Study inspired by tiger thing  tacklebox did yesterday/day before.

*Edit* One thing I'm noticing upon second observation is there is an inherent loss of the "feel" of water when I use broad strokes that remove detail in this manner. In a sense, instead of lots of smaller waves, you get larger waves averaging out the smaller stuff. This implies some kind of fluid with a viscosity much higher than water.

Earlier video games utilizing pixel shaders to depict water (like Monolith Productions' Lithtech engine) had this problem. When shaders were new it wasn't a big deal though. I'm going to have to try some chaotic splattery brushes or some heavy texture to include those smaller ripples.

Why does water of higher viscosity have larger waves? Wave attenuation is viscosity- and size-dependent via Stokes' law of sound attenuation. [1]

Attenuation = (2*viscosity*freq^2)/(2*density of fluid*(speed of sound in fluid)^2)

What about surface waves? Same dealiio, except the solutions are mildly different. However, power dissipation (thus amount of wave dampening) is still dependent on the square of the wave frequency even for surface waves, and that first order viscosity term still shows up. In fact, the amount of surface wave attenuation per frequency is dependent on viscosity and frequency in exactly the same way. [2]

(Power dissipation per unit area) = −2*viscosity*freq^2*(inviscid terms)

This basically means that smaller waves are more prone to disappearing faster, so regions of viscous fluid that are distant from the sources causing the waves are less likely to show those smaller ripples. However, water has a fairly low viscosity compared to what the fluid in the above picture looks like. So frequency-dependent wave attenuation should be much less pronounced. Basically: Because water has a relatively low viscosity, I need to be careful to allow the detail of those smaller waves so the fluid still feels like water.

[1] Stokes, G. G. On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic fluids (read April 1845). Transactions of the Cambridge Philosophical Society, 8, 287.

[2] Behroozi, F. (2003). Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy. European journal of physics, 25(1), 115.