Trough to Crest Wave Height Calculator

✖Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.ⓘ Water Depth for Cnoidal Wave [d_c]			+10% -10%
✖Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.ⓘ Distance from the Bottom to the Crest [y_c]			+10% -10%
✖Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.ⓘ Distance from the Bottom to the Wave Trough [y_t]			+10% -10%

✖Height of The Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Trough to Crest Wave Height [H_w]

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Formula

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Trough to Crest Wave Height

Formula

`"H"_{"w"} = "d"_{"c"}*(("y"_{"c"}/"d"_{"c"})-("y"_{"t"}/"d"_{"c"}))`

Example

`"14m"="16m"*(("35m"/"16m")-("21m"/"16m"))`

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Trough to Crest Wave Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))
H_w = d_c*((y_c/d_c)-(y_t/d_c))
This formula uses 4 Variables

Variables Used

Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.
Distance from the Bottom to the Crest - (Measured in Meter) - Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.
Distance from the Bottom to the Wave Trough - (Measured in Meter) - Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Distance from the Bottom to the Crest: 35 Meter --> 35 Meter No Conversion Required
Distance from the Bottom to the Wave Trough: 21 Meter --> 21 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_w = d_c*((y_c/d_c)-(y_t/d_c)) --> 16*((35/16)-(21/16))

Evaluating ... ...

H_w = 14

STEP 3: Convert Result to Output's Unit

14 Meter --> No Conversion Required

FINAL ANSWER

14 Meter <-- Height of The Wave

(Calculation completed in 00.004 seconds)

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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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< 14 Cnoidal Wave Theory Calculators

Wavelength for Distance from Bottom to Wave Trough

Go Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave)-1)))

Complete Elliptic Integral of Second Kind

Go Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind)

Wave Height given Distance from Bottom to Wave Trough and Water Depth

Go Height of The Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind)))

Wave Height Required to Produce Difference in Pressure on Seabed

Go Cnoidal Wave Height = Change in Pressure of Coast/((Density of Salt Water*[g])*(0.5+(0.5*sqrt(1-((3*Change in Pressure of Coast)/(Density of Salt Water*[g]*Water Depth for Cnoidal Wave))))))

Free Surface Elevation of Solitary Waves

Go Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))

Particle Velocities given Free Surface Elevation of Solitary Waves

Go Particle Velocity = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)/Height of The Wave

Distance from Bottom to Wave Trough

Go Distance from the Bottom to the Wave Trough = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Height of The Wave/Water Depth for Cnoidal Wave))

Distance from Bottom to Crest

Go Distance from the Bottom to the Crest = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of The Wave/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height

Go Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))

Wave Height when Free Surface Elevation of Solitary Waves

Go Cnoidal Wave Height = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)/(Particle Velocity*Water Depth for Cnoidal Wave)

Wavelength for Complete Elliptic Integral of First Kind

Go Wavelength of Wave = sqrt(16*Water Depth for Cnoidal Wave^3/(3*Height of The Wave))*Modulus of the Elliptic Integrals*Complete Elliptic Integral of the First Kind

Elevation above Bottom given Pressure under Cnoidal Wave in Hydrostatic Form

Go Elevation above the Bottom = -((Pressure Under Wave/(Density of Salt Water*[g]))-Ordinate of the Water Surface)

Ordinate of Water Surface given Pressure under Cnoidal Wave in Hydrostatic Form

Go Ordinate of the Water Surface = (Pressure Under Wave/(Density of Salt Water*[g]))+Elevation above the Bottom

Pressure under Cnoidal Wave in Hydrostatic Form

Go Pressure Under Wave = Density of Salt Water*[g]*(Ordinate of the Water Surface-Elevation above the Bottom)

Trough to Crest Wave Height Formula

What Causes Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves.

How to Calculate Trough to Crest Wave Height?

Trough to Crest Wave Height calculator uses Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)) to calculate the Height of The Wave, The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave. Height of The Wave is denoted by H_w symbol.

How to calculate Trough to Crest Wave Height using this online calculator? To use this online calculator for Trough to Crest Wave Height, enter Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Distance from the Bottom to the Wave Trough (y_t) and hit the calculate button. Here is how the Trough to Crest Wave Height calculation can be explained with given input values -> 14 = 16*((35/16)-(21/16)).

FAQ

What is Trough to Crest Wave Height?

The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave and is represented as H_w = d_c*((y_c/d_c)-(y_t/d_c)) or Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)). Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave & Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

How to calculate Trough to Crest Wave Height?

The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave is calculated using Height of The Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)). To calculate Trough to Crest Wave Height, you need Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Distance from the Bottom to the Wave Trough (y_t). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Distance from the Bottom to the Crest & Distance from the Bottom to the Wave Trough 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 Height of The Wave?

In this formula, Height of The Wave uses Water Depth for Cnoidal Wave, Distance from the Bottom to the Crest & Distance from the Bottom to the Wave Trough. We can use 1 other way(s) to calculate the same, which is/are as follows -

Height of The Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind)))

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