We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementary to the shape-dependence of the tumbling rate. We confirm this relationship using direct numerical simulations, showing how tumbling rate and spinning rate variances show complementary trends for rod-shaped and disk-shaped particles. We also consider a random but non-turbulent flow. This allows us to explore which of the features observed for rotation in turbulent flow are due to the effects of particle alignment in vortex tubes.

We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylor's frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.

The effects of particle inertia, particle shape, and fluid shear on particle rotation are examined using direct numerical simulation of turbulent channel flow. Particles at the channel center (nearly isotropic turbulence) and near the wall (highly sheared flow) show different rotation patterns and surprisingly different effects of particle inertia. Oblate particles at the center tend to rotate orthogonally to their symmetry axes, whereas prolate particles rotate around their symmetry axes. This trend is weakened by increasing inertia so that highly inertial oblate spheroids rotate nearly isotropically about their principle axes at the channel center. Near the walls, inertia does not move the rotation of spheroids towards isotropy but, rather, reverses the trend, causing oblate spheroids to rotate strongly about their symmetry axes and prolate spheroids to rotate normal to their symmetry axes. The observed phenomena are mostly ascribed to preferential orientations of the spheroids.

We investigate dilute suspensions of Taylor-microscale-sized particles in homogeneous isotropic turbulence. In particular, we focus on the effect of particle shape on particle–fluid interaction. We conduct laboratory experiments using a novel experimental technique to simultaneously measure the kinematics of fluid and particle phases. This uses transparent particles having the same refractive index as water, whose motion we track via embedded optical tracers. We compare the turbulent statistics of a single-phase flow to the turbulent statistics of the fluid phase in a particle–laden suspension. Two suspensions are compared, one in which the particles are spheres and the other in which they are prolate ellipsoids with aspect ratio 2. We find that spherical particles at volume fraction ${\phi }_{v} = 0. 14\hspace{0.167em} \% $ reduce the turbulent kinetic energy (TKE) by 15 % relative to the single-phase flow. At the same volume fraction (and slightly smaller total surface area), ellipsoidal particles have a much smaller effect: they reduce the TKE by 3 % relative to the single-phase flow. Spectral analysis shows the details of TKE reduction and redistribution across spatial scales: spherical particles remove energy from large scales and reinsert it at small scales, while ellipsoids remove relatively less TKE from large scales and reinsert relatively more at small scales. Shape effects are far less evident in the statistics of particle rotation, which are very similar for ellipsoids and spheres. Comparing these with fluid enstrophy statistics, we find that particle rotation is dominated by velocity gradients on scales much larger than the particle characteristic length scales.

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymptotically stable linear dynamics. Numerical experiments demonstrate that linear stability benefits from the presence of a hierarchy of modules and that this architecture improves the robustness of network stability to random perturbations in network structure. This work illustrates an approach to network science which is simultaneously structural and dynamical in nature.