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When wind blows over a water surface, waves are created. At high wind speeds the waves will start to break. Water droplets appear, but the water surface is still well defined. But if we consider stronger and stronger winds like in case of a hurricane, it seems to me that the water surface should break pretty much everywhere. If you descent from some altitude towards the surface, you'll enter a region of air mixed with water droplets and as you descent further the fraction of water in the air will increase without encountering a well defined boundary between the air and the water. A lot of air is also injected into the water, so even well below sea level there should be a lot of air bubbles, making the scene from there look quite similar to that well above sea level.

The question is then whether there is a well defined phase transition where at at low wind speeds when you do have some amount of water droplets in the air and air bubbles in the water, there is still a rigorously defined water surface while at higher winds speeds the water surface is gone. This can perhaps be treated using methods based on the dynamic renormalization group. In the case of low wind speeds, if we consider course graining and scaling such that we zoom out and we don't see the small details anymore, then the droplets will vanish from view and we're left with a calm sea. In the latter case, the dynamics could be scale invariant, so no matter how much you zoom out, you don't get to a calm sea surface anymore in the scaling limit.

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closed as unclear what you're asking by sammy gerbil, Jon Custer, honeste_vivere, JamalS, Yashas Aug 30 '17 at 12:47

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    $\begingroup$ This question needs some clarification. For example it doesn't include a definition of what a well defined surface means (it seems likely that the criteria for a surface will be met somewhere under all conditions), it seems to assume the existance of a poorly defined surface at high wind speeds (does anyone have some evidence for that?), and it seems to presuppose a distinguishable transition between well and poorly define surface states, rather than a continuous gradual effect at all wind speeds (Is there any physics to suggest a sharper transition?). $\endgroup$ – JMLCarter Aug 25 '17 at 21:12
  • $\begingroup$ High wind speeds cause turbulence; drops of water in the air tend to "dampen" turbulence. I suspect that means that you can expect there to be a probability distribution of "spray" with height; but when that layer gets thick enough it will tend to reduce the velocity of wind near the (now lower) "surface" of the water. But that's hand-wavy. I hope someone has the math skills to back this up. $\endgroup$ – Floris Aug 25 '17 at 21:18
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    $\begingroup$ Sounds like what you're interested in here is the Kelvin-Helmholtz instability between two layers, air and water in this case. Check out the Wikipedia article on the Kelvin-Helmholtz instability ( en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_instability ). It has a nice movie of a numerical simulation of the development of the instability, too. $\endgroup$ – Samuel Weir Aug 25 '17 at 22:36
  • $\begingroup$ W@Samuel Weir. Nice finding. Consider answering the question summarizing it. $\endgroup$ – Bob Bee Aug 26 '17 at 2:00