Wave Height represented by Rayleigh Distribution Calculator

✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%
✖Root Mean Square Wave Height is a parameter influencing the Breaker Height Index that is commonly used to define the wave height at breaking in the saturated zones.ⓘ Root Mean Square Wave Height [H_rms]			+10% -10%

✖Individual Wave Height may be regarded as a stochastic variable represented by a probability distribution function.ⓘ Wave Height represented by Rayleigh Distribution [PH]

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Formula

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Wave Height represented by Rayleigh Distribution

Formula

`"PH" = (2*"H"/"H"_{"rms"}^2)*exp(-("H"^2/"H"_{"rms"}^2))`

Example

`"0.074851m"=(2*"3m"/("8.4m")^2)*exp(-(("3m")^2/("8.4m")^2))`

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Wave Height represented by Rayleigh Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2))
PH = (2*H/H_rms^2)*exp(-(H^2/H_rms^2))
This formula uses 1 Functions, 3 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Individual Wave Height - (Measured in Meter) - Individual Wave Height may be regarded as a stochastic variable represented by a probability distribution function.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Root Mean Square Wave Height - (Measured in Meter) - Root Mean Square Wave Height is a parameter influencing the Breaker Height Index that is commonly used to define the wave height at breaking in the saturated zones.

STEP 1: Convert Input(s) to Base Unit

Wave Height: 3 Meter --> 3 Meter No Conversion Required
Root Mean Square Wave Height: 8.4 Meter --> 8.4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

PH = (2*H/H_rms^2)*exp(-(H^2/H_rms^2)) --> (2*3/8.4^2)*exp(-(3^2/8.4^2))

Evaluating ... ...

PH = 0.0748510632696055

STEP 3: Convert Result to Output's Unit

0.0748510632696055 Meter --> No Conversion Required

FINAL ANSWER

0.0748510632696055 ≈ 0.074851 Meter <-- Individual Wave Height

(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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NSS College of Engineering (NSSCE), Palakkad

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< 20 Wave Height Calculators

Wave Height for Horizontal Fluid Particle Displacements

Go Wave Height = -Fluid Particle Displacements*(4*pi*Wavelength)*(cosh(2*pi*Water Depth/Wavelength))/([g]*Wave Period^2)*((cosh(2*pi*(Distance above the Bottom)/Wavelength)))*sin(Phase Angle)

Wave Height for Vertical Fluid Particle Displacements

Go Wave Height = Fluid Particle Displacements*(4*pi*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period^2*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))

Wave Height for Vertical Component of Local Fluid Velocity

Go Wave Height = (Vertical Component of Velocity*2*Wavelength)*cosh(2*pi*Water Depth/Wavelength)/([g]*Wave Period*sinh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))

Wave Height for Horizontal Component of Local Fluid Velocity

Go Wave Height = Water Particle Velocity*2*Wavelength*cosh(2*pi*Depth of Water Wave/Wavelength)/([g]*Wave Period*cosh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle))

Wave height for local fluid particle acceleration of vertical component

Go Wave Height = -(Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)))

Wave height for local fluid particle acceleration of horizontal component

Go Wave Height = Local Fluid Particle Acceleration*Wavelength*cosh(2*pi*Water Depth/Wavelength)/([g]*pi*cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle))

Wave Height for simplified horizontal fluid particle displacements

Go Wave Height = -Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/cosh(2*pi*(Distance above the Bottom)/Wavelength)*sin(Phase Angle)

Wave Height for simplified vertical fluid particle displacements

Go Wave Height = Fluid Particle Displacements*2*sinh(2*pi*Water Depth/Wavelength)/sinh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)

Wave height for major horizontal semi-axis given wavelength and wave height

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

Wave height for minor vertical semi-axis given wavelength, wave height and water depth

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

Wave Height represented by Rayleigh Distribution

Go Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2))

Wave Height represented by Rayleigh Distribution under Narrow Band Condition

Go Individual Wave Height = 1-exp(-Wave Height^2/Root Mean Square Wave Height^2)

Mean Wave Period given Maximum Wave Period

Go Mean Wave Period = Maximum Wave Period/Coefficient Eckman

Wave Height given wave steepness

Go Wave Height = Wave Steepness*Wavelength

Wavelength given wave steepness

Go Wavelength = Wave Height/Wave Steepness

Significant Wave Height given Wave Period for North Sea

Go Significant Wave Height = (Wave Period/3.94)^1/0.376

Maximum Wave Height

Go Maximum Wave Height = 1.86*Significant Wave Height

Wave Height given Wave Period for Mediterranean Sea

Go Wave Height = ((Wave Period-4)/2)^(1/0.7)

Wave Height given Wave Amplitude

Go Wave Height = 2*Wave Amplitude

Wave Height given Wave Period for North Atlantic Ocean

Go Wave Height = Wave Period/2.5

Wave Height represented by Rayleigh Distribution Formula

Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2))
PH = (2*H/H_rms^2)*exp(-(H^2/H_rms^2))

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Wave Height represented by Rayleigh Distribution?

Wave Height represented by Rayleigh Distribution calculator uses Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2)) to calculate the Individual Wave Height, The Wave Height represented by Rayleigh Distribution is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering. Individual Wave Height is denoted by PH symbol.

How to calculate Wave Height represented by Rayleigh Distribution using this online calculator? To use this online calculator for Wave Height represented by Rayleigh Distribution, enter Wave Height (H) & Root Mean Square Wave Height (H_rms) and hit the calculate button. Here is how the Wave Height represented by Rayleigh Distribution calculation can be explained with given input values -> 0.009463 = (2*3/8.4^2)*exp(-(3^2/8.4^2)).

FAQ

What is Wave Height represented by Rayleigh Distribution?

The Wave Height represented by Rayleigh Distribution is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering and is represented as PH = (2*H/H_rms^2)*exp(-(H^2/H_rms^2)) or Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2)). Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough & Root Mean Square Wave Height is a parameter influencing the Breaker Height Index that is commonly used to define the wave height at breaking in the saturated zones.

How to calculate Wave Height represented by Rayleigh Distribution?

The Wave Height represented by Rayleigh Distribution is the difference between the elevations of a crest and a neighboring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering is calculated using Individual Wave Height = (2*Wave Height/Root Mean Square Wave Height^2)*exp(-(Wave Height^2/Root Mean Square Wave Height^2)). To calculate Wave Height represented by Rayleigh Distribution, you need Wave Height (H) & Root Mean Square Wave Height (H_rms). With our tool, you need to enter the respective value for Wave Height & Root Mean Square Wave Height 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 Individual Wave Height?

In this formula, Individual Wave Height uses Wave Height & Root Mean Square Wave Height. We can use 1 other way(s) to calculate the same, which is/are as follows -

Individual Wave Height = 1-exp(-Wave Height^2/Root Mean Square Wave Height^2)

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