Abstract
Oil droplet transport under a non-breaking deep water wave field is investigated herein using Computational Fluid dynamics (CFD). The Reynolds-averaged Navier–Stokes (RANS) equations were solved to simulate regular waves in the absence of wind stress, and the resulting water velocities agreed with Stokes theory for waves. The RANS velocity field was then used to predict the transport of buoyant particles representing oil droplets under the effect of non-locally generated turbulence. The RANS eddy viscosity exhibited an increase with depth until reaching a maximum at approximately a wave height below the mean water level. This was followed by a gradual decrease with depth. The impact of the turbulence was modeled using the local value of eddy diffusivity in a random walk framework with the added effects of the gradient of eddy diffusivity. The vertical gradient of eddy viscosity increased the residence time of droplets in the water column region of high diffusivity; neglecting the gradient of eddy diffusivity resulted in a deviation of the oil plume centroid by more than a half a wave height after 10 wave periods.
Highlights
Waves play an important role in the transport and fate of oil spills [1,2]
We focus on the particular problem of oil droplets spreading under non-breaking deep-water waves with turbulence advected into the domain by the waves and assess the effect of turbulence-engendered diffusion on the transport of the droplets
The current work is an extension of the earlier work of [11] in which Lagrangian tracking of oil particles was performed under regular surface waves in order to understand the combined effects of waves, turbulent diffusion, and buoyancy on the transport of oil droplets at sea
Summary
Waves play an important role in the transport and fate of oil spills [1,2]. Waves at sea are accompanied by breakers of various magnitudes due to the interaction of various waves and the presence of wind. Bakhoday-Paskyabi expanded on these works to consider various types of waves (regular, conidial, and solitary), in which theoretical arguments were given for the need to include the added mass for the conditions considered [16] These studies relied on the irrotational theory of waves, and neglected the impact of turbulence on droplet transport. We focus on the particular problem of oil droplets spreading under non-breaking deep-water waves with turbulence advected into the domain by the waves and assess the effect of turbulence-engendered diffusion on the transport of the droplets. In the present RANS (Reynolds-averaged Navier-Stokes) simulation, the turbulence is injected at the left boundary of the domain and is advected into the domain by the motion of the surface waves.
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