No abstract

The basic wave field resulting from Holmboe's instability is studied both numerically and experimentally. Comparisons between the direct numerical simulations (DNS) and laboratory experiments result in Holmboe waves that are similar in their appearance and phase speed. However, different boundary conditions result in mean flows that display gradual variations either temporally (in the simulations) or spatially (in the experiments). These differences are found to affect the evolution of the dominant wavenumber and amplitude of the wave field. The simulations exhibit a nonlinear ‘wave coarsening’ effect, whereby the energy is shifted to lower wavenumbers in discrete merging events. This process is typically found to result from either ejections of mixed fluid away from the density interface or vortex pairing. In the experiments, energy is transferred to lower wavenumbers by the ‘stretching’ of the wave field by a gradually varying mean velocity. This stretching results in a reduction of wave amplitude compared with the DNS.

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 angular particles.

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 assess the significance of particle/particle interaction and fluid and particle inertia. At the highest particle Reynolds number and volume fraction, the particle inertia plays a dominant role in the momentum balance and the fluid inertia is non-negligible, while the short-lived contact forces are negligible compared to these effects. For all other regimes, the fluid inertia is negligible, but the particle inertia and contact forces are important in the momentum balance. Reynolds stresses originated from velocity fluctuations do not contribute significantly to the suspension stresses in any of the regimes we have studied, while the reduction in the shear-induced particle rotation can be a reason for higher wall shear stress at Rep = 20. Finally, we study the kinematics of particles, including their velocity fluctuations, rotation, and diffusion over the depth of the Couette gap. The particle diffusion coefficients in the cross flow direction exhibit an abrupt increase at Rep = 20.

The effects of different initial perturbations on the evolution of stratified shear flows that are subject to Kelvin-Helmholtz instability and vortex pairing have been investigated through Direct Numerical Simulation (DNS). The effects of purely random perturbations of the background flow are sensitive to the phase of the subharmonic component of the perturbation that has a wavelength double that of the Kelvin-Helmholtz instability. If the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode is optimal, or close to it, vortex pairing occurs. Vortex paring is delayed when there is a phase difference, and this delay increases with increasing phase difference. In three dimensional simulations vortex pairing is suppressed if the phase difference is sufficiently large, reducing the amount of mixing and mixing efficiency. For a given phase difference close enough to the optimal phase, the response of the flow to eigenvalues perturbations is very similar to the response to random perturbations. In addition to traditional diagnostics, we show quantitatively that a non-modal Fourier component in a random perturbation quickly evolves to be modal and describe the process of vortex pairing using Lagrangian trajectories.