Surfactant effects on gravity-capillary waves

Surfactants at the air–sea interface are known to alter surface wave dynamics by modifying surface tension and Marangoni stresses. In this study, we perform two-dimensional direct numerical simulations of gravity-capillary waves with insoluble surfactants using a coupled phase field and volume-of-fluid method. We consider a nonlinear equation of state for surface tension and resolve Marangoni stresses induced by surfactant concentration gradients. We explore a broad parameter space characterised by initial wave steepness $ak$ , Bond number Bo (comparing gravity and surface tension), Reynolds number Re (comparing inertia and viscosity), and the importance of surfactant concentration and strength of the gradient, characterised by a surfactant parameter β . We analyse the impact of surfactants on wave patterns, surface roughness, wave breaking, energy dissipation and surface vorticity. Our results reveal a non-monotonic dependence of wave shape, roughness, vorticity and energy dissipation on β , which is found to be governed by Marangoni effects that peak at intermediate surfactant concentrations. Wave regime transition at high Bo is governed by an effective Bo , which accounts for the reduction in surface tension induced by surfactants. We further introduce a rescaled parameter Bo\,Re-1/2\,(ak)⁻¹ based on force balance, which collapses the transition boundaries across different Re . These findings provide a systematic understanding of surfactant-modulated wave dynamics for both laboratory and geophysical applications.