A Question of Bores

I was at a lengthy meeting this morning so naturally there popped into my mind the subject of bores. The most prominent of these that will be familiar to British folk is the Severn Bore, but they happen in a variety of locations, including Morecambe Bay (which is in the Midlands):

Tidal_Bore_-_geograph.org.uk_-_324581

As you can see, a bore consists of a steep wavefront that travels a long distance without disruption, and is one manifestation of a more general phenomenon called a hydraulic jump; in a coordinate frame that moves with the wavefront, a bore is basically identical to a stationary hydraulic jump.

Anyway, I while ago I decided to set an examination question about this, which I reproduce here in severely edited form for your amusement and edification; you can click on it to make it larger if you have difficulty reading the question. With the examination season over I’m sure there are many people out there missing the opportunity to grapple with physics problems! Or perhaps not…

Bore

If you need hints, I suggest first working out how the pressure P varies with depth and then using the result to work out to work out the balance of forces either side of the discontinuity. Then deploy Bernoulli’s theorem and Bob’s your uncle!

P.S. For another hint, try the yellow pages:

Boring

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6 Responses to “A Question of Bores”

  1. NotThe PeoplesAstronomer Says:

    Boring, Oregon, is also a twin town with Dull in Perthshire. And now the two are set to link up with Bland in Australia:

    http://www.scotsman.com/the-scotsman/scotland/dull-village-potential-link-with-boring-and-bland-1-2951534

  2. Anton Garrett Says:

    Solitons!

  3. John Peacock Says:

    I think the question is misleading as stated. Your equation for V_1 applies in the rest frame of the “shock”, so V_1 is the speed of propagation of a jump into a stationary body of water. If the river flows more slowly than this, the bore moves upstream. But the question implies that the upstream flow speed of the river determines the height ratio of the jump – which isn’t right if you make the reasonable assumption that an unqualified “flow speed” means relative to the bank.

    • telescoper Says:

      I take your point. That’s what happens when you edit things quickly! The actual exam question was much longer and had more intermediate steps..

  4. John Peacock Says:

    And actually, is Bernoulli applicable? It’s for streamline flow, whereas surely there is turbulent dissipation at the discontinuity. You normally solve a shock by conserving total mass flux and momentum flux across the boundary. The latter gives you a different equation from just applying Bernoulli to a streamline on the surface of the water (i.e. at constant P).

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