Shapes of waves in the surface of a pond when the breeze blows

Question

When I throw a stone into a pond while a breeze is blowing across its surface and the water is at rest, what would be the shapes of the waves?

Before the wind, the shape of the waves is circular. Then the interaction between the stone, the water, and the wind will influence the shapes of the waves.

Now the question is how the wind will affect the waves. If this is just a translation of the circles by the wind vector? Or it must be some deformation of the circle? For instance an ellipse!

When the stone is big, it creates bigger and stronger waves. How one must address this problem?

Answer 1

My first question would be "When I don't throw a stone into a pond while a breeze is blowing across its surface and the water is at rest, what would be the shapes of the waves?"

That may seem a bit zen, but...

If the 'breeze' isn't strong enough to ruffle the surface of still water then I predict that it is unlikely to have any significant (i.e. measurable) effect on rippled water.

If, on the other hand, the breeze is already strong enough to affect what would otherwise be undisturbed water, then before you attempt to calculate the effect on rippled water you would need to fully understand the effect of the breeze on 'still' water.

But regardless of the strength of the breeze, I also predict that it will almost certainly not result in elliptical wavefronts after throwing in a pebble (of any size). To do so would require the breeze to either reduce the velocity of ripples moving both upwind and downwind, or increase the velocity of ripples moving both upwind and downwind. That seems very counterintuitive.

On further investigation it appears that wind does not directly affect the velocity of an individual wave travelling over the surface of a liquid. What it can do though, is affect the magnitude of such waves - depending on their wavelength. Light wind can increase the magnitude of shorter wavelength waves moving in the same direction as the wind while higher wind speeds can increase the magnitude of higher wavelength waves moving in the same direction. In deep water the velocity of a wave is proportional to its wavelength (longer wavelength waves move faster than shorter wavelengths).

The net result of all this is that a breeze might preferentially change the spectral distribution of ripples moving in different directions relative to the breeze. But as to how that might affect the nature and shape of the ripple pattern - your guess is as good as mine. The mathematics to simulate/model this would be very complex.

In all probability, the only practical way to get an answer would be to do the experiment yourself. Find a smooth pond or slow-flowing stream, visit it when there is a light to moderate breeze, stand on a bridge over the water, drop a pebble and video the results.