For many insects in hovering flight, the stroke amplitude is relatively large (above $120^{\circ }$) and the lift is mainly produced by the leading-edge vortex (LEV) attaching to the wing (the delayed-stall mechanism). Mosquitoes have a very small stroke amplitude (${\approx}45^{\circ }$) and the LEV does not have enough time to form before a stroke ends; thus, the delayed-stall mechanism can not be used. In the present study, we show that their lift is produced by different aerodynamic mechanisms from those of insects with a large stroke amplitude: in a downstroke and upstroke, two large lift peaks and a relatively small one are generated. The first large lift peak (at the beginning of the stroke) mainly comes from the added-mass force caused by the large acceleration of the wing. The second large lift peak (in the mid-portion of the stroke) is produced by the ‘fast-pitching-up rotation’ mechanism: the wing fast pitches up while moving forward, generating a large-magnitude, opposite-sign vorticity at the trailing edge of the wing and near the leading edge of the wing; the rapid generation of opposite-sign vorticity at different locations of the wing results in a large time rate of change in the first moment of vorticity, hence a large aerodynamic force. The third lift peak, which is near the end of the stroke and is small, is a result of the fast-pitching-up rotation of a rapidly decelerating wing. Note that although the added-mass force contributes positive lift in the beginning part of the stroke when the wing is in acceleration, it gives negative lift in the next part of the stroke when the wing is in deceleration; i.e. the added-mass force has no effect on the time-average lift, but it greatly changes the time distribution of the lift.

Advancements in understanding the lateral migration of particles have helped in enhanced focusing in microfluidic devices. In this work, we investigate the effects of electrokinetics on particle migration in a viscoelastic flow, where the electric field is applied parallel to the flow. Through experiments and use of perturbation theory in conjunction with the reciprocal theorem, we show that the interaction of electrokinetic and rheological effects can result in an enhancement in migration by an order of magnitude. The theoretical analysis, in agreement with the experiments, demonstrates that the particles can be focused at different equilibrium positions based on their intrinsic electrical properties.

Direct statistical simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by direct numerical simulation (DNS). That low-order statistics usually evolve slowly compared with instantaneous dynamics is one important advantage of DSS. Depending on the symmetry of the problem and the choice of averaging operation, however, DSS is usually more expensive computationally than DNS because even low-order statistics typically have higher dimension than the underlying fields. Here we show that it is in some cases possible to go much further by using a form of unsupervised learning, proper orthogonal decomposition, to address the ‘curse of dimensionality’. We apply proper orthogonal decomposition directly to DSS in the form of expansions in equal-time cumulants to second order. We explore two averaging operations (zonal and ensemble) and test the approach on two idealized barotropic models of fluid on a rotating sphere (a jet that relaxes deterministically towards an unstable profile and a stochastically driven flow that spontaneously organizes into jets). We show that the method offers the possibility of parameter continuation, in the reduced basis, for the lower-order statistics of the flow. Order-of-magnitude savings in computational cost are sometimes obtained in the reduced basis, potentially enabling access to parameter regimes beyond the reach of DNS.

Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number $\mathit{Pr}=1.07$. Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of self-organized spatio-temporal convection patterns. Close to onset, these patterns have been explained in terms of linear stability analysis of primary and secondary flow states. At a larger temperature difference, far beyond onset, experiments and simulations show complex, dynamically evolving patterns that are not described by stability analysis and remain to be explained. Here we employ a dynamical systems approach. We construct stable and unstable exact invariant states, including equilibria and periodic orbits of the fully nonlinear three-dimensional Oberbeck–Boussinesq equations. These invariant states underlie the observed convection patterns beyond their onset. We identify state space trajectories that, starting from the unstable laminar flow, follow a sequence of dynamical connections between unstable invariant states until the dynamics approaches a stable attractor. Together, the network of dynamically connected invariant states mediates temporal transitions between coexisting invariant states and thereby supports the observed complex time-dependent dynamics in inclined layer convection.

Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a multitude of convection patterns is observed in experiments and numerical simulations. Several observed patterns have been linked to exact invariant states of the fully nonlinear three-dimensional Oberbeck–Boussinesq equations. These exact equilibria, travelling waves and periodic orbits reside in state space and, depending on their stability properties, are transiently visited by the dynamics or act as attractors. To explain the dependence of observed convection patterns on control parameters, we study the parameter dependence of the state space structure. Specifically, we identify the bifurcations that modify the existence, stability and connectivity of invariant states. We numerically continue exact invariant states underlying spatially periodic convection patterns at $Pr=1.07$ under changing control parameters for a temperature difference between the walls and inclination angle. The resulting state branches cover various inclinations from horizontal layer convection to vertical layer convection and beyond. The collection of all computed branches represents an extensive bifurcation network connecting 16 different invariant states across control parameter values. Individual bifurcation structures are discussed in detail and related to the observed complex dynamics of individual convection patterns. Together, the bifurcations and associated state branches indicate at what control parameter values which invariant states coexist. This provides a nonlinear framework to explain the multitude of complex flow dynamics arising in inclined layer convection.

Artificial microswimmers, or ‘microbots’, have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their environment. Traditionally, self-phoretic particles are point like, but slender phoretic rods have become an increasingly prevalent design. While there has been substantial interest in creating efficient asymptotic theories for slender phoretic rods, hitherto such theories have been restricted to straight rods with axisymmetric patterning. However, modern manufacturing methods will soon allow fabrication of slender phoretic filaments with complex three-dimensional shapes. In this paper, we develop a slender body theory for the solute of self-diffusiophoretic filaments of arbitrary three-dimensional shape and patterning. We demonstrate analytically that, unlike other slender body theories, first-order azimuthal variations arising from curvature and confinement can make a leading-order contribution to the swimming kinematics.

Only few rheological models in the literature simultaneously capture the two main non-Newtonian trends of non-colloidal suspensions, namely finite normal stress differences and transient effects. We address this issue by extending a previously proposed minimal model accounting for microstructure anisotropy through a conformation tensor, which was shown to correctly predict transient effects (Ozenda, Saramito & Chambon, J. Rheol., vol. 62 (4), 2018, pp. 889–903). A systematic sensitivity study was performed to provide insights into the physical interpretation of the various model terms. This new model is compared to a large experimental dataset involving varying volume fractions, from dilute to concentrated cases. Both apparent viscosity and normal stress differences in steady state are quantitatively reproduced in the whole range of volume fraction, and qualitative agreement for transient evolution of apparent viscosity during shear reversal is obtained. Furthermore, the model is validated against particle pressure measurements that were not used for parameter identification. Even if the proposed constitutive equation for the Cauchy stress tensor is more difficult to interpret than in the minimal model, this study opens the way for the use of conformation tensor rheological models in applications where the effect of normal stress differences is prominent, like elongational flows or particle migration processes.