Breaking wave speed given Hs and Tp

Discussion in 'Boat Design' started by floating, Feb 4, 2016.

  1. floating
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    floating Junior Member

    I would like to work out the horizontal speed of the fastest breaking wave for a given sea state and water depth. Is there a formula for this? For example, significant wave height of Hs=3m, average wave period Ta=5s, water depth of 1m. What is the speed of the fastest breaking wave?
     
  2. Ad Hoc
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    Ad Hoc Naval Architect

    The celerity of a wave is governed by the water depth.

    c = sqrt.(g.D)

    g = 9.81 m/s^2
    D = water depth , m.

    So if 1.0m depth c = sqrt(9.81 x 1.0) = 3.13 m/s = 6.1knots.
     
  3. TANSL
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    TANSL Senior Member

    I guess it must intervene some other variable or, perhaps, the above formula is valid only within certain limits because, applied as it is to a water depth of 100 m, the celerity will be 61 knots.
    Surely there is something I do not understand.
     
  4. Ad Hoc
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    Ad Hoc Naval Architect

    That's correct.
    Remember this is the maximum speed at which it may travel.

    The Tsunami waves from Fukushima several years ago and those of the Ache Earthquakes, they travelled across the oceans at some several hundred km/h!

    "...Where the ocean is deep, tsunamis can travel unnoticed on the surface at speeds up to 500 miles an hour (800 kilometers an hour), crossing an ocean in a day or less. Scientists are able to calculate arrival time of a tsunami in different parts of the world based on knowledge of water depths, distances, and when the event that generated the tsunami occurred..." *

    * http://news.nationalgeographic.com/news/2011/03/110311-tsunami-facts-japan-earthquake-hawaii/
     
  5. KJL38
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    KJL38 Junior Member

  6. floating
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    floating Junior Member

    Thanks all. I think I am clear now: So as long as waves are breaking due to shallow water, they are all traveling at the same speed no matter what the sea state, since period and height do not appear in that formula. But in the sea state, only waves which 'feel' the bottom will break, i.e. longest-period waves. I also found a few references like this one which say that the breakers travel slower than the phase speed,
    http://www.soest.hawaii.edu/PubServices/2005pdfs/Gemmrich.pdf
     
  7. DCockey
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    DCockey Senior Member

    "they are all traveling at the same speed no matter what the sea state, since period and height do not appear in that formula" applies only to waves of sufficiently small amplitude compared to the wave length and water depth for which the linearized theory is valid. As the amplitude increases simple linear wave theory does a poorer job of modeling wave behavior.

    I recall seeing an analysis which predicts waves breaking based on the angle of the wave crest becoming less than 60 degrees.
     
  8. jehardiman
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    jehardiman Senior Member

    Get a copy of Oceanographical Engineering by Robert L Weigel (the standard text). He devotes a whole chapter to this.
     
  9. TANSL
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    TANSL Senior Member

    It is an interesting topic. It makes me think that at some point will have to enter the energy that causes the waves. In the case of the tsunami, probably, we need to use a different formula to which we are talking.
     
  10. Ad Hoc
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    Ad Hoc Naval Architect

    No, same one.

    The shallow water celerity is simply a modified version owing to the depth. The full set of formulae, is noted/provided by KJL38 above.
     
  11. JRD
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    JRD Senior Member

    a bit off topic, but is the phenomenon of tide going out before the tsunami arrives at a shoreline due to the waveform and velocity causing a depression ahead of the wave driving a rapid back flow? Before reading this thread it never occurred to me to ponder the physics behind this.
     
  12. daiquiri
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    daiquiri Engineering and Design

    Wave motion is actually orbital, or circulatory. The bottom of a wave is pulling the water particles backwards, while the top is pushing forward. The reason for this is essentially (but not only) the conservation of mass. In any given bounded volume, so much waters enters in, so much has to go out. The vertical velocity component is a part of the picture too.

    It is well-illustrated in this slide, where you can see how the water in front of the wave is sucked towards the main wave body:

    [​IMG]

    - the above pic was taken from here: http://geologycafe.com/oceans/chapter10.html , which has a lots of other good info on surface waves.

    When the wave approaches the shore and the water depth start to decrease, the circular motion becomes skewed and the bottom layers of the water feel the friction force from the seabed. So they slow down respect to the top layers.
    Since the total wave energy is conserved but the kinetic energy of the wave decreases (slowing down due to friction), it means that the potential energy has to increase - i.e. the wave height increases. The wave starts to deform and the crest grows and assumes the forward-bulging form. The water in front of the wave is still sucked towards the crest, so it retreats from the shore.

    Hope it helps.
     
  13. NavalSArtichoke
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    NavalSArtichoke Senior Member

    The significant wave height is defined as the average of the heights of the 1/3 highest waves in a given sample. This is a statistical measure which roughly corresponds to the height of the waves which an observer sees when looking at a seaway. AFAIK, it only has meaning for deep-water waves, where the wavelength < water depth.

    In any event, it is tricky to have a single wave of height 3 m when the water depth is only 1 meter. You're going to have lots of dry bottom somewhere during the wave period.
     
  14. JRD
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    JRD Senior Member

    Thanks it helps alot, so huge wave = significant suction and backflow
     

  15. floating
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    floating Junior Member

    @NavalSArtichoke - Yikes, the water depth is 25m not 1m, which is indeed impossible to have Hs=3m in! My mistake, and thanks for catching it.
    @DCockey - Good point that in a steep sea state the small amplitude theory breaks down, but I haven't been able to find a rule of thumb for the speed distribution of breaking waves for a given Hs, though a did find some for breaking wave speed vs. phase speed and breaking wave speed vs. wind speed.
     
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