Undergrad Hydrodynamics - Wave of Translation

[jaumzaum]

Hello guys!

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.

 

[Arjan82]

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:

 

[jaumzaum]

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 $v_{ship}/\sqrt{gh} = 1,4$

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

That's why I think they actually disappears. But they don't provide a decent explanation. Ould you think of one?

 

[hutchphd]

Kelvin Wake

 

[Arjan82]

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.

 

[hutchphd]

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.