Small-scale Lagrangian modelling of air bubbles and oil droplets under breaking waves

Lagrangian transport modelling is commonly applied for marine environmental transport problems. When applied to problems on a timescale of days to weeks, such as marine oil spills, Lagrangian models are often forced with environmental data from operational models for atmosphere, waves and ocean currents. These models typically have a temporal resolution of around 1 hour. Effects that take place on shorter timescale, such as entrainment of oil droplets and air bubbles due to breaking waves, must therefore be parametereised.

On short timescales, the random flight approach is clearly more realistic than a random walk, since the particles have a well-defined and realistic velocity, regardless of the length of the timestep, and since particles in real turbulence do not instantaneously change their direction by arbitrarily large amounts. A consequence of this is that in random flight, particles exhibit superdiffusion on short timescales, and normal diffusion on long timescales, compared to the de-correlation time of the turbulent motion. Random walk methods, on the other hand, always behave as diffusion. Hence, random flight methods are expected to be more relevant for small-scale modelling of transport on short timescale under breaking waves.

Here, we consider small-scale modelling of oil droplet and air bubble entrainment, modelling the transport close to the surface, and at high temporal resolution. We use two different Lagrangian methods: random walk (AR0) and random flight (AR1), and compare the two modelling approaches to each other, as well as to pre-existing parameterisations of the average effects of entrainment. Input parameters to the Lagrangian models are informed by experimental turbulence measurements in a wave flume, and RANS-modelling of the breaking wave. Comparison of particle transport to observations in experimental flume work is ongoing.