What Is the Name of the Curve Traced by a Ball on a Ripple Wave?

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The equation describing the shape of a ripple wave is often related to the Schrödinger Wave equation, which serves as a good approximation for water surface waves. The curve traced by a ball rolling along the ripple wave is suggested to resemble an ellipsoid. Oceanographers typically utilize a "linear model" for wave analysis, but this model has limitations in extreme conditions. The discussion highlights the complexities of accurately modeling wave shapes and the paths of floating objects. Understanding these dynamics is crucial for advancements in oceanography and wave physics.
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Do you know if there is any name for the equation that describes the shape of a ripple wave? An example of that kind of wave can be found at http://en.wikipedia.org/wiki/Image:Elliptical_trajectory_on_ripples.png.
My question is: what would you call the curve traced by the ball rolling along the ripple wave curve?
 
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The best approximation to water surface waves currently in use is a version of the Shcrodinger Wave equation.

Oceanographers often use something called the "linear model" but it fails in extreme cases.

I believe that that path followed by a floating object is nearly an elipsiod.
 
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