Mona Rahmani

Free falling and rising of spherical and angular particles

Direct numerical simulations of freely falling and rising particles in an infinitely long domain, with periodic lateral boundary conditions, are performed. The focus is on characterizing the free motion of cubical and tetrahedral particles for different Reynolds numbers, as an extension to the well-studied behaviour of freely falling and rising spherical bodies. The vortical structure of the wake, dynamics of particle movement, and the interaction of the particle with its wake are studied. The results reveal mechanisms of path instabilities for angular particles, which are different from those for spherical ones. The rotation of the particle plays a more significant role in the transition to chaos for angular particles. Following a framework similar to that of Mougin and Magnaudet [“Wake-induced forces and torques on a zigzagging/spiralling bubble,” J. Fluid Mech. 567, 185–194 (2006)], the balance of forces and torques acting on particles is discussed to gain more insight into the path instabilities of an...

Evolution of a barotropic shear layer into elliptical vortices.

When a barotropic shear layer becomes unstable, it produces the well-known Kelvin-Helmholtz instability (KHI). The nonlinear manifestation of the KHI is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KHI characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counterpropagating vorticity waves is solely responsible for this KHI formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides a possible explanation for the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g., meddies, stratospheric polar vortices, Jovian vortices, Neptunes Great Dark Spot, and coherent vortices in the wind belts of Uranus.

The evolution of large and small-scale structures in Kelvin–Helmholtz instabilities

To better understand the dynamics of Kelvin–Helmholtz instabilities in environmental flows, their evolution is investigated using direct numerical simulations (DNS). Two-dimensional DNS is used to examine the large-scale and small-scale structures of the instability at high Reynolds and Prandtl numbers that represent real environmental flows. The semi-analytical model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) is used to explain the physics of these simulations prior to saturation of the KH billow, and also provide a computationally efficient prediction of the vortex dynamics of the instability. The DNS results show that the large-scale structure of the billow does not depend on the Reynolds number for sufficiently high Reynolds numbers. The billow structure reveals a less straightforward dependence on the Prandtl number. Predictions of the model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) improve as Reynolds number and Prandtl number increase. The small-scale structure of the vorticity and density fields vary with both Reynolds and Prandtl numbers. Three-dimensional DNS of KH flows and their transition to turbulence are used to study small length scales. Based on the thickness of the braid, a simple method is introduced to estimate the Batchelor scale, which can be used as a guide for the resolution required for the direct numerical simulation of two and three-dimensional Kelvin–Helmholtz flow fields.

Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow

Non-Brownian suspension of monodisperse spherical particles, with volume fractions ranging between ϕ = 0.05 and 0.38 and particle Reynolds numbers ranging between Rep = 0.002 and 20, in plane Couette shear flows is investigated using three-dimensional particle-resolved numerical simulations. We examine the effects of volume fraction and particle Reynolds number on the macroscopic and microscopic stresses in the fluid phase. The effective viscosity of the suspension is in a good agreement with the previous empirical and experimental studies. At Rep = 20, however, the effective viscosity increases significantly compared to the lower particle Reynolds number simulations in the Stokes flow regime. Examining the stresses over the depth of the Couette gap reveals that this increase in wall shear stresses at high particle Reynolds numbers is mainly due to the significantly higher particle phase stress contributions. Next, we examine the momentum balance in the fluid and particle phase for different regimes to as...

The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows

The effect of Prandtl number on mixing in temporally evolving Kelvin-Helmholtz (KH) instabilities at low to moderate Reynolds numbers is studied through direct numerical simulation. We distinguish between the mixing induced by the primary billow and the mixing generated by three-dimensional motions by performing each simulation in two and three dimensions. The results indicate that the time evolution of the rate of two- and three-dimensional mixing through different stages of the life cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects and develop significant three-dimensional instabilities. While the mixing generated in the two-dimensional flows, uniform in the span-wise direction, is not significantly dependent on the Prandtl number, the tu...