Hydrodynamics - Wave of Translation

In summary: It is only when waves are breaking on theshore--and this is when the leading transverse wave is the most significant--that one can see the leading transverse wave. In summary, Kelvin Wake says that the transverse wave disappears when the ship moves faster than the critical speed.
  • #1
jaumzaum
434
33
Hello guys!

ake-pattern-of-transverse-and-divergent-waves_Q640.jpg

I am studying the hydrodynamics of a ship in shallow water. In deep water the ship creates 2 wave patterns, one transverse and another divergent, both making an angle of 19°28'. Also, the maximum velocity of a wave in shallow water is given by ##\sqrt{gh}## where h is the depth of the water.

The part that I don't understand is why transverse the wave disappears if the ship starts moving faster than ##\sqrt{gh}## ?

I think that could happen in a plane also (but I am not sure), in the case the plane becomes supersonic.
 
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  • #2
I'm not sure you could say the transverse wave disappears. A kind of 'shock wave' or bore (if you can call it that) in front of the ship (a soliton apparently). This is because sqrt(gh) is the critical speed at which waves travel through the water at that depth. See this video:
 
  • #3
Thanks @Arjan82, excellent video.

Note at 3:06 the video says "supercritical speed: divergent waves are issued at approximately a 45 degree angle, having absorbed the transverse waves"

Actually the 45 degree angle only occurs when ## v_{ship}/\sqrt{gh} = 1,4 ##

1637721229872.png


Also, one of the most important books in the topic ( Principles of Naval Arquitecture) says

1637721186573.png

1637721209837.png
That's why I think they actually disappears. But they don't provide a decent explanation. Ould you think of one?
 
  • #5
Well, I think that what they are not showing here is the transversal wave that is in front of the ship (also see the video). This is a kind of shock wave because the ship is exceeding the transversal wave velocity. So by the time the ship has past the damage, so to speak, is already done and no other transversal wake is generated.
 
  • #6
I believe the physics of the tidal bore (which is often a "step"wave) require a confined channel as shown on the video. Also breaking waves on a shore are truly shock waves because of the slope (decreasing h) of the shoreline. In my experience the leading transverse wave is not very noticeable on open water shallow or not.
 

1. What is hydrodynamics?

Hydrodynamics is the branch of fluid mechanics that studies the motion of fluids, such as water, and the forces that act on them. It involves the study of how fluids behave and interact with their environment, including the effects of gravity, pressure, and viscosity.

2. What is a wave of translation in hydrodynamics?

A wave of translation is a type of wave that involves a disturbance or movement of an entire body of fluid, rather than just a localized disturbance. This type of wave is typically caused by an external force, such as wind or a moving object, and can travel long distances without losing much of its energy.

3. How is a wave of translation different from other types of waves?

Unlike other types of waves, such as surface waves or standing waves, a wave of translation does not have a fixed pattern or shape. Instead, it involves the movement of an entire body of fluid, which can vary in size and shape depending on the force causing the wave.

4. What factors affect the speed of a wave of translation?

The speed of a wave of translation is affected by several factors, including the density and viscosity of the fluid, the depth of the fluid, and the force causing the wave. In general, waves of translation tend to move faster in deeper and less viscous fluids.

5. How are waves of translation used in real-world applications?

Waves of translation have many practical applications, including in oceanography, meteorology, and engineering. They can be used to study and predict the behavior of ocean currents, weather patterns, and the movement of ships and other objects in water. They are also important in the design and construction of structures, such as offshore platforms and coastal protection systems.

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