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.

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.

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.

[1] Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31-and 131-million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near-wall bottom flow resembles boundary layer flow with several hairpin-like vortices oriented in the direction of the flow and preferential patterns of low-and high-speed streaks. The separation between low-speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low-speed streaks scales with the well-accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of KelvinHelmholtz vortices, which undergo sudden breakup and decay to small-scale turbulence. The effect of turbulence and three-dimensionality on the flow dynamics is addressed by comparing two-and three-dimensional simulations. Three-dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

The separated flow past a zero-thickness flat plate held normal to a free stream at Re=250 has been investigated through numerical experiments. The long-time signatures of the drag and lift coefficients clearly capture a low-frequency unsteadiness with a period of approximately 10 times the primary shedding period. The amplitude and frequency of drag and lift variations during the shedding process are strongly modulated by the low frequency. A physical interpretation of the low-frequency behaviour is that the flow gradually varies between two different regimes: a regime H of high mean drag and a regime L of low mean drag. It is observed that in regime H the shear layer rolls up closer to the plate to form coherent spanwise vortices, while in regime L the shear layer extends farther downstream and the rolled-up Kármán vortices are less coherent. In the high-drag regime three-dimensionality is characterized by coherent Kármán vortices and reasonably well-organized streamwise vortices connecting the Kármán vortices. With a non-dimensional spanwise wavelength of about 1.2, the three-dimensionality in this regime is reminiscent of mode-B three-dimensionality. It is observed that the high degree of spanwise coherence that exists in regime H breaks down in regime L. Based on detailed numerical flow visualization we conjecture that the formation of streamwise and spanwise vortices is not in perfect synchronization and that the low-frequency unsteadiness is the result of this imbalance (or phase mismatch).

The interaction of a planar shock wave with a dense particle curtain is investigated through modeling and experiments. The physics in the interaction between a shock wave with a dense gas-particle mixture is markedly differently from that with a dilute mixture. Following the passage of the shock wave, the dense particle curtain expands rapidly as it propagates downstream and pressures equilibrate throughout the flow field. In the simulations, the particles are viewed as point-particles and are traced in a Lagrangian framework. A physics-based model is then developed to account for interphase coupling. Compared to the standard drag law, four major improvements are made in the present interphase coupling model to take into account: (1) unsteady force contributions to particle force; (2) effect of compressibility on hydrodynamic forces; (3) effect of particle volume fraction on hydrodynamic forces; (4) effect of inter-particle collision. The complex behavior of the dense particle curtain is due to the interplay between two-way coupling, finite particle inertia, and unsteady forces. Incorporation of these effects through significant modeling improvements is essential for the simulation results to agree well with the experimental data. As a result of the large pressure gradient inside the particle curtain, the unsteady forces remain significant for a long time compared to the quasi-steady force and greatly influence the particle curtain motion.