Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline Calculator

✖Water Depth at Breaking is the depth of water where ocean surface waves start to break as they approach the shore which depends on the wave climate and is therefore highly variable.ⓘ Water Depth at Breaking [d_b]			+10% -10%
✖Setup at the Still-Water Shore Line is the increase in mean water level due to the presence of breaking waves.ⓘ Setup at the Still-Water Shore Line [η_s]			+10% -10%
✖Set Down at the Breaker Point where wave setdown is a wave-induced decrease of the mean water level before the waves break.ⓘ Set Down at the Breaker Point [η_b]			+10% -10%

✖Breaker Depth Index is the ratio of the wave height at breaking, to the water depth, at the breakpoint.ⓘ Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline [γ_b]

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Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline

Formula

`"γ"_{"b"} = sqrt(8/3*(("d"_{"b"}/("η"_{"s"}-"η"_{"b"}))-1))`

Example

`"0.335694"=sqrt(8/3*(("55m"/("53.0m"-"0.23m"))-1))`

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Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline Solution

STEP 0: Pre-Calculation Summary

Formula Used

Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1))
γ_b = sqrt(8/3*((d_b/(η_s-η_b))-1))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Breaker Depth Index - Breaker Depth Index is the ratio of the wave height at breaking, to the water depth, at the breakpoint.
Water Depth at Breaking - (Measured in Meter) - Water Depth at Breaking is the depth of water where ocean surface waves start to break as they approach the shore which depends on the wave climate and is therefore highly variable.
Setup at the Still-Water Shore Line - (Measured in Meter) - Setup at the Still-Water Shore Line is the increase in mean water level due to the presence of breaking waves.
Set Down at the Breaker Point - (Measured in Meter) - Set Down at the Breaker Point where wave setdown is a wave-induced decrease of the mean water level before the waves break.

STEP 1: Convert Input(s) to Base Unit

Water Depth at Breaking: 55 Meter --> 55 Meter No Conversion Required
Setup at the Still-Water Shore Line: 53 Meter --> 53 Meter No Conversion Required
Set Down at the Breaker Point: 0.23 Meter --> 0.23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ_b = sqrt(8/3*((d_b/(η_s-η_b))-1)) --> sqrt(8/3*((55/(53-0.23))-1))

Evaluating ... ...

γ_b = 0.335693746144917

STEP 3: Convert Result to Output's Unit

0.335693746144917 --> No Conversion Required

FINAL ANSWER

0.335693746144917 ≈ 0.335694 <-- Breaker Depth Index

(Calculation completed in 00.004 seconds)

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< 20 Wave Setup Calculators

Wave Height given Mean Water Surface Elevation Set down for Regular Waves

Go Wave Height = sqrt(Mean Water Surface Elevation of Coast*8*sinh(4*pi*Water Depth/Wavelength of Coast)/(2*pi/Wavelength of Coast))

Set down for Regular Waves

Go Mean Water Surface Elevation of Coast = (-1/8)*((Wave Height^2*(2*pi/Wavelength of Coast))/(sinh(4*pi*Water Depth/Wavelength of Coast)))

Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline

Go Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1))

Shoreward Displacement of Shoreline

Go Shoreward Displacement of the Shoreline = Setup at the Still-Water Shore Line/(tan(Beach Slope)-Cross-Shore Balance Momentum)

Wave Height given Cross-Shore Component

Go Wave Height = sqrt((16*Coastal Cross-Shore Component)/(3*Water Density*[g]*Water Depth))

Water Depth at Breaking given Setdown at Breaker Point at Still-Water Shoreline

Go Water Depth at Breaking = (Setup at the Still-Water Shore Line-Set Down at the Breaker Point)/(1/(1+(8/(3*Coastal Breaker Depth Index^2))))

Setdown at Breaker Point at Still-Water Shoreline

Go Set Down at the Breaker Point = Setup at the Still-Water Shore Line-(1/(1+(8/(3*Coastal Breaker Depth Index^2))))*Water Depth at Breaking

Setup at Still-Water Shoreline

Go Setup at the Still-Water Shore Line = Set Down at the Breaker Point+(1/(1+(8/(3*Coastal Breaker Depth Index^2))))*Water Depth at Breaking

Setup at Mean Shoreline

Go Setup at the Mean Shoreline = Setup at the Still-Water Shore Line+(Cross-Shore Balance Momentum*Shoreward Displacement of the Shoreline)

Water Depth given Cross Shore Component

Go Water Depth = Coastal Cross-Shore Component/((3/16)*Water Density*[g]*Wave Height^2)

Cross-Shore Component of Cross-Shore directed Radiation Stress

Go Coastal Cross-Shore Component = (3/16)*Water Density*[g]*Water Depth*Wave Height^2

Beach Slope given Nonbreaking Upper Limit of Runup

Go Beach Slope = pi/2*(Wave Runup/Deepwater Wave Height of Ocean*(2*pi)^0.5)^4

Deepwater Wave Height given Nonbreaking Upper Limit of Runup on Uniform Slope

Go Deepwater Wave Height = Wave Runup/((2*pi)^0.5*(pi/2*Beach Slope)^(1/4))

Nonbreaking Upper Limit of Runup on Uniform Slope

Go Wave Runup = Deepwater Wave Height*(2*pi)^0.5*(pi/(2*Beach Slope))^(1/4)

Surf Similarity Parameter given Wave Runup above Mean Water Level

Go Deepwater Surf Similarity Parameter = Wave Runup/Deepwater Wave Height

Deepwater Wave Height given Wave Runup above Mean Water Level

Go Deepwater Wave Height = Wave Runup/Deepwater Surf Similarity Parameter

Wave Runup above Mean Water Level

Go Wave Runup = Deepwater Wave Height*Deepwater Surf Similarity Parameter

Mean Water Surface Elevation given Total Water Depth

Go Mean Water Surface Elevation = Coastal Water Depth-Still-Water Depth

Still Water Depth given Total Water Depth

Go Still-Water Depth = Coastal Water Depth-Mean Water Surface Elevation

Total Water Depth

Go Coastal Water Depth = Still-Water Depth+Mean Water Surface Elevation

Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline Formula

Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1))
γ_b = sqrt(8/3*((d_b/(η_s-η_b))-1))

What is Wave Runup & Wave Setup and Setdown?

Wave runup is the maximum vertical extent of wave uprush on a beach or structure above the still water level (SWL). It is the sum of wave set-up and swash uprush (see Swash Zone Dynamics) and must be added to the water level reached as a result of tides and wind set-up.
The wave setup is the increase in mean water level due to the presence of breaking waves. Similarly, wave set down is a wave-induced decrease of the mean water level before the waves break.
The wave setdown is a wave-induced decrease of the mean water level before the waves break (during the shoaling process). For short, the whole phenomenon is often denoted as wave setup, including both increase and decrease of mean elevation.

Define Breaking Wave & cause of Regular Waves.

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 causing large amounts of wave energy to be transformed into turbulent kinetic energy.
Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As the 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 causes waves.

How to Calculate Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline?

Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline calculator uses Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1)) to calculate the Breaker Depth Index, The Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline formula is defined as the ratio of wave height and still water depth at the shoreface location where waves start breaking. Breaker Depth Index is denoted by γ_b symbol.

How to calculate Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline using this online calculator? To use this online calculator for Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline, enter Water Depth at Breaking (d_b), Setup at the Still-Water Shore Line (η_s) & Set Down at the Breaker Point (η_b) and hit the calculate button. Here is how the Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline calculation can be explained with given input values -> 0.62361 = sqrt(8/3*((55/(53-0.23))-1)).

FAQ

What is Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline?

The Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline formula is defined as the ratio of wave height and still water depth at the shoreface location where waves start breaking and is represented as γ_b = sqrt(8/3*((d_b/(η_s-η_b))-1)) or Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1)). Water Depth at Breaking is the depth of water where ocean surface waves start to break as they approach the shore which depends on the wave climate and is therefore highly variable, Setup at the Still-Water Shore Line is the increase in mean water level due to the presence of breaking waves & Set Down at the Breaker Point where wave setdown is a wave-induced decrease of the mean water level before the waves break.

How to calculate Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline?

The Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline formula is defined as the ratio of wave height and still water depth at the shoreface location where waves start breaking is calculated using Breaker Depth Index = sqrt(8/3*((Water Depth at Breaking/(Setup at the Still-Water Shore Line-Set Down at the Breaker Point))-1)). To calculate Breaker Depth Index given Set-down at Breaker Point at Still-Water Shoreline, you need Water Depth at Breaking (d_b), Setup at the Still-Water Shore Line (η_s) & Set Down at the Breaker Point (η_b). With our tool, you need to enter the respective value for Water Depth at Breaking, Setup at the Still-Water Shore Line & Set Down at the Breaker Point and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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