Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point Calculator

✖Breaking Wave or breaker is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur.ⓘ Breaking Wave [ξ]			+10% -10%
✖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%
✖Beach slope refers to the incline or gradient of the shoreline, determining the rate at which the beach elevation changes horizontally with distance from the water.ⓘ Beach Slope [β]			+10% -10%

✖Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength.ⓘ Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point [λ_o]

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Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point

Formula

`"λ"_{"o"} = ("ξ"^2*"H"_{"w"})/"β"^2`

Example

`"6.992133m"=(("0.229")^2*"3m")/("0.15rad")^2`

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Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2
λ_o = (ξ^2*H_w)/β^2
This formula uses 4 Variables

Variables Used

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.
Breaking Wave - Breaking Wave or breaker is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur.
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.
Beach Slope - (Measured in Radian) - Beach slope refers to the incline or gradient of the shoreline, determining the rate at which the beach elevation changes horizontally with distance from the water.

STEP 1: Convert Input(s) to Base Unit

Breaking Wave: 0.229 --> No Conversion Required
Wave Height for Surface Gravity Waves: 3 Meter --> 3 Meter No Conversion Required
Beach Slope: 0.15 Radian --> 0.15 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ_o = (ξ^2*H_w)/β^2 --> (0.229^2*3)/0.15^2

Evaluating ... ...

λ_o = 6.99213333333333

STEP 3: Convert Result to Output's Unit

6.99213333333333 Meter --> No Conversion Required

FINAL ANSWER

6.99213333333333 ≈ 6.992133 Meter <-- Deep-Water Wavelength

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Shoaling, Refraction and Breaking » Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point

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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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National Institute of Technology (NIT), Warangal

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< 16 Shoaling, Refraction and Breaking Calculators

Shoaling Coefficient

Go Shoaling Coefficient = (tanh(Wave Number for Water Wave*Coastal Mean Depth)*(1+(2*Wave Number for Water Wave*Coastal Mean Depth/sinh(2*Wave Number for Water Wave*Coastal Mean Depth))))^-0.5

Shoaling Coefficient given Wave Celerity

Go Shoaling Coefficient = sqrt(Deepwater Wave Celerity/(Celerity of the Wave*2*Ratio of Group Velocity to Phase Velocity))

Beach Slope given Breaking Wave and Wave Height at Breaking Point

Go Beach Slope = Breaking Wave*sqrt(Wave Height for Surface Gravity Waves/Deep-Water Wavelength)

Breaking Wave given wave height at Breaking Point

Go Breaking Wave = Beach Slope/sqrt(Wave Height for Surface Gravity Waves/Deep-Water Wavelength)

Deepwater Wave Height for Shoaling Coefficient and Refraction Coefficient

Go Wave Height in Deepwater = Wave Height for Surface Gravity Waves/(Shoaling Coefficient*Refraction Coefficient)

Refraction Coefficient given Relative Change of Wave Height

Go Refraction Coefficient = Wave Height for Surface Gravity Waves/(Wave Height in Deepwater*Shoaling Coefficient)

Wave Height given Shoaling Coefficient and Refraction Coefficient

Go Wave Height for Surface Gravity Waves = Wave Height in Deepwater*Shoaling Coefficient*Refraction Coefficient

Refraction Coefficient

Go Refraction Coefficient = sqrt(Distance Between Two Rays at Deepwater/Distance Between Two Rays)

Wave Height at Breaking Point given Breaking Wave and Wave Height at Breaking Point

Go Wave Height for Surface Gravity Waves = (Deep-Water Wavelength*Beach Slope^2)/Breaking Wave^2

Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point

Go Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2

Distance between Two Rays at General Point

Go Distance Between Two Rays = Distance Between Two Rays at Deepwater/Refraction Coefficient^2

Shoaling Coefficient in Shallow Water

Go Shoaling Coefficient = 0.4466*(Deep-Water Wavelength/Water Depth in Ocean)^(1/4)

Water Depth when Reduced Shoaling Coefficient in shallow Water

Go Water Depth in Ocean = Deep-Water Wavelength/(Shoaling Coefficient/0.2821)^2

Deepwater Wavelength for Shoaling Coefficient in Shallow Water

Go Deep-Water Wavelength = (Shoaling Coefficient/0.4466)^4*Water Depth in Ocean

Wave Length for Reduced Shoaling Coefficient in Shallow Water

Go Deep-Water Wavelength = Water Depth in Ocean*(Shoaling Coefficient/0.2821)^2

Water Depth given Shoaling Coefficient in Shallow Water

Go Water Depth in Ocean = Deep-Water Wavelength/(Shoaling Coefficient/0.4466)^4

Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point Formula

Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2
λ_o = (ξ^2*H_w)/β^2

What is Breaking Wave?

In fluid dynamics, a breaking wave or breaker is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy.

How to Calculate Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point?

Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point calculator uses Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2 to calculate the Deep-Water Wavelength, The Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point is defined as the distance between any two corresponding points on successive wave crests or troughs. Deep-Water Wavelength is denoted by λ_o symbol.

How to calculate Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point using this online calculator? To use this online calculator for Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point, enter Breaking Wave (ξ), Wave Height for Surface Gravity Waves (H_w) & Beach Slope (β) and hit the calculate button. Here is how the Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point calculation can be explained with given input values -> 5.333333 = (0.229^2*3)/0.15^2.

FAQ

What is Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point?

The Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point is defined as the distance between any two corresponding points on successive wave crests or troughs and is represented as λ_o = (ξ^2*H_w)/β^2 or Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2. Breaking Wave or breaker is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur, 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 & Beach slope refers to the incline or gradient of the shoreline, determining the rate at which the beach elevation changes horizontally with distance from the water.

How to calculate Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point?

The Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point is defined as the distance between any two corresponding points on successive wave crests or troughs is calculated using Deep-Water Wavelength = (Breaking Wave^2*Wave Height for Surface Gravity Waves)/Beach Slope^2. To calculate Deepwater Wavelength given Wave Breaking and Wave Height at Breaking Point, you need Breaking Wave (ξ), Wave Height for Surface Gravity Waves (H_w) & Beach Slope (β). With our tool, you need to enter the respective value for Breaking Wave, Wave Height for Surface Gravity Waves & Beach Slope 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 Deep-Water Wavelength?

In this formula, Deep-Water Wavelength uses Breaking Wave, Wave Height for Surface Gravity Waves & Beach Slope. We can use 2 other way(s) to calculate the same, which is/are as follows -

Deep-Water Wavelength = Water Depth in Ocean*(Shoaling Coefficient/0.2821)^2
Deep-Water Wavelength = (Shoaling Coefficient/0.4466)^4*Water Depth in Ocean

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