The finite-Reynolds-number two-dimensional flow in a channel bounded by a porous medium is studied numerically. The medium is modelled by aligned cylinders in a square or staggered arrangement. Detailed results on the flow structure and slip coefficient are reported. The hydrodynamic force and couple acting on the cylinder layer bounding the porous medium are also evaluated as a function of the Reynolds number. In particular, it is shown that, at finite Reynolds numbers, a lift force acts on the bodies, which may be significant for the mobilization of bottom sediments.

An experimental study is carried out to elucidate the structure of a high Reynolds number (~105) turbulent pulsed jet. Particle image velocimetry measurements showed that the near flow field is dominated by a series of vortex rings with jet-like flows in between. The data show that the vortex rings convect at nearly constant speed of 0.6Uj (Uj: mean jet exit velocity) and the spacing between the rings assumes a value of about 0.6/St (St: Strouhal number=fd/Uj, where f is the pulsing frequency and d is the nozzle exit diameter). With increasing Strouhal number, the rings are closely spaced and the flow tends to assume a steady jet character at five diameters downstream of the nozzle exit. At lower Strouhal numbers there is a distinct region of jet flow in between the rings. Many of the global characteristics, entrainment, mass and momentum flux are essentially determined by the strength and spacing of the rings which, in turn, depend on St. We show that the increase in momentum is due to both increased momentum flux and overpressure at the exit in accordance with Krueger & Gharib (AIAA J., vol. 43 (4), 2005, p. 792). This increase in momentum comes at the expense of higher energy required to produce the jet. We also present results of organized and random components of the fluctuations and production of the random turbulence in a pulsed jet. The two regions of dominant turbulence production are identified with the ring and the trailing jet shear layers.

The unsteady drag and lift generated by the interaction of a gravity current with a bottom-mounted square cylinder are investigated by means of high-resolution Navier–Stokes simulations. Two-dimensional simulations for Reynolds numbers (Re) O(1000) and three-dimensional simulations for Re = O(10000) demonstrate that the drag coefficient increases exponentially towards a maximum as the current meets the cylinder, then undergoes strong fluctuations and eventually approaches a quasi-steady value. The simulation results show that the maximum drag coefficient can reach a value of 3, with the quasi-steady value being O(1), which should aid in selecting a design drag coefficient for submarine structures under the potential impact of gravity currents. The transient drag and lift fluctuations after impact are associated with the Kelvin–Helmholtz vortices in the mixing layer between the gravity current and the ambient fluid. As these vortices pass over the cylinder, they cause the convection of separated flow regions along the bottom wall towards the cylinder. In two-dimensional simulations at Re = O(10000), these flow structures are seen to be unrealistically coherent and to persist throughout the interaction, thus resulting in a noticeable overprediction of the drag and lift fluctuations. On the other hand, the impact of the current on the cylinder is seen to be very well captured by two-dimensional simulations at all Re values. Three-dimensional simulations lead to excellent agreement with available experimental data throughout the flow/structure interaction. They show that the spanwise variation of the drag is determined by the gravity current's lobe-and-cleft structure at impact and by an unsteady cellular flow structure similar to that found in constant-density flows at later times. A comparison between gravity-current flows and corresponding constant-density flows shows the hydrostatic drag component to be important for gravity currents.

We consider the solution in the time domain of water-wave scattering by arrays of bottom-mounted cylinders. It has already been shown that near trapping occurs for certain arrangements of cylinders and we are especially focused on this phenomenon. We begin with the well-known single-frequency solution to the problem of a group of cylinders, and the extension of this solution to complex frequencies. It has been shown that singularities (scattering frequencies or resonances) occur for certain values of the complex frequency and these singularities are associated with the near-trapped mode. We show that it is possible to approximate the solution near these singularities, and produce a modal shape which is associated with the near-trapped mode. We then consider the time-dependent problem, beginning with the well-known incident plane wave packet solution. We also show how the problem of an arbitrary initial displacement can be found using the single-frequency solutions. This latter result relies on a special inner product which gives a generalized eigenfunction expansion (because the operator has a continuous spectrum). We then consider the approximation of the time-dependent motion using special mode shapes associated with the scattering frequencies. This approximation relies on the scattering frequencies lying close to the real axis. We present numerical results which show that this approximation is accurate for sufficiently large time.

Balance laws are derived for the swimming of a deformable body due to prescribed shape changes and the effect of the wake vorticity. The underlying balances of momenta, though classical in nature, provide a unifying framework for the swimming of three-dimensional and planar bodies and they hold even in the presence of viscosity. The derived equations are consistent with Lighthill's reactive force theory for the swimming of slender bodies and, when neglecting vorticity, reduce to the model developed in Kanso et al. (J. Nonlinear Sci., vol. 15, 2005, p. 255) for swimming in potential flow. The locomotion of a deformable body is examined through two sets of examples: the first set studies the effect of cyclic shape deformations, both flapping and undulatory, on the locomotion in potential flow while the second examines the effect of the wake vorticity on the net locomotion. In the latter, the vortex wake is modelled using pairs of point vortices shed periodically from the tail of the deformable body.

Numerical simulations are carried out to investigate vertical fluid particle dispersion in uniformly stratified stationary turbulent flows. The results are compared with the analysis of Lindborg & Brethouwer (J. Fluid Mech., vol. 614, 2008, pp. 303–314), who derived long- and short-time relations for the mean square vertical displacement 〈δz〉 of fluid particles. Several direct numerical simulations (DNSs) with different degrees of stratification and different buoyancy Reynolds numbers are carried out to test the long-time relation 〈δz2〉 = 2ϵPt/N2. Here, ϵP is the mean dissipation of turbulent potential energy; N is the Brunt–Väisälä frequency; and t is time. The DNSs show good agreement with this relation, with a weak dependence on the buoyancy Reynolds number. Simulations with hyperviscosity are carried out to test the relation 〈δz2〉 = (1+πCPL)2ϵPt/N2, which should be valid for shorter time scales in the range N−1 ≪ t ≪ T, where T is the turbulent eddy turnover time. The results of the hyperviscosity simulations come closer to this prediction with CPL about 3 with increasing stratification. However, even in the simulation with the strongest stratification the growth of 〈δz2〉 is somewhat slower than linear in this regime. Based on the simulation results it is argued that the time scale determining the evolution of 〈δz2〉 is the eddy turnover time, T, rather than the buoyancy time scale N−1, as suggested in previous studies. The simulation results are also consistent with the prediction of Lindborg & Brethouwer (2008) that the nearly flat plateau of 〈δz2〉 observed at t ~ T should scale as 4EP/N2, where EP is the mean turbulent potential energy.

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film in the presence of an inclined temperature gradient is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. It has been found that for sufficiently large values of the ratio between the longitudinal and transverse Marangoni numbers, the real part of the linear growth rate does not depend on the direction of the wavenumber, except the case of nearly longitudinal disturbances. Numerous types of nonlinear evolution have been observed, among them are ordered systems of droplets, ‘splashes’, oblique waves, modulated transverse and longitudinal structures.

Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 103 between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.

A long-standing unresolved problem in non-Newtonian fluid mechanics, namely, the relationship between friction drag and flow rate in inertialess complex kinematics flows of dilute polymeric solutions is investigated via self-consistent multiscale flow simulations. Specifically, flow of a highly elastic dilute polymeric solution, described by first principles micromechanical models, through a 4:1:4 axisymmetric contraction and expansion geometry is examined utilizing our recently developed highly efficient multiscale flow simulation algorithm (Koppol, Sureshkumar & Khomami, J. Non-Newtonian Fluid Mech., vol. 141, 2007, p. 180). Comparison with experimental measurements (Rothstein & McKinley, J. Non-Newtonian Fluid Mech., vol. 86, 1999, p. 61) shows that the pressure drop evolution as a function of flow rate can be accurately predicted when the chain dynamics is described by multi-segment bead-spring micromechanical models that closely capture the transient extensional viscosity of the experimental fluid. Specifically, for the first time the experimentally observed doubling of the dimensionless excess pressure drop at intermediate flow rates is predicted. Moreover, based on an energy dissipation analysis it has been shown that the variation of the excess pressure drop with the flow rate is controlled by the flow-microstructure coupling in the extensional flow dominated region of the flow. Finally, the influence of the macromolecular chain extensibility on the vortex dynamics, i.e. growth of the upstream corner vortex at low chain extensibility or the shrinkage of the upstream corner vortex coupled with the formation of a lip vortex that eventually merges with the upstream corner vortex at high chain extensibility is elucidated.

When DC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. In this paper, we apply lubrication theory to examine the possibility of using AC electric fields to exert further control over the size and shape of the pillars. For perfect dielectric films, linear stability analysis shows that the influence of an AC field can be understood by considering an effective DC field. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and it reveals that high frequencies may be used to inhibit the accumulation of interfacial free charge, leading to a lowering of growth rates and wavenumbers. Nonlinear simulations confirm the results of the linear stability analysis while also uncovering additional mechanisms for tuning overall pillar height and width. The results presented here may be of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics.

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Reτ based on the friction velocity uτ and the channel half-width δ in the range 2 × 103 to 2 × 107. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Reτ = 2003 and maintain an O(1) grid dependence on Reτ.

The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Low-dimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier–Stokes flow solver. The approach adopted here is primarily motivated by the quest to develop insights into the fin function and associated hydrodynamics, which are specifically useful for the design of a biomimetic, pectoral fin propulsor. The POD analysis shows that the complex kinematics of the pectoral fin can be described by a few (<5) POD modes and that the first three POD modes are highly distinct. The significance of these modes for thrust production is examined by synthesizing a sequence of fin gaits from these modes and simulating the flow associated with these gaits. We also conduct a scale study of the pectoral fin in order to understand the effect of the two key non-dimensional parameters, Reynolds number and Strouhal number, on the propulsive performance. The implications of the POD analysis and performance scaling on the design of a robotic pectoral fin are discussed.

In this study, the theory of micropolar fluids is employed to study the stability problem of flow between two concentric rotating cylinders. The field equations subject to no-slip conditions (non-zero velocity and microrotation velocity components) at the wall surfaces are solved. The analytical solutions of the velocity and microrotation velocity fields as well as the shear stress difference, couple stress and strain rate for basic flow are obtained. The equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. It is found that non-zero wall-surface microrotation velocity makes the flow faster and more unstable. Moreover, it tends to reduce the limits of critical non-axisymmetric disturbances. The effect on the stability characteristics can be magnified by increasing the microstructure or couple-stress parameter or the microinertia parameter for the cases of corotating cylinders and a stationary outer cylinder or by decreasing the radius ratio or the microinertia parameter for the case of counterrotating cylinders.

A general method is suggested for deriving exact solutions to the Stokes equations in spherical geometries. The method is applied to derive exact solutions for a class of flows in and around a sphere or between concentric spheres, which are generated by meridional driving on the spherical boundaries. The resulting flow fields consist of toroidal eddies or pairs of counter-rotating toroidal eddies. For the concentric sphere case the exact solution when the inner sphere is in instantaneous translation is also derived. Although these solutions are axisymmetric, they can be combined with swirl about a different axis to generate fully three-dimensional fields described exactly by simple formulae. Examples of such complex fields are given. The solutions given here should be useful for, among other things, studying the mixing properties of three-dimensional flows.

A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.

Multi-layer, continuous liquid coating is the most efficient way to manufacture films that require more than one layer for optimal performance. Dual-layer slot coating is one of different coating methods largely used to deposit two thin, uniform liquid layers on to a moving substrate. The two liquid phases are separated by an inter-layer that starts at the separation point (or line, in three dimensions) attached to the die surface. The stability of the two-phase flow and the location of the separation point are directly related to the quality of the final product. Ideally, the separation point should be attached to the downstream corner of the mid die piece of a dual slot-coating die. However, its location may change as operating conditions vary, leading to undesired flow states, with microvortices and periodic oscillation. The movement of the separation point from its desired location along the die surface is usually referred to as mid-gap invasion and can be associated with the onset of coating defects. It is crucial to determine the set of flow conditions at which it occurs. We study the evolution of the separation-point location and the inter-layer configuration as a function of operating conditions by flow visualization and by solving the two-dimensional Navier–Stokes equation for free-surface flows. The results reveal two different mechanisms for mid-gap invasion, depending on the viscosity ratio of the two liquid layers. They also show that the most critical parameter responsible for the onset of mid-gap invasion is the bottom-layer wet thickness (flow rate). Although the movement of the separation point involves an evolution of complex flow states, a simple but accurate criterion based on rectilinear flow approximation is proposed.

This paper extends previous studies of saline gravity currents at high Reynolds number flowing along a tank with a V-shaped valley. We use experiments and a box model to determine the primary features of the flow. The particulate gravity currents were initiated by releasing a fixed volume of fluid consisting of pure water mixed with silicon carbide particles from a lock at one end of the tank. The resulting motion and deposit pattern differ significantly from those for the propagation of a particulate gravity current along a flat-bottomed tank. The front of the current, seen from above, is approximately parabolic (with axis parallel to the flow direction) in contrast to the current in a flat-bottomed tank where it is nearly a straight line perpendicular to the flow. This feature mimics the results for pure saline currents. When seen in profile the currents do not have a clearly defined raised head, which is a feature of the flat-bottomed currents. The mass deposited per unit area varies nearly monotonically with respect to distance down the tank, again in contrast to the case of the flat-bottomed tank. The exceptions to this are the two experiments which have the highest ratio of lock height to length. The mass deposited per unit area across the V-shaped valley is much larger in the central part of the valley than it is on the flanks for any position along the valley. We find that the results can be described with remarkable accuracy by a box model using a generalization of the equation for sedimentation from a turbulent medium due to Martin and Nokes. Our results further show that the factor used in the deposition rate equation which is commonly assumed to be 1 should be smaller, typically 0.7.