Shoaling Coefficient Calculator

✖Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.ⓘ Wave Number for Water Wave [k]			+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%

✖Shoaling Coefficient is defined as the ratio of wave height (Hi) at a particular point of interest to the original or deep water wave height (Ho).ⓘ Shoaling Coefficient [K_s]

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Formula

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Shoaling Coefficient

Formula

`"K"_{"s"} = (tanh("k"*"d")*(1+(2*"k"*"d"/sinh(2*"k"*"d"))))^-0.5`

Example

`"0.951161"=(tanh("0.2"*"10m")*(1+(2*"0.2"*"10m"/sinh(2*"0.2"*"10m"))))^-0.5`

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Shoaling Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
K_s = (tanh(k*d)*(1+(2*k*d/sinh(2*k*d))))^-0.5
This formula uses 2 Functions, 3 Variables

Functions Used

sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)
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

Shoaling Coefficient - Shoaling Coefficient is defined as the ratio of wave height (Hi) at a particular point of interest to the original or deep water wave height (Ho).
Wave Number for Water Wave - Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.
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 Number for Water Wave: 0.2 --> No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_s = (tanh(k*d)*(1+(2*k*d/sinh(2*k*d))))^-0.5 --> (tanh(0.2*10)*(1+(2*0.2*10/sinh(2*0.2*10))))^-0.5

Evaluating ... ...

K_s = 0.951161301745107

STEP 3: Convert Result to Output's Unit

0.951161301745107 --> No Conversion Required

FINAL ANSWER

0.951161301745107 ≈ 0.951161 <-- Shoaling Coefficient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Shoaling, Refraction and Breaking » Shoaling Coefficient

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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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< 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

Shoaling Coefficient Formula

What is the Process of Wave Shoaling?

In fluid dynamics, Wave Shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth.

How to Calculate Shoaling Coefficient?

Shoaling Coefficient calculator uses 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 to calculate the Shoaling Coefficient, The Shoaling Coefficient is defined as the ratio of wave height (Hi) at a particular point of interest (xi) to the original or deep water wave height (Ho). Shoaling Coefficient is denoted by K_s symbol.

How to calculate Shoaling Coefficient using this online calculator? To use this online calculator for Shoaling Coefficient, enter Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Shoaling Coefficient calculation can be explained with given input values -> 0.951161 = (tanh(0.2*10)*(1+(2*0.2*10/sinh(2*0.2*10))))^-0.5.

FAQ

What is Shoaling Coefficient?

The Shoaling Coefficient is defined as the ratio of wave height (Hi) at a particular point of interest (xi) to the original or deep water wave height (Ho) and is represented as K_s = (tanh(k*d)*(1+(2*k*d/sinh(2*k*d))))^-0.5 or 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. Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance & 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 Shoaling Coefficient?

The Shoaling Coefficient is defined as the ratio of wave height (Hi) at a particular point of interest (xi) to the original or deep water wave height (Ho) is calculated using 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. To calculate Shoaling Coefficient, you need Wave Number for Water Wave (k) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Wave Number for Water Wave & Coastal Mean Depth 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 Shoaling Coefficient?

In this formula, Shoaling Coefficient uses Wave Number for Water Wave & Coastal Mean Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -

Shoaling Coefficient = sqrt(Deepwater Wave Celerity/(Celerity of the Wave*2*Ratio of Group Velocity to Phase Velocity))
Shoaling Coefficient = 0.4466*(Deep-Water Wavelength/Water Depth in Ocean)^(1/4)

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