Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic “active turbulence.” Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact coherent structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant exact coherent structures and connecting orbits in a preturbulent active nematic channel flow, which enables a fully nonlinear but highly reduced-order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate- to high-activity regime.

The effect of slip surfaces on the laminar–turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. In laminar flows, the inclusion of the slip surfaces results in a drag reduction of over 10 %, which is in good agreement with previous studies and the theory of laminar slip flows. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. We show that slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and the likelihood is further decreased as slip length is increased. A more deterministic analysis of the effects of slip surfaces on a transition to turbulence is performed by using nonlinear travelling-wave solutions to the Navier–Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham, J. Fluid Mech., vol. 782, 2015, pp. 430–454). Additionally, they exhibit distinct flow structures – the P3 and P4 are denoted as core mode and critical-layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin-friction evolution, linear growth rate and phase-space projection of transitional trajectories. The slip surface appears to modify the transition dynamics very little for the core mode, but quite considerably for the critical-layer mode. Most importantly, the slip surface promotes different transition dynamics – an early and bypass-like transition for the core mode and a delayed and H- or K-type-like transition for the critical-layer mode. We explain these distinct transition dynamics based on spatio-temporal and quadrant analyses. It is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while long sustained ejection events are present in the region of the $\unicode[STIX]{x1D6EC}$ -shaped vortex cores close to the critical layer, resulting in a delayed transition. This should motivate flow control strategies to fully exploit these distinct transition dynamics for transition to turbulence.

Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at $R{e}_{\tau }=u_{\tau }h/\nu$ between 70 and 100, where $u_{\tau }$, h and $\nu$ are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for $R{e}_{\tau }$ between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at $R{e}_{\tau }$ = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for $R{e}_{\tau }$ = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events.

The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $\unicode[STIX]{x1D719}\approx 35\,\%$ , the particle dynamics seems to be hindered by the increase in the magnitude of excluded volume interactions with concentration. However, a non-trivial suspension behaviour is observed in concentrated regimes, where the hydrodynamic diffusivity starts to increase with the volume fraction at $\unicode[STIX]{x1D719}\approx 35\,\%$ , before reaching a local maximum, and then drastically decreases on approaching random close packing. Similar non-trivial behaviours are observed in the particle velocity and number-density fluctuations around volume fractions at which the non-trivial behaviour of the hydrodynamic diffusion is observed. We explain these non-trivial behaviours as a consequence of particle contacts, which are related to the dominant mechanism of particle pairings. The particle contacts are classified into attractive and repulsive classes by the nature of contacts, and in particular, the strong repulsive contact becomes predominant at $\unicode[STIX]{x1D719}>20\,\%$ . Moreover, this transition is visible in the pair distribution functions, which also reveal the change in the suspension microstructure in concentrated regimes. It appears that strong and massive repulsive contacts along the direction perpendicular to an electric field promote the non-trivial suspension behaviours observed in concentrated regimes.

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECSs). ECSs are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECSs in the preturbulent regime by performing a comprehensive study of stable and unstable ECSs for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we compute more than 200 unstable ECSs that coexist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECSs before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic-type ECSs in the turbulent regime.

The United Arab Emirates (UAE) relies on groundwater as well as desalinated water which are very expensive and energy-concentrated. Despite the lack of water resources, only 54% of wastewater was recycled in the UAE in 2016. In this study, a Sustainable Farming Compartment (SFC) with an evaporative cooling system is investigated as an alternative to reusing wastewater and the optimal design is identified experimentally and numerically. First, the applicability of the SFC was examined to reduce the ambient temperature in the system. A prototype SFC was tested in the environmentally constrained laboratory and field site considering an extreme climate condition (with high temperature and humidity) in Abu Dhabi to evaluate the temperature drop and humidity change of the SFC. The experimental results showed that the temperature of the SFC significantly decreases by 7–15 °C when the initial relative humidity is 50%. For validation, an energy modeling using dynamic numerical simulations was performed that shows statistically good agreement with the experimental results. Based on the parametric studies of the system components, the optimal cooling performance of the system in terms of locations of inlet and outlet, the variation of Reynolds number was evaluated. The study suggested an optimized design for the SFC with an evaporative cooling system.