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 = (Sxy*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 used to calculate Radiation Stress Component.
Radiation Stress Component - Radiation Stress Component using linear wave theory.
Mass Density - (Measured in Kilogram per Cubic Meter) - The Mass Density of a substance is its mass per unit volume.
Wave Height - (Measured in Meter) - The Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Wave Crest Angle - (Measured in Radian) - Wave Crest Angle relative to bottom contours.
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 = (Sxy*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)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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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)))

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 = (Sxy*8)/(ρ*[g]*H^2*cos(α)*sin(α))

What is Longshore Current?

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.

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 formula is defined as a parameter influencing the Radiation Stress Component of wind forcing. 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 (Sxy), 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 -> 0.003149 = (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 formula is defined as a parameter influencing the Radiation Stress Component of wind forcing and is represented as n = (Sxy*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 using linear wave theory, The Mass Density of a substance is its mass per unit volume, The Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough & Wave Crest Angle relative to bottom contours.
How to calculate Ratio of Wave Group Speed and Phase Speed?
The Ratio of Wave Group Speed and Phase Speed formula is defined as a parameter influencing the Radiation Stress Component of wind forcing 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 (Sxy), 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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