A novel design concept for a wave energy converter (WEC) is presented and analysed. Its purpose is to balance the theoretical capacity for power absorption against engineering design issues which plague many existing WEC concepts. The WEC comprises a fully submerged buoyant circular cylinder tethered to the sea bed by a simple mooring system which permits coupled surge and roll motions of the cylinder. Inside the cylinder a mechanical system of pendulums rotate with power generated by the relative rotation rates of the pendulums and the cylinder. The attractive features of this design include: making use of the mooring system as a passive component of the power take off (PTO); using a submerged device to protect it from excessive forces associated with extreme wave conditions; locating the PTO within the device and using a PTO mechanism which does not need to be constrained; exploiting multiple resonances of the system to provide a broad-banded response. A mathematical model is developed which couples the hydrodynamic waves forces on the device with the internal pendulums under a linearized framework. For a cylinder spanning a wave tank (equivalent to a two-dimensional assumption) maximum theoretical power for this WEC device is limited to 50 % maximum efficiency. However, numerical results show that a systematically optimized system can generate theoretical efficiencies of more than 45 % over a 6 s range of wave period containing most of the energy in a typical energy spectrum. Furthermore, three-dimensional results for a cylinder of finite length provide evidence that a cylinder device twice the length of its diameter can produce more than its own length in the power of an equivalent incident wave crest.

In this paper we examine the invariants $p$ and $q$ of the reduced $2\times 2$ velocity gradient tensor (VGT) formed from a two-dimensional (2D) slice of an incompressible three-dimensional (3D) flow. Using data from both 2D particle image velocimetry (PIV) measurements and 3D direct numerical simulations of various turbulent flows, we show that the joint probability density functions (p.d.f.s) of $p$ and $q$ exhibit a common characteristic asymmetric shape consistent with $\langle pq\rangle \lt 0$. An explanation for this inequality is proposed. Assuming local homogeneity we derive $\langle p\rangle = 0$ and $\langle q\rangle = 0$. With the addition of local isotropy the sign of $\langle pq\rangle $ is proved to be the same as that of the skewness of $\partial {u}_{1} / \partial {x}_{1} $, hence negative. This suggests that the observed asymmetry in the joint p.d.f.s of $p{{\ndash}}q$ stems from the universal predominance of vortex stretching at the smallest scales. Some advantages of this joint p.d.f. compared with that of $Q{{\ndash}}R$ obtained from the full $3\times 3$ VGT are discussed. Analysing the eigenvalues of the reduced strain-rate matrix associated with the reduced VGT, we prove that in some cases the 2D data can unambiguously discriminate between the bi-axial (sheet-forming) and axial (tube-forming) strain-rate configurations of the full $3\times 3$ strain-rate tensor.

This paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

The onset of transition for the rotating-disk flow was identified by Lingwood (J. Fluid. Mech., vol. 299, 1995, pp. 17–33) as being highly reproducible, which motivated her to look for absolute instability of the boundary-layer flow; the flow was found to be locally absolutely unstable above a Reynolds number of 507. Global instability, if associated with laminar–turbulent transition, implies that the onset of transition should be highly repeatable across different experimental facilities. While it has previously been shown that local absolute instability does not necessarily lead to linear global instability: Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) has shown, using the linearized complex Ginzburg–Landau equation, that if the finite nature of the flow domain is accounted for, then local absolute instability can give rise to linear global instability and lead directly to a nonlinear global mode. Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) also showed that there is a weak stabilizing effect as the steep front to the nonlinear global mode approaches the edge of the disk, and suggested that this might explain some reports of slightly higher transition Reynolds numbers, when located close to the edge. Here we look closely at the effects the edge of the disk have on laminar–turbulent transition of the rotating-disk boundary-layer flow. We present data for three different edge configurations and various edge Reynolds numbers, which show no obvious variation in the transition Reynolds number due to proximity to the edge of the disk. These data, together with the application (as far as possible) of a consistent definition for the onset of transition to others’ results, reduce the already relatively small scatter in reported transition Reynolds numbers, suggesting even greater reproducibility than previously thought for ‘clean’ disk experiments. The present results suggest that the finite nature of the disk, present in all real experiments, may indeed, as Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) suggests, lead to linear global instability as a first step in the onset of transition but we have not been able to verify a correlation between the transition Reynolds number and edge Reynolds number.

A laboratory experiment was performed to study the dynamically rich interaction of a turbulent open channel flow with a bed-mounted axial-flow hydrokinetic turbine. An acoustic Doppler velocimeter and a torque transducer were used to simultaneously measure at high temporal resolution the three velocity components of the flow at various locations upstream of the turbine and in the wake region and turbine power, respectively. Results show that for sufficiently low frequencies the instantaneous power generated by the turbine is modulated by the turbulent structure of the approach flow. The critical frequency above which the response of the turbine is decoupled from the turbulent flow structure is shown to vary linearly with the angular frequency of the rotor. The measurements elucidate the structure of the turbulent turbine wake, which is shown to persist for at least fifteen rotor diameters downstream of the rotor, and a new approach is proposed to quantify the wake recovery, based on the growth of the largest scale motions in the flow. Spectral analysis is employed to demonstrate the dominant effect of the tip vortices in the energy distribution in the near-wake region and uncover meandering motions.

The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of $N$ spheres moving along a fixed line. The spheres are linked to each other by arms with their lengths changing periodically. We use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that self-propulsion velocity appears (in the main approximation) as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, four- and five-sphere swimmers are calculated.

We examine pulse interaction and bound-state formation in interfacial turbulence using the problem of a falling liquid film as a model system. We perform direct numerical simulations (DNSs) of the full Navier–Stokes equations and associated wall and free-surface boundary conditions and we examine both analytically and numerically a low-dimensional (LD) model for the film. For a two-pulse system, DNSs reveal the existence of very rich and complex pulse interactions, characterized by either overdamped, underdamped or self-sustained oscillating behaviours, all of them found to be in excellent agreement with LD results. Having demonstrated the reliability of the LD model for two-pulse systems/smaller domains, we use it to investigate larger domains with many interacting pulses, where DNSs are computationally expensive. We demonstrate that such systems are likely to be dominated by a self-sustained oscillatory dynamics.

Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally $2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $ for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

We report results of a combined numerical and experimental study on axisymmetric and non-axisymmetric flow states in a finite-length, co-rotating Taylor–Couette system in the Taylor vortex regime but also in the Rayleigh stable regime for moderate Reynolds numbers (${\leq }1000$). We found the dominant boundary-driven axisymmetric circulation to play a crucial role in the mode selection and the bifurcation behaviour in this flow. A sequence of partially hysteretic transitions to other axisymmetric multi-cell flow states is observed. Furthermore, we observed spiral states bifurcating via a supercritical Hopf bifurcation out of these multi-cell states which strongly determine the shape of the spiral. Finally, an excellent agreement between experimental and numerical results of the full Navier–Stokes equations is found.

We analyse axisymmetric gravity currents of power-law fluids theoretically and experimentally. We use aqueous suspensions of Xanthan gum in laboratory experiments of constant-volume and constant-flux release to resolve the rheological parameters of the fluid, which we then compare with measurements made using a strain-controlled rheometer. We find that the constant-volume release of highly shear-thinning fluids involves an early-time evolution dominated by inertia, and non-convex free surfaces that make the application of similarity solutions of the late-time viscously dominated evolution inefficient at resolving material properties. In contrast, constant-flux release of the same fluids can be viscously dominated and consistent with the self-similar solution from early in the evolution, which makes it a more useful method for measuring rheological parameters.

Chapman–Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier–Stokes–Fourier order these models, known as Burnett hydrodynamic-regime equations, violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series expansion. A close comparison with the conventional Burnett hydrodynamic set of equations is made and the linear stabilities around an equilibrium point under small perturbations are presented.

We report on near-turbulent thermal convection of a nematic liquid crystal heated from below in a cylindrical cell with an aspect ratio (diameter/height) equal to 0.50 for Rayleigh numbers $2\times 1{0}^{7} \lesssim \mathit{Ra}\lesssim 3\times 1{0}^{8} $ and a Prandtl number of about 355. The Nusselt number $\mathit{Nu}$ as a function of $\mathit{Ra}$ did not differ significantly from that of an isotropic fluid. In a vertical magnetic field $\mathbi{H}$, we found $\mathit{Nu}(H)/ \mathit{Nu}(0)= 1+ a(\mathit{Ra}){H}^{2} $, with $a(\mathit{Ra})= 0. 24{\mathit{Ra}}^{0. 75} ~{\mathrm{G} }^{- 2} $. We present a model that describes the $H$ dependence in terms of a change of the thermal conductivity in the thermal boundary layers due to a field-induced director alignment.

We consider the development of Dean vortices in a curved channel of finite aspect ratio. Solutions to the axisymmetric Navier–Stokes equations are obtained through a finite-element analysis, allowing us to explore the complex and rich bifurcation pattern of the flow as the aspect ratio and Dean number vary. We demonstrate a new class of finite-amplitude vortices and discuss their relationship to similar structures seen in finite-length Taylor–Couette flow.

Using high-speed photography coupled with optical interference, we experimentally study the air entrapment during a liquid drop impacting a solid substrate. We observe the formation of a compressed air film before the liquid touches the substrate, with internal pressure considerably higher than the atmospheric value. The degree of compression highly depends on the impact velocity, as explained by balancing the liquid deceleration with the large pressure of the compressed air. After contact, the air film expands vertically at the edge, reducing its pressure within a few tens of microseconds and producing a thick rim on the perimeter. This thick-rimmed air film subsequently contracts into an air bubble, governed by the complex interaction between surface tension, inertia and viscous drag. Such a process is universally observed for impacts above a few centimetres high.

Three-dimensional direct numerical simulation of horizontal convection is reported for a large Rayleigh number, $\mathit{Ra}\sim O(1{0}^{12} )$, and boundary conditions that allow comparison with previous laboratory experiments. The convection is forced by heating over half of the horizontal base of a long channel and cooling over the other half of the base. The solutions are consistent with the experiments, including small-scale streamwise roll instability developing into a convectively mixed layer within the bottom thermal boundary layer, and a turbulent endwall plume. The mechanical energy budget is shown to be dominated by conversions of available potential energy to kinetic energy by buoyancy flux in the plume and the reverse in the interior of the circulation. These local conversions are three orders of magnitude greater than the total rate of viscous dissipation. The total irreversible mixing is exactly equal to the generation of available potential energy by buoyancy forcing, and one order of magnitude larger than the viscous dissipation. This confirms that dissipation rate is not an indicator of the strength of the circulation and explains why horizontal convection is more energetic than might be expected.

We investigate the shape of bubbles in liquid oxygen under magnetic levitation conditions: a magnetic field is applied that polarizes bulk oxygen, and its spatial variation induces a body force opposed to its weight. In these conditions, bubbles appear to have a smooth ellipsoidal shape, which may be prolate (elongated in the vertical direction), oblate (elongated in the horizontal plane) or perfectly spherical. The dependence of the elongation ratio $\eta $ on the volume and levitation position is explored. It is found that the bubble shape is prescribed by the minimization of the sum of surface tension, demagnetization and magnetic–gravitational potential energies.

Experimental results for instabilities present in a rotating Hagen–Poiseuille flow are reported in this study through fluid flow visualization. First, we found a very good agreement between the experimental and the theoretical predictions for the onset of convective hydrodynamic instabilities. Our analysis in a space–time domain is able to obtain quantitative data, so the wavelengths and the frequencies are also estimated. The comparison of the predicted theoretical frequencies with the experimental ones shows the suitability of the parallel, spatial and linear stability analysis, even though the problem is spatially developing. Special attention is focused on the transition from convective to absolute instabilities, where we observe that the entire pipe presents wavy patterns, and the experimental frequencies collapse with the theoretical results for the absolute frequencies. Thus, we provide experimental evidence of absolute instabilities in a pipe flow, confirming that the rotating pipe flow may be absolutely unstable for moderate values of Reynolds numbers and low values of the swirl parameter.

The linear stability of core–annular fluid arrangements are considered in which two concentric viscous fluid layers occupy the annular region within a straight pipe with a solid rod mounted on its axis when the interface between the fluids is coated with an insoluble surfactant. The linear stability of this arrangement is studied in two scenarios: one for core–annular flow in the absence of the rod and the second for rod–annular flow when the rod moves parallel to itself along the pipe axis at a prescribed velocity. In the latter case the effect of convective motion on a quiescent fluid configuration is also considered. For both flows the emphasis is placed on non-axisymmetric modes; in particular their impact on the recent stabilization to axisymmetric modes at zero Reynolds number discovered by Bassom, Blyth and Papageorgiou (J. Fluid. Mech., vol. 704, 2012, pp. 333–359) is assessed. It is found that in general non-axisymmetric disturbances do not undermine this stabilization, but under certain conditions the flow may be linearly stable to axisymmetric disturbances but linearly unstable to non-axisymmetric disturbances.

We consider the mixing of passive scalars transported in turbulent flow, with a molecular diffusivity that is large compared to the kinematic viscosity of the fluid. This particular case of mixing has not received much attention in experiment or simulation even though the first putative theory, due to Batchelor, Howells & Townsend (J. Fluid Mech., vol. 5, 1959, pp. 134–139), is now more than 50 years old. We study the problem using direct numerical simulation of decaying scalar fields in steadily sustained homogeneous turbulence as the Schmidt number (the ratio of the kinematic viscosity of the fluid to the molecular diffusivity of the scalar) is allowed to vary from $1/ 8$ to $1/ 2048$ for two values of the microscale Reynolds number, ${R}_{\lambda } \approx 140$ and $\approx $240. The simulations show that the passive scalar spectrum assumes a slope of $- 17/ 3$ in a range of scales, as predicted by the theory, when the Schmidt number is small and the Reynolds number is simultaneously large. The observed agreement between theory and simulation in the prefactor in the spectrum is not perfect. We assess the reasons for this discrepancy by a careful examination of the scalar evolution equation in the light of the assumptions of the theory, and conclude that the finite range of scales resolved in simulations is the main reason. Numerical issues specific to the regime of very low Schmidt numbers are also addressed briefly.