The velocity of a wave group (also known as 'group celerity')

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/engineering/waves/group_celerity.h>

using namespace Engineering::Waves;

double

group_celerity_k (double k, double depth=0, double gravity=9.8066) Uses a linear dispersion relationship to compute the wave group velocity

Function Documentation

Within a train of waves the movement of energy is usually slower than that of the waves. As such is you study a short train of waves they will develop at the back of the group, travel forward through the group and disappear at the front of the group.

[DIAGRAM]

The definition of group velocity is:

In deep water, where , group velocity is merely While in shallow water the form is a little more complicated, i.e.

Using this second form, we can plot as an example the relationship between Cg and wave-number, k :

Example 1:

#include <stdio.h>
#include <codecogs/engineering/waves/group_celerity.h>
using namespace Engineering::Waves;
 
int main()
{
  printf("   k         Cg ");
  for(double k=0.01; k<1;k+=0.1)
  {
    printf("\n %.6lf", k);
    double w=group_celerity_k(k,2);
    printf("  %.3lf", w);
  }
}

Output:

k         Cg
??

Parameters:

k	wave-number defines as (). [rad/m]
depth	the depth of the water to mean sea level. A value of zero or less corresponds to deep water. [m]
gravity	acceleration due to gravity (default 9.8066 m/s^2). [m/s^2]

Returns:

wave-frequency (). [rad/s]

Authors:

Will Bateman (February 2005)