Beach Slope Modified for Wave Setup Calculator

✖Beach Slope refers to the slope of the beach face as a dynamic feature that changes with changes in wave conditions as well as the gain or loss of different sediment sizes on the beach face.ⓘ Beach Slope [β]			+10% -10%
✖Breaker Depth Index is the ratio of the wave height at breaking, to the water depth, at the breakpoint.ⓘ Breaker Depth Index [γ_b]			+10% -10%

✖Modified Beach Slope for Wave setup depends on beach slope and breaker depth index.ⓘ Beach Slope Modified for Wave Setup [β^*]

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Formula

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Beach Slope Modified for Wave Setup

Formula

`"β"^{"*"} = atan(tan("β")/(1+(3*"γ"_{"b"}^2/8)))`

Example

`"0.144531"=atan(tan("0.15")/(1+(3*("0.32")^2/8)))`

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Beach Slope Modified for Wave Setup Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8)))
β^* = atan(tan(β)/(1+(3*γ_b^2/8)))
This formula uses 2 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Modified Beach Slope - Modified Beach Slope for Wave setup depends on beach slope and breaker depth index.
Beach Slope - Beach Slope refers to the slope of the beach face as a dynamic feature that changes with changes in wave conditions as well as the gain or loss of different sediment sizes on the beach face.
Breaker Depth Index - Breaker Depth Index is the ratio of the wave height at breaking, to the water depth, at the breakpoint.

STEP 1: Convert Input(s) to Base Unit

Beach Slope: 0.15 --> No Conversion Required
Breaker Depth Index: 0.32 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

β^* = atan(tan(β)/(1+(3*γ_b^2/8))) --> atan(tan(0.15)/(1+(3*0.32^2/8)))

Evaluating ... ...

β^* = 0.144531374260377

STEP 3: Convert Result to Output's Unit

0.144531374260377 --> No Conversion Required

FINAL ANSWER

0.144531374260377 ≈ 0.144531 <-- Modified Beach Slope

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Nearshore Currents » Longshore Current » Beach Slope Modified for Wave Setup

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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< 7 Longshore Current Calculators

Longshore Current Speed

Go Longshore Current Speed = (5*pi/16)*tan(Modified Beach Slope)*Breaker Depth Index*sqrt([g]*Water Depth)*sin(Wave Crest Angle)*cos(Wave Crest Angle)/Bottom Friction Coefficient

Ratio of Wave Group Speed and Phase Speed

Go Ratio of Wave Group Speed and Phase Speed = (Radiation Stress Component*8)/(Mass Density*[g]*Wave Height^2*cos(Wave Crest Angle)*sin(Wave Crest Angle))

Radiation Stress Component

Go Radiation Stress Component = (Ratio of Wave Group Speed and Phase Speed/8)*Mass Density*[g]*(Wave Height^2)*cos(Wave Crest Angle)*sin(Wave Crest Angle)

Wave Height given Radiation Stress Component

Go Wave Height = sqrt((Radiation Stress Component*8)/Mass Density*[g]*cos(Wave Crest Angle)*sin(Wave Crest Angle))

Longshore Current at Mid-Surf Zone

Go Longshore Current at the Mid-Surf Zone = 1.17*sqrt([g]*Root Mean Square Wave Height)*sin(Wave Crest Angle)*cos(Wave Crest Angle)

Root Mean Square Wave Height at Breaking given Longshore Current at Mid-Surf Zone

Go Root Mean Square Wave Height = ((Longshore Current at the Mid-Surf Zone/(1.17*sin(Wave Crest Angle)*cos(Wave Crest Angle)))^0.5)/[g]

Beach Slope Modified for Wave Setup

Go Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8)))

Beach Slope Modified for Wave Setup Formula

Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8)))
β^* = atan(tan(β)/(1+(3*γ_b^2/8)))

What is Longshore Drift & Longshore Current?

Longshore drift from longshore current is a geological process that consists of the transportation of sediments along a coast parallel to the shoreline, which is dependent on oblique incoming wave direction.
Wave and Wind induced longshore currents flow parallel to the shoreline and are strongest in the surf zone, decaying rapidly seaward of the breakers. These currents are generated by gradients in momentum flux (radiation stress) due to the decay of obliquely incident waves and the longshore component of the wind.

What is Wave setup and Wave setdown?

In fluid dynamics, 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.

How to Calculate Beach Slope Modified for Wave Setup?

Beach Slope Modified for Wave Setup calculator uses Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8))) to calculate the Modified Beach Slope, The Beach Slope Modified for Wave Setup formula is defined as the slope of the beach when there is an increase in mean water level due to the presence of breaking waves and it depends on the original beach slope and the breaker depth index. Modified Beach Slope is denoted by β^* symbol.

How to calculate Beach Slope Modified for Wave Setup using this online calculator? To use this online calculator for Beach Slope Modified for Wave Setup, enter Beach Slope (β) & Breaker Depth Index (γ_b) and hit the calculate button. Here is how the Beach Slope Modified for Wave Setup calculation can be explained with given input values -> 0.147816 = atan(tan(0.15)/(1+(3*0.32^2/8))).

FAQ

What is Beach Slope Modified for Wave Setup?

The Beach Slope Modified for Wave Setup formula is defined as the slope of the beach when there is an increase in mean water level due to the presence of breaking waves and it depends on the original beach slope and the breaker depth index and is represented as β^* = atan(tan(β)/(1+(3*γ_b^2/8))) or Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8))). Beach Slope refers to the slope of the beach face as a dynamic feature that changes with changes in wave conditions as well as the gain or loss of different sediment sizes on the beach face & Breaker Depth Index is the ratio of the wave height at breaking, to the water depth, at the breakpoint.

How to calculate Beach Slope Modified for Wave Setup?

The Beach Slope Modified for Wave Setup formula is defined as the slope of the beach when there is an increase in mean water level due to the presence of breaking waves and it depends on the original beach slope and the breaker depth index is calculated using Modified Beach Slope = atan(tan(Beach Slope)/(1+(3*Breaker Depth Index^2/8))). To calculate Beach Slope Modified for Wave Setup, you need Beach Slope (β) & Breaker Depth Index (γ_b). With our tool, you need to enter the respective value for Beach Slope & Breaker Depth Index 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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