✖Radiation Stress Component is the momentum transferred through the water body per unit of time (the flux of momentum) by wave orbital motion.ⓘ Radiation Stress Component [S_xy]			+10% -10%
✖Mass Density is a physical quantity that represents the mass of a substance per unit volume.ⓘ Mass Density [ρ]			+10% -10%
✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighbouring trough.ⓘ Wave Height [H]			+10% -10%
✖Wave Crest Angle is the angle at which the crest of a wave approaches or intersects with another medium, such as the shoreline or another wave.ⓘ Wave Crest Angle [α]			+10% -10%

✖Ratio of Wave Group Speed and Phase Speed is ratio of the group speed (cg) the speed with which the energy of the waves moves, while the phase speed (c) the velocity of a wave crest.ⓘ Ratio of Wave Group Speed and Phase Speed [n]

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Formula

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Ratio of Wave Group Speed and Phase Speed

Formula

`"n" = ("S"_{"xy"}*8)/("ρ"*"[g]"*"H"^2*cos("α")*sin("α"))`

Example

`"0.055599"=("15"*8)/("997kg/m³"*"[g]"*("0.714m")^2*cos("60°")*sin("60°"))`

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Ratio of Wave Group Speed and Phase Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
n = (S_xy*8)/(ρ*[g]*H^2*cos(α)*sin(α))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Ratio of Wave Group Speed and Phase Speed - Ratio of Wave Group Speed and Phase Speed is ratio of the group speed (cg) the speed with which the energy of the waves moves, while the phase speed (c) the velocity of a wave crest.
Radiation Stress Component - Radiation Stress Component is the momentum transferred through the water body per unit of time (the flux of momentum) by wave orbital motion.
Mass Density - (Measured in Kilogram per Cubic Meter) - Mass Density is a physical quantity that represents the mass of a substance per unit volume.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighbouring trough.
Wave Crest Angle - (Measured in Radian) - Wave Crest Angle is the angle at which the crest of a wave approaches or intersects with another medium, such as the shoreline or another wave.

STEP 1: Convert Input(s) to Base Unit

Radiation Stress Component: 15 --> No Conversion Required
Mass Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Wave Height: 0.714 Meter --> 0.714 Meter No Conversion Required
Wave Crest Angle: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = (S_xy*8)/(ρ*[g]*H^2*cos(α)*sin(α)) --> (15*8)/(997*[g]*0.714^2*cos(1.0471975511964)*sin(1.0471975511964))

Evaluating ... ...

n = 0.0555991756603236

STEP 3: Convert Result to Output's Unit

0.0555991756603236 --> No Conversion Required

FINAL ANSWER

0.0555991756603236 ≈ 0.055599 <-- Ratio of Wave Group Speed and Phase Speed

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Nearshore Currents » Longshore Current » Ratio of Wave Group Speed and Phase Speed

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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)))

Ratio of Wave Group Speed and Phase Speed Formula

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))
n = (S_xy*8)/(ρ*[g]*H^2*cos(α)*sin(α))

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 set down?

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 Ratio of Wave Group Speed and Phase Speed?

Ratio of Wave Group Speed and Phase Speed calculator uses 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)) to calculate the Ratio of Wave Group Speed and Phase Speed, The Ratio of Wave Group Speed and Phase Speed is defined as the ratio of the speed at which a wave packet, or group of waves, travels to the speed at which the phase of a wave travels. Ratio of Wave Group Speed and Phase Speed is denoted by n symbol.

How to calculate Ratio of Wave Group Speed and Phase Speed using this online calculator? To use this online calculator for Ratio of Wave Group Speed and Phase Speed, enter Radiation Stress Component (S_xy), Mass Density (ρ), Wave Height (H) & Wave Crest Angle (α) and hit the calculate button. Here is how the Ratio of Wave Group Speed and Phase Speed calculation can be explained with given input values -> 0.055599 = (15*8)/(997*[g]*0.714^2*cos(1.0471975511964)*sin(1.0471975511964)).

FAQ

What is Ratio of Wave Group Speed and Phase Speed?

The Ratio of Wave Group Speed and Phase Speed is defined as the ratio of the speed at which a wave packet, or group of waves, travels to the speed at which the phase of a wave travels and is represented as n = (S_xy*8)/(ρ*[g]*H^2*cos(α)*sin(α)) or 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 is the momentum transferred through the water body per unit of time (the flux of momentum) by wave orbital motion, Mass Density is a physical quantity that represents the mass of a substance per unit volume, Wave Height of a surface wave is the difference between the elevations of a crest and a neighbouring trough & Wave Crest Angle is the angle at which the crest of a wave approaches or intersects with another medium, such as the shoreline or another wave.

How to calculate Ratio of Wave Group Speed and Phase Speed?

The Ratio of Wave Group Speed and Phase Speed is defined as the ratio of the speed at which a wave packet, or group of waves, travels to the speed at which the phase of a wave travels is calculated using 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)). To calculate Ratio of Wave Group Speed and Phase Speed, you need Radiation Stress Component (S_xy), Mass Density (ρ), Wave Height (H) & Wave Crest Angle (α). With our tool, you need to enter the respective value for Radiation Stress Component, Mass Density, Wave Height & Wave Crest Angle 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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