Deep water phenomena


A wavy water surface presents caustics: the light beams are refracted in very choppy directions, the coincidence of rays intensifies, leading to very bright regions on every surface under the water:


Formation of caustics is illustrated on the next figure:


Caustics are bright regions where the light beams coincident


The same physical effects which cause caustics can create Godrays (described in [1]). The changing water surface focuses and defocuses light rays. The small particles floating in the water can get into these focus points and become visible for a short period. The continuously changing patterns created by these effects are called Godrays which are visible if you are looking from underwater towards the light source. A rendered example is shown on the next figure:


Godrays - The image was created by the Typhoon engine. [3]

Whitecaps and foam

Breaking waves produce foam, and the scummy parts of the breaking waves are called whitecaps. According to [4], the area of whitecaps depends on the temperature of the water and the air and on water chemistry. They used an empirical formula to approximate the fraction of the water covered by foam that modifies optical properties on the water's surface:

f = 1.59 * 10-5 U2.55 exp[0.086 * (Tw - Ta )]

Where f is the fractional area, U is the wind speed, Tw and Ta are the water and air temperature in degrees Celsius.

The Kelvin wedge

On open water, moving ships generate waves. These waves cannot be in any reasonable approximation treated as exclusively longitudinal. The phenomenon, the so-called Kelvin wedge was first analyzed by Lord Kelvin. An ideal example is visualized on the next figure:


The complicated wave pattern behind a ship is influenced by the viscosity of the water, by the moving directions, gravity, not to mention non-linear effects which become significant when the amplitude is large. Stern waves and bow waves are superposed on one another, and not infrequently, other wave systems may be discerned originating from somewhere between the bow and stern. The fact, that the angle enclosed by the Kelvin wedge is independent of the speed of the boot can be surprising, but the explanation is out of the scope of this paper. For more details, see [2].

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