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Relationship between "Coriolis Effect" and "Gold Ratio"?

  1. Jan 14, 2016 #1
    A common claim that hurricanes and cyclones have geometrical proportions that resemble a logarithmic golden spiral. Knowing that cyclones and hurricanes rotate because of the well-known Coriolis Effect, is it possible that the Golden Ratio is just a natural manifestation of the Coriolis effect?
     
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  3. Jan 14, 2016 #2
    The strength of the Coriolis effect varies with latitude. This means that the hurricanes' shape will vary accordingly to latitude. Furthermore, there are certainly many other factors that would effect the spiral, the dominant factor being the wind speed. There is absolutely no reason a hurricane is going to assume the shape of a golden ratio spiral. They are not perfect spirals either especially when they are not stationary.
     
  4. Jan 14, 2016 #3

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    The Fibonacci numbers and the related Golden Ratio has a property that several spirals can be made that minimize interferance and are evenly spaced. This is true in the formation of plant leaves (so they don't cast a shadow on leaves below), flower pedals, and many other things in nature. I suspect that the formation of hurricane spiral arms has a lot of similarity with the leaf positions. One arm (leaf) can starve (shade) any other arm (leaf) that is positioned too close. There is an interesting (and I think entertaining) series of three videos by Vi Hart that may be shed some light on the subject. (see the link below). The third video describes how the simple act of each newly forming hurricane arm being repelled by the existing arms may cause patterns involving the Golden Ratio.

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    Last edited: Jan 14, 2016
  5. Jan 14, 2016 #4
    The Coriolis effect is well-understood. The golden ratio does not seem to play any role at all in the Coriolis effect
     
  6. Jan 15, 2016 #5

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    I can't imagine any connection between the Coriolis effect and the golden ratio. Coriolis is just linear motion in a rotating coordinate system. But I do believe there is a connection between the golden ratio and the spacing of spiral arms around a hurricane. If the physics of one spiral arm prevents others to form near it, the spacing of arms based on the golden ratio is a natural consequence.
     
  7. Jan 16, 2016 #6
    I grant you the Coriolis Force is important in considering hurricane development. I do not know for sure what you are saying about the golden ratio and the spacing of spiral arms in the hurricane. But suppose I did grant you this suggestion. This would show a connection between coriolis force and hurricane development and a connection between golden ratio and hurricane development. It would still be possible that the golden ratio could have no connection at all to the Coriolis force.
    It is a common exercise to derive the Coriolis force as a consequence of Newton's equations in a rotating reference frame (no golden ratio required). I have also seen derivations of the Coriolis force using differential geometry, using the affine connection. In neither case does the golden ratio come up.
     
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