Portuguese Man Of War Colony - 2D Wind Drift Map

Drift as a drag balance

The gas-filled float and crest catch the wind, the submerged float and tentacles feel the water. With the animal moving at v, the air force is F_a = ½ ρ_a C_a A_a (U - v)² and the water force is F_w = ½ ρ_w C_w A_w (v - u_c)², where U is the wind speed and u_c the surface current. The equation of motion is m_eff dv/dt = F_a - F_w. At steady state the forces balance, giving v = (k_a U + k_w u_c) / (k_a + k_w) with k = sqrt(ρ C A). The page integrates the ODE with RK4 and compares the late-time speed with this closed form.

Feeding

Fishing tentacles sweep a swath of length L and effective width w through water at the relative speed |v - u_c|; with prey density n the encounter rate is n L w |v - u_c|.

Honest simplifications: drag coefficients are constants, the drift deflection angle is an input (real animals sail at an angle that depends on which way the crest leans), waves and tentacle contraction are ignored, and the effective mass is a rough estimate. It is a teaching model, not a forecast of where real animals will wash up.