Ursell Number Calculator

✖The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level.ⓘ Wave Height for Surface Gravity Waves [H_w]			+10% -10%
✖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%

✖Ursell Number is defined as the ratio of the square of the wave height to the product of the wavelength and the water depth.ⓘ Ursell Number [U]

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Formula

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Ursell Number

Formula

`"U" = ("H"_{"w"}*"λ"_{"o"}^2)/"d"^3`

Example

`"0.147"=("3m"*("7m")^2)/("10m")^3`

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Ursell Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3
U = (H_w*λ_o^2)/d^3
This formula uses 4 Variables

Variables Used

Ursell Number - Ursell Number is defined as the ratio of the square of the wave height to the product of the wavelength and the water depth.
Wave Height for Surface Gravity Waves - (Measured in Meter) - The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level.
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

Wave Height for Surface Gravity Waves: 3 Meter --> 3 Meter No Conversion Required
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

U = (H_w*λ_o^2)/d^3 --> (3*7^2)/10^3

Evaluating ... ...

U = 0.147

STEP 3: Convert Result to Output's Unit

0.147 --> No Conversion Required

FINAL ANSWER

0.147 <-- Ursell Number

(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!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 14 Non-Linear Wave Theory Calculators

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

Ursell Number Formula

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

What is Cnoidal Theory?

The Cnoidal Theory for the steady water wave problem follows from a shallow water approximation, in which it is assumed that the waves are much longer than the water is deep.
Various versions of cnoidal theory have been presented. Fenton (1979) gave a fifth-order theory, which assumed that current was zero. This was corrected in a review article by Fenton (1990), and a more modern version was given in another review article by Fenton (1999a).

How to Calculate Ursell Number?

Ursell Number calculator uses Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3 to calculate the Ursell Number, The Ursell Number is defined as the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953. Ursell Number is denoted by U symbol.

How to calculate Ursell Number using this online calculator? To use this online calculator for Ursell Number, enter Wave Height for Surface Gravity Waves (H_w), Deep-Water Wavelength (λ_o) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Ursell Number calculation can be explained with given input values -> 0.147 = (3*7^2)/10^3.

FAQ

What is Ursell Number?

The Ursell Number is defined as the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953 and is represented as U = (H_w*λ_o^2)/d^3 or Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3. The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level, 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 Ursell Number?

The Ursell Number is defined as the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953 is calculated using Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3. To calculate Ursell Number, you need Wave Height for Surface Gravity Waves (H_w), Deep-Water Wavelength (λ_o) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Wave Height for Surface Gravity Waves, 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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