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Thread: Guntersville Yacht club

  1. #1
    Join Date
    Oct 2006
    The Heart of Dixie

    Guntersville Yacht club

    We have had our share of bad weather lately. Tornadoes, bad thunderstorms. Then we had a rare phenomenon called a Gravity wave hit us. You can Google it but it meant sustained 50 mph winds and gusts up to near 70 for about an hour. Not part of a storm either, just strong winds. After all the rain the down town area was a mess. Lots of trees down and leaves everywhere!

    I heard that that Yacht club was a real mess and that I needed to drive over and see it. What I saw was a major surprise!

    Drive up I see this. Now you shouldn't see this here.

    I get up closed I just had to pull off the road, I couldn't believe it.

    The winds broke two(?) floating sections loose from their anchors and down onto the causeway. The far end is wedged on the bank and the causeway. Bascially wrapped around a few boats.

    If you look and see the boats in the distance. That is where the Yachtclub used to be. About a 1/4 mile away.

    God grant me the senility to forget the people I never liked anyway,
    the good fortune to run into the ones I do,
    and the eyesight to tell the difference.

    Kudzu Craft Lightweight Skin on frame Kayaks.
    Custom built boats and Kits

  2. #2
    Join Date
    Jul 2008
    Alexandria, Virginia
    This should help explain gravity waves:

    The phase speed c of a linear gravity wave with wavenumber k is given by the formula

    where g is the acceleration due to gravity. When surface tension is important, this is modified to

    where g is the acceleration due to gravity, σ is the surface tension coefficient, ρ is the density, and k is the wavenumber of the disturbance.

    The gravity wave represents a perturbation around a stationary state, in which there is no velocity. Thus, the perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude, Because the fluid is assumed incompressible, this velocity field has the streamfunction representation
    where the subscripts indicate partial derivatives. In this derivation it suffices to work in two dimensions , where gravity points in the negative z-direction. Next, in an initially stationary incompressible fluid, there is no vorticity, and the fluid stays irrotational, hence . In the streamfunction representation, Next, because of the translational invariance of the system in the x-direction, it is possible to make the ansatz
    where k is a spatial wavenumber. Thus, the problem reduces to solving the equation
    We work in a sea of infinite depth, so the boundary condition is at z = − ∞. The undisturbed surface is at z = 0, and the disturbed or wavy surface is at z = η, where η is small in magnigude. If no fluid is to leak out of the bottom, we must have the condition
    . Hence, Ψ = Aekz on , where A and the wave speed c are constants to be determined from conditions at the interface.
    The free-surface condition: At the free surface , the kinematic condition holds:
    Linearizing, this is simply
    where the velocity is linearized on to the surface . Using the normal-mode and streamfunction representations, this condition is , the second interfacial condition.
    Pressure relation across the interface: For the case with surface tension, the pressure difference over the interface at z = η is given by the Young–Laplace equation:
    where σ is the surface tension and κ is the curvature of the interface, which in a linear approximation is
    However, this condition refers to the total pressure (base+perturbed), thus
    (As usual, The perturbed quantities can be linearized onto the surface z=0.) Using hydrostatic balance, in the form P = − ρgz + Const.,
    this becomes
    The perturbed pressures are evaluated in terms of streamfunctions, using the horizontal momentum equation of the linearised Euler equations for the perturbations,
    to yield p' = ρcDΨ.
    Putting this last equation and the jump condition together,
    Substituting the second interfacial condition and using the normal-mode representation, this relation becomes cDΨ = gΨρ + σk2Ψ.
    Using the solution Ψ = ekz, this gives

    Since c = ω / k is the phase speed in terms of the frequency ω and the wavenumber, the gravity wave frequency can be expressed as

    The group velocity of a wave (that is, the speed at which a wave packet travels) is given by

    and thus for a gravity wave,

    The group velocity is one half the phase velocity. A wave in which the group and phase velocities differ is called dispersive.

    Any questions?

  3. #3
    Thanks Frank, now I understand perfectly.

  4. #4
    Join Date
    Jul 2008
    Alexandria, Virginia
    Happy to help Alan!

  5. #5
    Join Date
    Oct 2008
    Kea'au Hawaii. Just down the road from Hilo town!
    Geez, Frank your fast on the keys!! I was just going to say the same thing@

    What goes around, comes around.

  6. #6
    Join Date
    Oct 2006
    ABQ NM
    C'mon, Frank...everybody knows that already. I even remember the rhyme we learned in school to keep the theory straight:

    If today,

    Then for me.

    Jeff, that looks like one heck of a wind.
    When the going gets weird, the weird turn pro. - Hunter S. Thompson
    When the weird get going, they start their own forum. - Vaughn McMillan

  7. #7
    Join Date
    Jul 2008
    Alexandria, Virginia
    Thanks Royall and Vaughn.
    You know me, a big show-off!
    breaks me up every time!

  8. #8
    Join Date
    Dec 2008
    falcon heights, minnesota
    i'm just waiting for larry to chime in on this one...
    benedictione omnes bene

    check out my etsy store, buroviejowoodworking

  9. #9
    Join Date
    Jan 2007
    New Springfield OH
    Just wait a gosh darn minute,,,,, I was told there would be no maths
    Throw Apples out the Windows, but make sure not to hit the Penguin.

    If the world should blow itself up, the last audible voice would be that of an expert saying it can’t be done.

  10. #10
    Join Date
    Oct 2006
    ABQ NM
    When the going gets weird, the weird turn pro. - Hunter S. Thompson
    When the weird get going, they start their own forum. - Vaughn McMillan

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