Beyond Stokes drift -- Lagrangian transport in evolving gravity waves

Abstract

Finite-amplitude gravity waves at the air-water interface induce net fluid and particle transport, known as Stokes drift. While this mechanism is well understood for steady waves, transport under unsteady, evolving conditions remains poorly characterized. Here, we investigate Lagrangian transport in freely decaying waves using high-resolution two-phase simulations and a perturbative analytical model. Wave decay modifies the classical Lagrangian drift by introducing both first- and second-order corrections in the wave amplitude expansion, and generates a net vertical transport, governed by the balance between inertia and viscosity. These effects alter particle trajectories and enhance anisotropic mixing, with implications for interpreting field observations and modelling surface transport processes.