Dispersion of a vertical jet of buoyant particles in a stably stratified wind-driven Ekman layer

Dispersion of a buoyant jet of particles (i.e. fresh water) in a salt water thermally stratified environment is investigated. The carrying flow field is a wind-driven mid-latitude Ekman layer. The investigation is carried out using Large Eddy Simulation. The dispersed phase is simulated in a Lagrangian way, solving a modified form of the Maxey and Riley equation for each particle of the jet. In order to simulate a large Reynolds number flow, the thin wall layer is not directly resolved and the wall stress and the wall heat flux are directly imposed at the free surface. Results of the simulations show that the presence of incoming heat flux produces a thin region of large density gradients below the free surface and inhibits turbulent transport. In particular, the turbulent penetration depth is strongly reduced by stratification as well as the level of the turbulent fluctuations. In order to consider the effect of the actual density field on the particle dynamics, an improved version of the particle-motion equation is here proposed. The results of our simulations show that the dispersion of the buoyant plume of particles is dramatically modified by stratification. In the neutral case, the plume is spread over the horizontal direction in the free surface region and is driven by the mean Ekman current. In the stratified case, the particles remain entrapped in wavy motion present in the region of large mean density gradients. The horizontal transport is strongly reduced for two reasons: first in the region where large density gradients develop the mean velocity is small compared with the value reached at the free surface; second, the turbulent transport is very small due to the suppression of velocity fluctuations. Finally, our results show that very inaccurate predictions are obtained if the variation of density due to the vertical stratification is not taken into account in the particle motion equation.