The interaction of oblique monochromatic incident waves with horizontal/inclined/dual porous plates is investigated in the context of two-dimensional linear potential theory and Darcy's law (the normal velocity of fluid passing through a thin porous plate is linearly proportional to the pressure difference across it). The developed theory is verified by both small-scale and full-scale experiments. First, matched eigenfunction expansion (MEE) solutions for a horizontal porous plate are obtained. The relationship between the plate porosity and the porous parameter is obtained from systematic model tests by using six porous plates with different sizes and spacing of circular holes. Secondly, a multi-domain boundary-element method (BEM) using simple-sources (second-kind modified Bessel function) is developed to confirm the MEE solutions and to apply to more general cases including inclined or multiple porous plates. The BEM-based inner solutions are matched to the eigenfunction-based outer solutions to satisfy the outgoing radiation condition in the far field. Both analytical and BEM solutions with the developed empirical porous parameter agree with each other and correlate well with both small-scale data from a two-dimensional wave-tank test and full-scale measurement in a large wave basin. Using the developed predictive tools, wave-absorption efficiency is assessed for various combinations of porosity, water depth, submergence depth, wave heading, and plate/wave characteristics. In particular, it is found that the performance can be improved by imposing the proper inclination angle near the free surface. The optimal porosity is near porosity P=0.1 and the optimal inclination angle is around 10° as long as the plate length is greater than 20% of the wavelength. Based on the selected optimal parameters (porosity=0.1 and inclination angle=11.3°), the effective wave-absorption system for MOERI's square basin is designed.

We investigate the effect of microbubbles on Taylor–Couette flow by means of direct numerical simulations. We employ an Eulerian–Lagrangian approach with a gas–fluid coupling based on the point-force approximation. Added mass, drag, lift and gravity are taken into account in the modelling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number ≲10) induce a robust statistically steady drag reduction (up to 20%) in the wavy vortex flow regime (Re=600–2500). The Reynolds number dependence of the normalized torque (the so-called torque reduction ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. Conf. Ser. vol. 14, 2005, p. 143). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When it is neglected, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified. Movies are available with the online version of the paper.

Electrokinetic flows with heterogeneous conductivity configuration occur widely in microfluidic applications such as sample stacking and multidimensional assays. Electromechanical coupling in these flows may lead to complex flow phenomena, such as sample dispersion due to electro-osmotic velocity mismatch, and electrokinetic instability (EKI). In this work we develop a generalized electrokinetic model suitable for the study of microchannel flows with conductivity gradients and shallow-channel geometry. An asymptotic analysis is performed with the channel depth-to-width ratio as a smallness parameter, and the three-dimensional equations are reduced to a set of depth-averaged equations governing in-plane flow dynamics. The momentum equation uses a Darcy–Brinkman–Forchheimer-type formulation, and the convective–diffusive transport of the conductivity field in the depth direction manifests itself as a dispersion effect on the in-plane conductivity field. The validity of the model is assessed by comparing the numerical results with full three-dimensional direct numerical simulations, and experimental data. The depth-averaged equations provide the accuracy of three-dimensional modelling with a convenient two-dimensional equation set applicable to a wide class of microfluidic devices.

We consider the flow in a spherical chamber undergoing periodic torsional oscillations about an axis through its centre, and analyse it both theoretically and experimentally. We calculate the flow in the limit of small-amplitude oscillations in the form of a series expansion in powers of the amplitude, finding that at second order, a steady streaming flow develops consisting of two toroidal cells. This streaming behaviour is also observed in our experiments. We find good quantitative agreement between theory and experiments, and we discuss the dependence of the steady streaming behaviour as both the oscillation frequency and amplitude are varied.

Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number ReD=44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding Kármán number R+, based on pipe radius R, is 1142, and the computational domain length is 15R. The computed mean flow statistics agree well with Princeton Superpipe data at ReD=41727 and at ReD=74000. Second-order turbulence statistics show good agreement with experimental data at ReD=38000. Near the wall the gradient of with respect to ln(1−r)+ varies with radius except for a narrow region, 70 < (1−r)+ < 120, within which the gradient is approximately 0.149. The gradient of with respect to ln{(1−r)++a+} at the present relatively low Reynolds number of ReD=44000 is not consistent with the proposition that the mean axial velocity is logarithmic with respect to the sum of the wall distance (1−r)+ and an additive constant a+ within a mesolayer below 300 wall units. For the standard case of a+=0 within the narrow region from (1−r)+=50 to 90, the gradient of with respect to ln{(1−r)++a+} is approximately 2.35. Computational results at the lower Reynolds number ReD=5300 also agree well with existing data. The gradient of with respect to 1−r at ReD=44000 is approximately equal to that at ReD=5300 for the region of 1−r > 0.4. For 5300 < ReD < 44000, bulk-velocity-normalized mean velocity defect profiles from the present DNS and from previous experiments collapse within the same radial range of 1−r > 0.4. A rationale based on the curvature of mean velocity gradient profile is proposed to understand the perplexing existence of logarithmic mean velocity profile in very-low-Reynolds-number pipe flows. Beyond ReD=44000, axial turbulence intensity varies linearly with radius within the range of 0.15 < 1−r < 0.7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at ReD=44000 and 5300 when measured in wall units. When normalized in outer units, streamwise coherence and azimuthal dimension of the large-scale structures in the pipe core away from the wall are also comparable at these two Reynolds numbers.

Dissipation elements are identified for various direct numerical simulation (DNS) fields of homogeneous shear turbulence. The fields are those of the fluctuations of a passive scalar, of the three components of velocity and vorticity, of the second invariant of the velocity gradient tensor, turbulent kinetic energy and viscous dissipation. In each of these fields trajectories starting from every grid point are calculated in the direction of ascending and descending gradients, reaching a local maximum and minimum point, respectively. Dissipation elements are defined as spatial regions containing all the grid points from which the same pair of minimum and maximum points is reached. They are parameterized by the linear length between these points and the difference of the field variable at these points.

In analysing the changes that occur during one time step in the linear length as well as in the number of grid points contained in the elements, it is found that rapid splitting and attachment processes occur between elements. These processes are much more frequent than the previously identified processes of cutting and reconnection. The model for the length-scale distribution function that had previously been proposed is modified to include these additional processes. Comparisons of the length-scale distribution function for the various fields with the proposed model show satisfactory agreement.

The conditional mean difference of the field variable at the minimum and maximum points of dissipation elements is calculated for the passive scalar field and the three components of velocity. While the conditional mean difference follows the 1/3 inertial-range Kolmogorov scaling for the passive scalar field, the scaling exponent differs from the 1/3 law for each of the three components of velocity. This is thought to be due to the relatively high shear rate of the DNS calculations.

The conditional mean viscous dissipation shows, differently from all other field variables analysed, a pronounced dependence on the linear length of elements. This is explained by intermittency. This finding is used to evaluate the production and the dissipation term of the empirically derived ϵ-equation that is often used in engineering calculations.

The valveless impedance pump is a simple design that allows the producion or amplification of a flow without the requirement for valves or impellers. It is based on fluid-filled flexible tubing, connected to tubing of different impedances. Pumping is achieved by a periodic excitation at an off-centre position relative to the tube ends. This paper presents a comprehensive study of the fluid and structural dynamics in an impedance pump model using numerical simulations. An axisymmetric finite-element model of both the fluid and solid domains is used with direct coupling at the interface. By examining a wide range of parameters, the pump's resonance nature is described and the concept of resonance wave pumping is discussed. The main driving mechanism of the flow in the tube is the reflection of waves at the tube boundary and the wave dynamics in the passive tube. This concept is supported by three different analyses: (i) time-dependent pressure and flow wave dynamics along the tube, (ii) calculations of pressure–flow loop areas along the passive tube for a description of energy conversion, and (iii) an integral description of total work done by the pump on the fluid. It is shown that at some frequencies, the energy given to the system by the excitation is converted by the elastic tube to kinetic energy at the tube outlet, resulting in an efficient pumping mechanism and thus significantly higher flow rate. It is also shown that pumping can be achieved with any impedance mismatch at one boundary and that the outlet configuration does not necessarily need to be a tube.

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Two-dimensional, finite-depth periodic steady water waves with variable vorticity ω=γ(ψ) and large amplitude a are computed for a large number of cases. In particular, the effect of a shear layer at the top, the middle or the bottom is considered. The maximum amplitude amax varies monotonically with the vorticity function γ(ċ). It is increasing if the stagnation point is at the crest, and is decreasing if the stagnation point is in the interior of the fluid or on the bottom. Relationships between the amplitude, hydraulic head, depth and mass flux are investigated.

The problem of a non-perturbative description of unsteady premixed flames with arbitrary gas expansion is addressed in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps, we show that the flame-front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the downstream gas velocity is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit expression for the rotational component near the flame front. We prove that the unknown potential component is left bounded and divergence-free by this procedure, and hence can be eliminated using the dispersion relation for its on-shell value (i.e. the value along the flame front). The resulting system of integro-differential equations relates the on-shell fresh-gas velocity and the front position. As limiting cases, these equations contain all the theoretical results on flame dynamics established so far, including the linear equation describing the Darrieus–Landau instability of planar flames, and the nonlinear Sivashinsky–Clavin equation for flames with weak gas expansion.

Determining characteristic growth rates for water waves travelling more slowly than the wind has continued to be a key unresolved problem of air–sea interaction for over half a century. Analysis of previously reported and recently acquired laboratory wave data shows a systematic decline in normalized wave growth with increasing mean wave steepness that has not previously been identified. The normalized growth dynamic range is comparable with previously observed scatter amongst other laboratory data gathered in the slow wave range. Strong normalized growth rates are observed at low wave steepnesses, implying an efficient wave-coherent tangential stress contribution. Data obtained during this study show quantitative agreement with the predictions of others of the interactions between short wind waves and the longer lower-frequency waves. Measured normalized wave growth rates are consistent with numerically predicted growth due to wave drag augmented by significant wave-coherent tangential stress.

The rough, hairy surfaces of many insects and spiders serve to render them water-repellent; consequently, when submerged, many are able to survive by virtue of a thin air layer trapped along their exteriors. The diffusion of dissolved oxygen from the ambient water may allow this layer to function as a respiratory bubble or ‘plastron’, and so enable certain species to remain underwater indefinitely. Maintenance of the plastron requires that the curvature pressure balance the pressure difference between the plastron and ambient. Moreover, viable plastrons must be of sufficient area to accommodate the interfacial exchange of O2 and CO2 necessary to meet metabolic demands. By coupling the bubble mechanics, surface and gas-phase chemistry, we enumerate criteria for plastron viability and thereby deduce the range of environmental conditions and dive depths over which plastron breathers can survive. The influence of an external flow on plastron breathing is also examined. Dynamic pressure may become significant for respiration in fast-flowing, shallow and well-aerated streams. Moreover, flow effects are generally significant because they sharpen chemical gradients and so enhance mass transfer across the plastron interface. Modelling this process provides a rationale for the ventilation movements documented in the biology literature, whereby arthropods enhance plastron respiration by flapping their limbs or antennae. Biomimetic implications of our results are discussed.

Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3=C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re≈2000. For Fr > 10 and Re≲120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re≳120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr≲10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7≲Fr≲100 and 15≲Re≲1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

The arbitrary motion of a solid sphere released in a solid-body rotating fluid is investigated theoretically in the limit of small Reynolds and Taylor numbers. The angular velocity of the fluid is assumed to be constant and under the premise that Ta1/2 ≫ Re, the simplicity of the unperturbed flow enables us to calculate analytically the force acting on a particle moving with a harmonic slip velocity (by means of matched asymptotic expansions), when both inertia and unsteady effects are taken into account. Subsequently, these single-frequency results are used in order to determine the temporal expression of the force acting on an arbitrarily moving sphere, since the problem under study is linear. This force is first determined in a co-rotating reference frame and takes the form of two convolution products involving the particle acceleration and the particle velocity. For convenience, the corresponding expression of this force is also derived in the laboratory reference frame, and the particle motion equation obtained is thereafter illustrated by dealing with two practical situations, where unsteady and inertia effects must be taken into account to predict the particle dynamics accurately.

Motivated by applications in solids formation and handling processes we numerically investigate the force and torque required for maintaining a fixed contact between two equally sized solid spheres immersed in fluid flow. The direct numerical procedure applied is based on solving the Navier–Stokes equations by means of the lattice-Boltzmann method, with no-slip conditions at the surfaces of the moving spheres. It is validated by means of the analytical results due to Nir & Acrivos (1973) for sphere doublets in creeping flow. Subsequently, doublets are released in turbulent flows. In these cases, the contact force and torque strongly fluctuate, with peak levels much higher than would follow from simple dimensional analysis. The force fluctuation levels have been quantified by a linear relation in the ratio of sphere radius over Kolmogorov length scale.

Recent experiments in rotating convection have shown that the spatio-temporal bulk convective state with Küppers–Lortz dynamics can be suppressed by small-amplitude modulations of the rotation rate. The resultant axisymmetric pulsed target patterns were observed to develop into axisymmetric travelling target patterns as the modulation amplitude and Rayleigh number were increased. Using the Navier–Stokes–Boussinesq equations with physical boundary conditions, we are able to numerically reproduce the experimental results and gain physical insight into the responsible mechanism, relating the onset of the travelling target patterns to a symmetry-restoring saddle-node on an invariant circle bifurcation. Movies are available with the online version of the paper.

This paper provides an intuitive interpretation of the long-wave inertialess instability of a two-layer film flow. The underlying mechanism is elucidated by inspecting the longitudinal perturbation velocity associated with the surface and interfacial deflections. The velocity is expressed by the composition of three parts, related to the shear stress at the free surface, the continuity condition at the interface, and the pressure disturbance induced by gravity. The effect of each velocity component on the evolutions of the surface and the interface is examined in detail. Specifically, the growth of the free surface is caused by the continuity-induced first-order velocity disturbance associated with an additional phase shift between the surface and interfacial waves, while the growth of the interface is due to the pressure-driven flow. The proposed mechanism gives an alternatively reliable prediction of the wave velocity and growth rate.

A simple two-phase model for steady fully developed flows of particles and water over erodible inclined beds is developed for situations in which the water and particles have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Numerical solutions of the resulting differential equations and boundary conditions provide velocity profiles of the fluid and particles, the concentration profile of the particles, and the depth of the flow at a given angle of inclination of the bed. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that agree with the numerical solutions and those measured in experiments.