Gravity-Capillary Wave Dispersion

σ (mN/m) 72 mN/m ρ (kg/m³) 1000 g (m/s²) 9.81 Depth h (m) 100 m

k_0 (1/m) 360 /m Δk width 80 /m

c_p (m/s)—

c_g (m/s)—

λ (mm)—

c_min (m/s)—

k_min (1/m)—

Regime—

Dispersion relation:

ω²=(gk + σk³/ρ)·tanh(kh)

Phase velocity: c_p = ω/k

Group velocity: c_g = dω/dk

Minimum phase speed:

c_min = (4gσ/ρ)^(1/4)

k_min = (gρ/σ)^(1/2)

k ≪ k_min: gravity waves, c_g=c_p/2
k ≫ k_min: capillary waves, c_g=3c_p/2