defined as an empirical expression for the relative height of the highest wave Hm/d as a function of wavelength obtained by Fenton (1990) and is represented as Hmd = (0.141063*(λ_o/d)+0.0095721*(λ_o/d)^2+0.0077829*(λ_o/d)^3)/(1+0.078834*(λ_o/d)+0.0317567*(λ_o/d)^2+0.0093407*(λ_o/d)^3) or Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3). Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength & Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

How to calculate Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton?

The Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton is defined as an empirical expression for the relative height of the highest wave Hm/d as a function of wavelength obtained by Fenton (1990) is calculated using Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3). To calculate Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton, you need Deep-Water Wavelength (λ_o) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Deep-Water Wavelength & Coastal Mean Depth 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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