Wave direction and speed of propagation

In summary, the conversation revolves around modifying a partial differential equation to make a wave propagate in the negative z direction. The equation is simplified and plotted for better understanding, and the conversation also delves into other functions and their behavior in the given scenario.
  • #1
kasnay
10
1
TL;DR Summary
Wave direction and speed propagation
I have an answer to a partial differential equation.
I have the equation coded as followed. I am trying to get this wave to propagate back after it hits a given z value. Can anyone help me figure out the direction in this equation?

upsilon=sqrt(3*((1-nu)/(1+nu))*(B/row));expansion=exp(-z/zeta).*(1-.5.*exp(-upsilon.*step(t)/zeta))-.5.*exp(-abs(z-upsilon.*step(t))/zeta).*sign(z-upsilon.*step(t));eta=(1-R)*((Q*Beta)/(A*zeta*C))*((1+nu)/(1-nu))*expansion;
 
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  • #2
However I am not confident to have read or understood the equation you wrote well, only z, not x,y, seems to appear in it. So I suppose the direction which the equation determines would be z.
 
  • #3
Sorry please let me clarify. We are ignoring the y and x planes. The wave is traveling in the z direction away from the surface as time increase. What I am trying to do is modify the equation so that the wave starts at infinity far away and moves toward the surface as time increases.
In essence I am trying to change my wave velocity to negative. I have tried inversing my terms with z and t but this creates an infinitely building wave.
 
  • #4
Thanks. I have another preliminary observation that exp(-z/zeta) would diverge at z=##-\infty## for zeta > 0.
 
  • #5
the pde that i worked through (which was also previously done by another) was defined that boundary conditions are from z=0 to z=infinity.
 
  • #6
It is not clear what your function is. What is step? You need to write the equation as a simple function of z and t; i.e. eliminate constants by setting them to convenient values (for example upsilon=1, zeta=1 and eta=1*expansion or are z and t buried in these terms) and use the formatting tools on PF so that it is readable.
 
  • #7
once again, i apologize. i have never used a forum for this before.
n(z,t)=(3/2)(1.5/.5)(e-z(1-.5e-3t)-.5e-abs(z-3t)*sgn(z-3t))
 
  • #8
Let’s simplify further
m(z,t) = e-z(1-.5e-3t)-.5e-abs(z-3t)*sgn(z-3t)
= e-z-.5e-(z+3t)-.5e-abs(z-3t)*sgn(z-3t)
= f(z) + g(z+3t) + h(z-3t)
which is a spacially dependent background + a left going wave + a right going wave
Are you sure everything you wrote is transcribed correctly?
 
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  • #10
So i didnt think to expand the exp(1-.5exp) so that actually made it easy to look at.
Your plot is in essence what i get when I use matlab. I programmed your simplified model and I get that same graph. A crest and trough that moves in the positive direction as time goes toward infinity.
So I also noticed what you are saying about the background left and right wave. Just playing around with it, when I remove the g(z+3t) The wave does not have a noticeable change. However If I remove the h(z-3t) then it just becomes a exponential with no movement in time.

I appreciate your help.
 
  • #12
Notice at t=0, g=h in the region of interest
For t>0, g quickly runs outside the region leaving its exponentially decaying tail while h moves to the right.
 
  • #13
sorry for the late responce, thank you for your help
 

Related to Wave direction and speed of propagation

1. What is the direction of wave propagation?

The direction of wave propagation is the direction in which the wave travels. This can be determined by looking at the direction of the wave's crest or trough.

2. How is wave direction measured?

Wave direction is typically measured using a compass or by observing the angle of the wave's crest or trough in relation to a fixed point, such as the shoreline.

3. What factors affect the speed of wave propagation?

The speed of wave propagation can be affected by several factors, including the medium through which the wave is traveling, the wavelength of the wave, and the frequency of the wave.

4. Can wave direction change?

Yes, wave direction can change when the wave encounters a change in the medium it is traveling through, such as when it reaches a different depth or encounters a barrier.

5. How does wave direction impact ocean currents?

Wave direction can impact ocean currents by influencing the direction and strength of the currents. For example, waves that are perpendicular to the direction of the current can cause the current to change direction, while waves that are parallel to the current can strengthen or weaken the current.

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