We analyse the currently popular vortex identification criteria that are based on pointwise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The interrelationships between the different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These interrelationships provide a new interpretation of the various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered for when similarity or differences can be expected in the vortical structures educed using the different criteria.

We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For $Re\,{<}\,100$, we observe the lift coefficient to decrease with both Reynolds number and distance from the wall. In this regime the present results are in good agreement with the low-Reynolds-number theory of Vasseur & Cox (1977), with the recent experiments of Takemura & Magnaudet (2003) and with the simulations of Kim et al. (1993). The most surprising result from the present simulations is that the wall-induced lift coefficient increases dramatically with increasing $Re$ above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness.

Chaotic advection can be produced whenever the kinematic equations of motion for passively advected particles give rise to a nonintegrable dynamical system. Although this interpretation of the phenomenon immediately shows that it is possible for flows at any value of Reynolds number, the notion of stochastic particle motion within laminar flows runs counter to common intuition to such a degree that the range of applicability of early model results has been questioned. To dispel lingering doubts of this type a study of advection in a two-dimensional Stokes flow slowly modulated in time is presented. Even for this very low Reynolds number, manifestly ‘‘laminar’’ flow chaotic particle motion is readily realizable. Standard diagnostics of chaos are computed for various methods of time modulation. Relations to the general ideas of parametric resonance and adiabatic invariance are pointed out.

Studying particle-laden oscillatory channel flow constitutes an important step towards understanding practical application. This study aims to take a step forward in our understanding of the role of turbulence on fine-particle transport in an oscillatory channel and the back effect of fine particles on turbulence modulation using an Eulerian-Eulerian framework. In particular, simulations presented in this study are selected to investigate wave-induced fine sediment transport processes in a typical coastal setting. Our modelling framework is based on a simplified two-way coupled formulation that is accurate for particles of small Stokes number (St). As a first step, the instantaneous particle velocity is calculated as the superposition of the local fluid velocity and the particle settling velocity while the higher-order particle inertia effect neglected. Correspondingly, only the modulation of carrier flow is due to particle-induced density stratification quantified by the bulk Richardson number, Ri. In this paper, we fixed the Reynolds number to be Re ∆ = 1000 and varied the bulk Richardson number over a range (Ri = 0, 1 × 10 −4 , 3 × 10 −4 and 6 × 10 −4 ). The simulation results reveal critical processes due to different degrees of the particle-turbulence interaction. Essentially, four different regimes of particle transport for the given Re ∆ are observed: (i) the regime where virtually no turbulence modulation in the case of very dilute condition, i.e. Ri ∼ 0; (ii) slightly modified regime where slight turbulence attenuation is observed near the top of the oscillatory boundary layer. However, in this regime a significant change can be observed in the concentration profile with the formation of a lutocline; (iii) regime where flow laminarization occurs during the peak flow, followed by shear instability during the flow reversal. A significant reduction in the oscillatory boundary layer thickness is also observed; (iv) complete laminarization due to strong particle-induced stable density stratification.

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.