This paper presents a linear stability analysis as well as some numerical results for the motion of heavy particles in the flow field of a Burgers vortex, under the combined effects of particle inertia, Stokes drag, and gravity. By rendering the particle motion equations dimensionless, the particle Stokes number, a Froude number, and a vortex Reynolds number are obtained as the governing three parameters. In the absence of gravity, the vortex center represents a stable equilibrium point for particles up to a critical value of the Stokes number, as the inward drag overcomes the destabilizing centrifugal force on the particle. Particles exceeding the critical Stokes number value asymptotically approach closed circular orbits. Under the influence of gravity, one or three equilibrium points appear away from the vortex center. Both their locations and their stability characteristics are derived analytically. These stability characteristics can furthermore be related to the nature of the critical points in a related directional force field. These findings are expected to be applicable to the coupling between the small-scale turbulent flow structures and the 'motion of suspended particles. Q 1995 American Institute of Physics.

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The dynamics of small, heavy, spherical particles are investigated in an analytical model of the stretched counterrotating streamwise braid vortices commonly found in three-dimensionally evolving mixing layers. The flow field consists of two superimposed rows of Stuart vortices of opposite sign, with an additional two-dimensional strain field. The particle dynamics are determined by a balance of inertial, gravitational, and viscous drag forces, i.e., the dimensionless Stokes and Froude numbers, St and Fr, as well as by the dimensionless strain rate, and the Stuart vortex family parameter. Equilibrium points for the particles, as well as their stability criteria, are determined analytically, both in the absence and in the presence of gravity, and for different orientations of the gravity vector. In the absence of gravity, accumulation of low St particles can occur at the center of the braid vortices. An analytical expression for the critical particle diameter, below which accumulation is possible, is derived. The presence of gravity can lead to the emergence of multiple equilibrium points, whose stability properties depend on their locations. For a horizontal mixing layer flow and strong gravity effects, unconditional accumulation can occur midway between the streamwise braid vortices in the upwelling regions. Conditionally stable accumulation regions exist a short horizontal distance away from the centers of the braid vortices. If the gravity vector lies within the plane of the mixing layer, accumulation points exist only for moderate strengths of gravity. Under these circumstances, conditional accumulation is possible near the streamwise vortex centers.

A computational investigation of the nonlinear dynamics of heavy particles in a row of counterrotating strained vortices is presented. By tracking the particles numerically in the quasi-two-dimensional fluid velocity field, information is obtained on the nature of their trajectories, as well as on probability distribution functions and potential accumulation regions. The particle behavior is discussed as a function of the dimensionless strain rate, the particle Stokes number St, and the dimensionless gravity parameter Fr. Only for very low values of the St can the particles accumulate at the vortex centers. For moderate values of St, they remain trapped on closed trajectories around the vortex centers. Increasing St leads to periodic open trajectories that allow for spanwise transport of the particles. Further bifurcations lead to the generation of multiple trajectories, as well as to subharmonic solutions. Eventually, intermittent and chaotic particle dynamics are observed. In the chaotic regime, a simplified flow model is employed in order to derive various scaling laws for the particle concentration field. For strong levels of gravity, the accumulation of large numbers of particles is observed in the upwelling regions predicted in part I of the present investigation ͓B.

Navier-Stokes simulations of a temporally growing mixing layer are employed to investigate three-dimensional mechanisms for the dispersion and accumulation of small, heavy, spherical particles. It is found that in particular the presence of the streamwise braid vortices gives rise to additional dynamical effects that modify the concentration, dispersion, and suspension patterns observed in two-dimensional situations. Intense stretching and folding by the evolving three-dimensional vorticity field, when combined with inertial effects such as ejection by the concentrated streamwise vortices, strongly distorts the geometry of both clear fluid and particle laden regions. Different time scales can be associated with the spanwise and streamwise vortices, so that these distinct vortical systems can selectively affect different classes of particles.