Small surface ripples are modelled by the linear wave equation ∂²h/∂t² = c² ∇²h − γ ∂h/∂t on a 150 × 96 grid (cell 2 cm). It is integrated with a leapfrog scheme, stable for Courant number cΔt/Δx ≤ 1/√2 (here 0.5). A pulse spreads as a ring at radius r = c t and its amplitude falls roughly as 1/√r in 2D.

Banks reflect the waves (zero-slope boundary), so rings interfere. Simplifications: real water ripples are dispersive (capillary and gravity waves travel at different speeds, c ≈ √(g/k + σk/ρ)); this non-dispersive model keeps shapes sharp and is meant to show propagation, reflection and interference. Educational model.