Underwater Currents & Wave Speed - Philipp's Question

[philipp2020]

Hi

Ive got a short question:

Lets say there is an underwater current with 10 m/s going right.

Then I have a device which creates waves standing still in this current at one point. Are the waves sent out by this device faster in this current than if there wouldn't be any current at all?

And second, if the device is moving with let's say 5 m/s and send out waves are the waves faster than when the device is not moving?

Thanks for answer

Philipp

 

[quasar987]

Hi Philipp,

Let's say there is an underwater current with 10 m/s going right.

Then I have a device which creates waves standing still in this current at one point. Are the waves sent out by this device faster in this current than if there wouldn't be any current at all?

Yes, the speed of the waves relative to the still device would be given by simple addition of the speed of the waves relative to the water + the speed of the current.

And second, if the device is moving with let's say 5 m/s and send out waves are the waves faster than when the device is not moving?

No. The speed at which waves propagate in a medium is solely dependent on the medium itself. What will happen though is that since the source of the wave is moving, then the distance between two crests of the wave will be shorter or longer depending on wheter the source is moving towards the wave or away from them respectively. In other words, the wavelength of the wave will be different. This phenomenon is called the Doppler effect.

As I said, the speed of the wave relative to the medium of propagation depends only on the physical properties of the medium. Some mediums, which we call dispersive mediums, have the property that the speed of a wave is dependent upon its wavelength. As an exemple, water in the middle of the ocean (deep water) is dispersive, but water near the shore is non-dispersive. So if you are in deep water and give the source of your waves a speed such that the wavelength is changed, the speed of the waves will be changed as well.

 

[Doc Al]

Mechanical waves move at a speed in the medium (which in this case is water) that is determined by its physical characteristics. If the medium is moving with respect to you (the observer), then the speed of the wave with respect to you will be the vector sum of the velocity of the wave with respect to the medium plus the velocity of the medium with respect to you.

Looks like quasar987 beat me too it!

 

[Clausius2]

No. The speed at which waves propagate in a medium is solely dependent on the medium itself. What will happen though is that since the source of the wave is moving, then the distance between two crests of the wave will be shorter or longer depending on wheter the source is moving towards the wave or away from them respectively. In other words, the wavelength of the wave will be different. This phenomenon is called the Doppler effect.

As I said, the speed of the wave relative to the medium of propagation depends only on the physical properties of the medium. Some mediums, which we call dispersive mediums, have the property that the speed of a wave is dependent upon its wavelength. As an exemple, water in the middle of the ocean (deep water) is dispersive, but water near the shore is non-dispersive. So if you are in deep water and give the source of your waves a speed such that the wavelength is changed, the speed of the waves will be changed as well.

I disagree with that consideration. Talking about fluid mechanics and not about the elastic wave propagated through a solid, there is a phenomenon called Advection. In this example, the waves are Advected by the fluid. It happens with superficial waves (shallow water waves as you referred) caused by flow over topography. In laboratory experiments, and solving analitically the subcritical flow over the obstacle, one can see two waves going upstream and downstream, each one with an absolute velocity $$U-\sqrt{gH}$$ and $$U+\sqrt{gH}$$ respectively.

 

[quasar987]

In english?

Seriously, what you're saying sounds interesting but it is too technical for me to comprehend. Which parts of what I said do you disagree with, and with what would you replace the falacies?

 

[Clausius2]

In english?

Seriously, what you're saying sounds interesting but it is too technical for me to comprehend. Which parts of what I said do you disagree with, and with what would you replace the falacies?

Jokay,

what I am trying to say is that the bulk (the inertia) motion of the fluid adds an additional transport to waves. For instance, in linear acoustics the velocity of the fluid is so small compared with the speed of sound that one neglects such transport and in first approximation the waves move with the propagation speed $$c$$, which as you said it may only depend on the properties of the medium. Linear acoustics is employed with waves in water ($$c$$ depends on the elastic properties) and low mach gases ($$c$$ depends on the local temperature, but if one assumes isentropic flow the flow ends up to be isothermal because of the incompressibility assumption). In non linear acoustics, when the velocity is of the same order than the speed of sound, the transport of waves by means of advection or convection cannot be neglected, and in fact one can see the effective velocity of propagation looking at the Riemann equation of non linear acoustics, where it appears transported scalars like $$F(x-(U+ct)$$ and so on (U is the bulk velocity of the fluid).

To sum up:

- If $$U/c<<1$$, which is the case of linear acoustics the waves are transported with the wave speed at first approximation.

-If $$U/c\sim O(1)$$ or larger, the waves are transported with the wave speed plus the bulk velocity of the fluid.