The wake of a duck


There’s something that’s been on my mind for over a year now. The angle of the wake of a duck moving with constant velocity in deep water is independent of the velocity of the duck (~39 degrees).  Why is this? (This makes me regret not sitting in on the Part II fluid dynamics course this past term.)

According to Bertrand Le Roy:

This is because the speed of the waves depends on the wavelength in such a subtle way as to cancel the dispersion that a single wavelength wave would show.

According to Tony Zee’s 2004 ASTI lecture on back of the envelope physics, one can make a solid argument based on dimensional analysis.

Unfortunately I haven’t been able to think this one through yet, and any thoughts would be appreciated.


5 Responses to “The wake of a duck”

  1. 1 sid

    There’s a discussion of the derivation (I haven’t read it yet, so I don’t know how good it is) in the comments section of the Bertrand Le Roy link you posted.

  2. Thanks Peter! My regards to Kimi. 🙂

  3. 4 robert

    A very good discussion of the Kelvin wake, with impeccable Cantabrigiensis credentials, is to be found in Lighthill’s ‘Waves in Fluids’ Section 3.10. It’s all down to the phase velocity being twice the group velocity (that’s where the dispersion relation w^2=kg comes in), the duck’s velocity coinciding with the former and the propagation of energy at the latter.

    Lighthill was at DAMTP years ago; he was a hero with amazing physical insight and very wide ranging interests. He could also swim himself; sadly he drowned while taking his annual dip that involved the circumnavigation of the Isle of Wight – he was in his late sixties. His work on how fish swim is excellent – you might also want to look at the connections between gauge theories and hydrodynamics that crop up in the description of the motions of paramecium and other ciliates. (Frank Wilczek was rather keen on this)

  4. Thanks Robert! I’ll look into that.

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