Sand transport and morphological change occur in the wave bottom boundary layer due to sand particle interactions with an oscillatory flow and granular interactions between particles. Although these interactions depend strongly on the characteristics of the particle population, i.e. size and shape, little is known about how natural sand particles behave under oscillatory conditions and how variations in particle size influence transport behaviour. To enable this to be studied numerically, an Euler-Lagrange point-particle model is developed which can capture the individual and collective dynamics of subaqueous natural sand grains. Special treatments for particle collision, friction and hydrodynamic interactions are included to take into account the wide size and shape variations in natural sands. The model is used to simulate sand particle dynamics in two asymmetric oscillatory flow conditions corresponding to the vortex ripple experiments of Van der Werf et al. (J. Geophys. Res., vol. 112, 2007, F02012) and the sheet-flow experiments of O'Donoghue & Wright (Coast. Engng, vol. 50, 2004, pp. 117-138). A comparison of the phase resolved velocity and concentration fields shows overall excellent agreement between simulation and experiments. The particle based datasets are used to investigate the spatio-temporal dynamics of the particle-size distribution and the influence of three-dimensional vortical features on particle entrainment and suspension processes. For the first time, it is demonstrated that even for the relatively well-sorted medium-size sands considered here, the characteristics of the local grain size population exhibit significant space-time variation. Both conditions demonstrate a distinct coarse-over-fine armouring at the bed surface during low-velocity phases, which restricts the vertical mobility of finer fractions in the bed, and also results in strong pickup events involving disproportionately coarse fractions. The near-bed layer composition is seen to be very dynamic in the sheet-flow condition, while it remains coarse through most of the cycle in the vortex ripple condition. Particles in suspension spend more time sampling the upward directed parts of these flows, especially the smaller fractions, which delays particle settling and enhances the vertical size sorting of grains in suspension. For the submillimetre grain sizes considered, most † Email address for correspondence: J.Finn@liv.ac.uk

We show that a nanoresonator can be prepared in mesoscopic superposition states merely by monitoring a qubit coupled to the square of the resonator's position. This works for thermal initial states, and does not require a third-order nonlinearity. The required coupling can be generated using a simple open-loop control protocol, obtained with optimal control theory. We simulate the complete preparation process, including environmental noise. Our results indicate the power of open-loop control for state engineering and measurement in quantum nanosystems.

SUMMARYAn Eulerian-Lagrangian approach is developed for the simulation of turbulent bubbly flows in complex systems. The liquid phase is treated as a continuum and the Navier-Stokes equations are solved in an unstructured grid, finite volume framework for turbulent flows. The dynamics of the disperse phase is modeled in a Lagrangian frame and includes models for the motion of each individual bubble, bubble size variations due to the local pressure changes, and interactions among the bubbles and with boundaries. The bubble growth/collapse is modeled by the Rayleigh-Plesset (RP) equation. Three modeling approaches are considered: (a) one-way coupling, where the influence of the bubble on the fluid flow is neglected, (b) two-way coupling, where the momentum-exchange between the fluid and the bubbles is modeled, and (c) volumetric coupling, where the volumetric displacement of the fluid by the bubble motion and the momentum-exchange are modeled. A novel adaptive time-stepping scheme based on stability-analysis of the non-linear bubble dynamics equations is developed. The numerical approach is verified for various single bubble test cases to show second-order accuracy. Interactions of multiple bubbles with vortical flows are simulated to study the effectiveness of the volumetric coupling approach in predicting the flow features observed experimentally. Finally, the numerical approach is used to perform a large-eddy simulation in two configurations: (i) flow over a cavity to predict small-scale cavitation and inception and (ii) a rising dense bubble plume in a stationary water column. The results show good predictive capability of the numerical algorithm in capturing complex flow features.

Direct numerical simulations (DNS) are performed in a triply periodic unit cell of a face-centred cubic (FCC) lattice covering the unsteady inertial, to fully turbulent, flow regimes. The DNS data are used to quantify the flow topology, integral scales, turbulent kinetic energy (TKE) transport and anisotropy distribution in the tortuous geometry. Several unique flow features are observed within this low porosity configuration, where the mean flow undergoes strong acceleration and deceleration regions with presence of three-dimensional helical motions, weak wake-like structures behind spheres, stagnation and jet-impingement-like flows together with merging and spreading jets in the main pore space. The jet-impingement and weak wake-like flow structures give rise to regions with negative total TKE production. Unlike flows in complex shaped ducts, the turbulence intensity levels in the cross-stream directions are found to be larger than those in the streamwise direction. Furthermore, due to the compact nature and confined geometry of the FCC packing, the turbulent integral length scales are estimated to be less than 10 % of the bead diameter even for the lowest Reynolds number studied, indicating the absence of macroscale turbulence structures for this configuration. This finding suggests that even for the highly anisotropic flow within the pore, the upscaled flow statistics are captured well by the representative volumes defined by the unit cell.

Simulations of bubble entrainment and interactions with two dimensional vortical flows are preformed using a discrete element model. In this Eulerian-Lagrangian approach, solution to the carrier phase is obtained using direct numerical simulation whereas motion of subgrid bubbles is modeled using Lagrangian tracking. The volumetric displacement of the fluid by the finite size of the bubbles is modeled along with interphase momentum-exchange for a realistic coupling of the bubbles to the carrier phase. In order to assess the importance of this volumetric coupling effect, even at low overall volume loading, simulations of a small number of microbubbles entrained in a traveling vortex tube are studied in detail. The test case resembles the experiments conducted by Sridhar and Katz ͓JFM, 1999͔ on bubble entrainment in vortex rings. It is shown that under some conditions, the entrainment of eight small bubbles, 1100 m or less in diameter, result in significant levels of vortex distortion when modeled using the volumetric coupling effect. Neglecting these effects, however, does not result in any vortex distortion due to entrained bubbles. The nondimensionalized vortex strength versus bubble settling locations are compared with experimental data to show collapse of the data along the trends observed in experiments only when the volumetric effects are modeled. Qualitative and quantitative assessments of this distortion observed with volumetric coupling are made using three methods; bubble induced vortex asymmetry, relative change in the decay of angular momentum, and relative change in the peak vorticity. It is found that in all cases the volumetric effects result in a relative increase of the vortex decay rate. The concept of a relative reaction force, defined as the ratio of net bubble to fluid reaction to the local driving force of the vortex, is introduced to analyze this effect. It is shown that the global increases in vortex decay rate are directly proportional to the magnitude of this highly local relative reaction force.