Rain Ripples (2D): Circular Wave Superposition on Water

Rain

Rain rate 12 drops/s

Wind drift 0.0 m/s

Wave Physics

Wave speed (c) 3.0 m/s

Damping (1/τ) 0.60 /s

Live Readout

Elapsed time

0.0 s

Splashes

Active ripples

Mean height

0.000

How it works

Every raindrop that reaches the water spawns a circular wave. Each ripple's surface displacement at radius r and age t follows the damped circular wave equation, evaluated at every point of a coarse grid and summed:

h(r,t) = A0 · sin(k·(r − c·t)) · e^(−t/τ) / sqrt(1 + r)
k = 2π / λ,   τ = 1 / damping

The grid samples this sum for every active ripple at each cell, so overlapping ripples truly interfere — crests add, troughs cancel — exactly as real circular water waves do. The 1/√(1+r) term models geometric spreading loss (the same energy spread over a growing circumference), and the exponential term is viscous damping. Brightness in the render maps directly to the signed height field.

Wave speed (c) — how fast the wavefront radius grows per second.
Damping — how quickly a ripple's amplitude decays; higher damping keeps water calmer.
Rain rate / wind — control how many ripples spawn per second and how far drops drift sideways as they fall before splashing.

Falling rain Ripple wavefront Water surface