Maximum Wave Steepness for Waves Travelling Calculator

✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%
✖Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.ⓘ Wavelength [λ]			+10% -10%

✖Wave Steepness is defined as the ratio of wave height H to the wavelength λ.ⓘ Maximum Wave Steepness for Waves Travelling [ε_s]

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Formula

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Maximum Wave Steepness for Waves Travelling

Formula

`"ε"_{"s"} = 0.142*tanh(2*pi*"d"/"λ")`

Example

`"0.142"=0.142*tanh(2*pi*"1.05m"/"2.1nm")`

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Maximum Wave Steepness for Waves Travelling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength)
ε_s = 0.142*tanh(2*pi*d/λ)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Wave Steepness - Wave Steepness is defined as the ratio of wave height H to the wavelength λ.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.
Wavelength - (Measured in Meter) - Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.

STEP 1: Convert Input(s) to Base Unit

Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
Wavelength: 2.1 Nanometer --> 2.1E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_s = 0.142*tanh(2*pi*d/λ) --> 0.142*tanh(2*pi*1.05/2.1E-09)

Evaluating ... ...

ε_s = 0.142

STEP 3: Convert Result to Output's Unit

0.142 --> No Conversion Required

FINAL ANSWER

0.142 <-- Wave Steepness

(Calculation completed in 00.004 seconds)

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Credits

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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< 18 Wave Parameters Calculators

Major horizontal semi-axis given wavelength, wave height and water depth

Go Horizontal Semi-axis of water particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength)

Minor vertical semi-axis given wavelength, wave height and water depth

Go Vertical Semi-axis = (Wave Height/2)*(sinh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength)

Eckart's Equation for Wavelength

Go Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g]))

Water Depth for maximum wave steepness of waves travelling

Go Water Depth = Wavelength*atanh(Wave Steepness/0.142)/(2*pi)

Wavelength for maximum wave steepness

Go Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142)

Maximum Wave Steepness for Waves Travelling

Go Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength)

Wave Amplitude given Elevation of Water Surface Relative to SWL

Go Wave Amplitude = Elevation of Water Surface/cos(Theta)

Elevation of Water Surface Relative to SWL

Go Elevation of Water Surface = Wave Amplitude*cos(Theta)

Phase Velocity or Wave Celerity given Radian Frequency and Wavenumber

Go Celerity of The Wave = Wave Angular Frequency/Wave Number

Radian Frequency given Wave Celerity

Go Wave Angular Frequency = Celerity of The Wave*Wave Number

Wave Number given Wave Celerity

Go Wave Number = Wave Angular Frequency/Celerity of The Wave

Phase Velocity or Wave Celerity

Go Celerity of The Wave = Wavelength/Wave Period

Angular of Radian Frequency of Wave

Go Wave Angular Frequency = 2*pi/Wave Period

Wave Steepness

Go Wave Steepness = Wave Height/Wavelength

Wave number given wavelength

Go Wave Number = 2*pi/Wavelength

Wave Height given Maximum Wave Steepness Limit by Michell

Go Wave Height = Wavelength*0.142

Wavelength given Maximum Wave Steepness Limit by Michell

Go Wavelength = Wave Height/0.142

Wave Amplitude

Go Wave Amplitude = Wave Height/2

Maximum Wave Steepness for Waves Travelling Formula

Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength)
ε_s = 0.142*tanh(2*pi*d/λ)

What causes wave?

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 Maximum Wave Steepness for Waves Travelling?

Maximum Wave Steepness for Waves Travelling calculator uses Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength) to calculate the Wave Steepness, The Maximum Wave Steepness for Waves Travelling in Depths less than Lo/2 by Michell is defined as the ratio of wave height H to the wavelength λ.The maximum wave height occurs for a wave steepness H / λ ≈ 0.1412, above which no periodic surface gravity waves exist. Wave Steepness is denoted by ε_s symbol.

How to calculate Maximum Wave Steepness for Waves Travelling using this online calculator? To use this online calculator for Maximum Wave Steepness for Waves Travelling, enter Water Depth (d) & Wavelength (λ) and hit the calculate button. Here is how the Maximum Wave Steepness for Waves Travelling calculation can be explained with given input values -> 0.142 = 0.142*tanh(2*pi*1.05/2.1E-09).

FAQ

What is Maximum Wave Steepness for Waves Travelling?

The Maximum Wave Steepness for Waves Travelling in Depths less than Lo/2 by Michell is defined as the ratio of wave height H to the wavelength λ.The maximum wave height occurs for a wave steepness H / λ ≈ 0.1412, above which no periodic surface gravity waves exist and is represented as ε_s = 0.142*tanh(2*pi*d/λ) or Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength). Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body & Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.

How to calculate Maximum Wave Steepness for Waves Travelling?

The Maximum Wave Steepness for Waves Travelling in Depths less than Lo/2 by Michell is defined as the ratio of wave height H to the wavelength λ.The maximum wave height occurs for a wave steepness H / λ ≈ 0.1412, above which no periodic surface gravity waves exist is calculated using Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength). To calculate Maximum Wave Steepness for Waves Travelling, you need Water Depth (d) & Wavelength (λ). With our tool, you need to enter the respective value for Water Depth & Wavelength 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 Wave Steepness?

In this formula, Wave Steepness uses Water Depth & Wavelength. We can use 1 other way(s) to calculate the same, which is/are as follows -

Wave Steepness = Wave Height/Wavelength

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