Inertial particles in stratified turbulence

 The turbulent dispersion of particles plays an important role in oceanic and atmospheric flows. In these flows often a stable density stratification is present which affects the dispersion, especially in vertical direction. In combination with factors such as the available amount of sunlight and the presence of nutrients and predators, algal blooms can occur in coastal areas or lakes. In the atmosphere, topics that receive a lot of attention nowadays are air pollution by high concentrations of aerosols or the dispersion of genetically modified seeds.

In this study we focus on a model system: the dispersion of particles in statistically stationary homogeneous stably stratified turbulent flows. In such flows a negative vertical density gradient is present, the average density of the fluid decreases with increasing height. The resulting flow displays thin layers of large horizontal vortical structures with strong vertical shear between these layers. The particles of interest in this study are fluid particles, heavy inertial particles (particle density much larger than that of the surrounding fluid, e.g. aerosols in air) and light inertial particles (particle density of the same order of the fluid density, e.g. plankton or sand in water).

This study is performed by means of Direct Numerical Simulations. A parallel pseudo-spectral code is used and the simulations are carried out on the national supercomputers Aster & Huygens at SARA in Amsterdam. The Navier-Stokes equations with Boussinesq approximation are solved in combination with an equation of motion for the particles. When mass and inertia of the particles are taken into account, particles do not exactly follow the flow as do fluid particles. In both isotropic turbulence and stably stratified turbulence we observe the effect of preferential concentration; particles are distributed highly non-uniform over the domain.

Due to the stable background stratification, a fluid particle that is displaced from its original equilibrium height will return to that equilibrium height. As a result, vertical dispersion is suppressed, an effect that we find for both fluid particles and inertial particles. This suppression of vertical dispersion becomes less pronounced for particles with higher inertia, because inertial forces become stronger than the restoring gravitational forces. In horizontal direction dispersion in stably stratified turbulence is found to be increased compared to isotropic turbulence and the influence of inertia on this result is limited.

Next to the dispersion of single particles, we also report about the dispersion of pairs of particles and clusters of four particles. This is relevant for future applications in which clustering and aggregate formation of, for example, micro-organisms plays a role. Furthermore, for inertial particles a study on the importance of the different forces acting on the particles is carried out and their effect on particle dispersion in both isotropic and stably stratified turbulence is examined.

Particle positions in a vertical cross-section of the domain for isotropic turbulence, from a run with $10^{6}$ heavy particles with Stokes number $0.96$. The colored background shows the absolute value of the vorticity field.

Positions of 2000 particles after release in a small blob in the center of the domain, at different times: (a) t=0, (b) t=6T, (c) t=9.5 T and (d) t=20T, with T the eddy turnover time. The dispersion in the vertical direction is clearly suppressed.