Although developments in fluid mechanics continue at a heady pace, and are reported in JFM at about 800 pages per month, things in the editorial management of JFM change only slowly. There is a continuity among the JFM Editorial Team and among the policies they espouse and implement that appears to be appreciated by the fluid mechanics community. A major change has, however, occurred from January 1999, in that George Batchelor has, after 43 years as Editor, stepped down from the day-to-day handling of papers and from the formulation of policies and practices, and allowed himself to be named on our masthead as Founding Editor. I say ‘allowed’ because George's initial wish was not to be so named, feeling that this might be seen as an immodest and presumptuous title. But Founding Editor is exactly what George was and is. He launched JFM in May 1956, having persuaded Taylor & Francis to be the publisher and printer, and having enlisted the help of G. F. Carrier, W. C. Griffith and M. J. Lighthill as Associate Editors, and T. Brooke Benjamin and I. Proudman as Assistant Editors. Then, as now, all members of the JFM Editorial Team were to work autonomously in the handling of papers, with complete delegated authority and similar workloads, but all following similar procedures and with similar philosophies, and all under the watchful eye of G. K. B.

The scaling behaviour of high-order structure functions Gp(r) =〈(u(x+r)−u(x))p〉 is studied in a variety of laboratory turbulent flows. The statistical accuracy of the structure function benefits from novel instrumentation for its real-time measurement. The nature of statistical errors is discussed extensively. It is argued that integration times must increase for decreasing separations r. Based on the statistical properties of probability density functions we derive a simple estimate of the required integration time for moments of a given order. We further give a way for improving this accuracy through careful extrapolation of probability density functions of velocity differences.

Structure functions are studied in two different kinematical situations. The (standard) longitudinal structure functions are measured using Taylor's hypothesis. In the transverse case an array of probes is used and no recourse to Taylor's hypothesis is needed. The measured scaling exponents deviate from Kolmogorov's (1941) prediction, more strongly so for the transverse exponents.

The experimental results are discussed in the light of the multifractal model that explains intermittency in a geometrical framework. We discuss a prediction of this model for the form of the structure function at scales where viscosity becomes of importance.

A direct numerical simulation of transitional pipe flow is carried out with the help of a spectral element method and used to investigate the localized regions of ‘turbulent’ flow that are observed in experiments. Two types of such regions can be distinguished: the puff and the slug. The puff, which is generally found at low values of the Reynolds numbers, is simulated for Re = 2200 where the Reynolds number Re is based on the mean velocity UB and pipe diameter D. The slug occurs at a higher Reynolds number and it is simulated for Re = 5000. The computations start with a laminar pipe flow to which is added a prescribed velocity disturbance at a given axial position and for a finite time. The disturbance then evolves further into a puff or slug structure.

The simulations confirm the experimentally observed fact that for a puff the velocity near the leading edge changes more gradually than for a slug where an almost discontinuous change is observed. The positions of the leading and trailing edges of the puff and slug are computed from the simulations as a function of time. The propagation velocity of the leading edge is found to be constant and equal to 1.56UB and 1.69UB for the puff and slug, respectively. For the trailing edge the velocity is found to be 0.73UB and 0.52UB, respectively. By rescaling the simulation results obtained at various times to a fixed length, we define an ensemble average. This method is used to compute the average characteristics of the puff and slug such as the spatial distribution of the mean velocity, the turbulent velocity fluctuations and also the wall shear stress. By computing particle trajectories we have investigated the entrainment and detrainment of fluid by a puff and slug. We find that the puff detrains through its trailing edge and entrains through its leading edge. The slug entrains fluid through its leading and through most of its trailing edge. As a consequence the fluid inside the puff is constantly exchanged with fluid outside whereas the fluid inside a slug remains there. These entrainment/detrainment properties which are in agreement with the measurements of Wygnanski & Champagne (1973) imply that the puff has the characteristics of a wave phenomenon while the slug can be characterized more as a material property which travels with the flow.

Finally, we have investigated in more detail the velocity field within the puff. In a coordinate system that travels with the mean velocity we find recirculation regions both near the trailing and leading edges which agrees at least qualitatively with experimental data. We also find streamwise vortices, predominantly in the trailing-edge region which have been also observed in experiments and which are believed to play an important role in the dynamics of the transition process.

The rise and deformation of a gas bubble in an otherwise stationary liquid contained in a closed, right vertical cylinder is investigated using a modified volume-of-fluid (VOF) method incorporating surface tension stresses. Starting from a perfectly spherical bubble which is initially at rest, the upward motion of the bubble in a gravitational field is studied by tracking the liquid–gas interface. The gas in the bubble can be treated as incompressible. The problem is simulated using primitive variables in a control-volume formulation in conjunction with a pressure–velocity coupling based on the SIMPLE algorithm. The modified VOF method used in this study is able to identify and physically treat features such as bubble deformation, cusp formation, breakup and joining. Results in a two-dimensional as well as a three-dimensional coordinate framework are presented. The bubble deformation and its motion are characterized by the Reynolds number, the Bond number, the density ratio, and the viscosity ratio. The effects of these parameters on the bubble rise are demonstrated. Physical mechanisms are discussed for the computational results obtained, especially the formation of a toroidal bubble. The results agree with experiments reported in the literature.

This study considers the linear stability of shear flows in shallow water. It explores instabilities related to the classical incompressible (Rayleigh) instability, and those caused by the over-reflection of surface gravity waves. Numerical solutions of the linear stability problem are presented, together with analytical arguments elucidating the role of finite potential vorticity gradients. The slow development of marginally unstable modes is considered for almost inviscid flows. This is described by an evolution equation for the amplitude of the unstable mode, coupled to a critical-layer potential vorticity equation. This reduced system presents a compact description of the linear stability problem and allows exploration of viscous effects.

We examine the nature of detachment experimentally and numerically in steady axisymmetric flows through sinusoidally constricted tubes with Re varying from 10−4 to 102. Various regions can be distinguished, including flow detachment at the lowest Re used. Further, the transition in the pressure drop from a linear Poiseuille-like behaviour to a nonlinear pressure-drop–velocity relationship is not generally related to the appearance of detachment regions but rather to their form and to the nature of their growth. For the geometries considered here, the relationship between the start of nonlinearity in the pressure drop and incipient detachment depends on whether detachment is symmetric (detachment point at the bottom of a trough): for flow geometries with symmetric incipient detachment kinematic changes occur at Re lower than or the same as that at which dynamic changes can be detected, whereas for those with asymmetric incipient detachment they occur at higher Re. We look at various possible criteria for determining the transition from the viscous to the inertial range. Finally, we discuss the effect of elongational terms in the energy dissipation on flow through periodically constricted tubes and compare this flow with flow through porous media.

The development of a turbulent streamwise vortex core in the wake of a half delta wing has been examined using high-resolution DPIV. The objective of this work was to gain understanding of the transport processes at work a short distance downstream of the wing trailing edge as the wake vortex developed. Experiments were conducted in the Rutgers Free Surface Water Tunnel using an in-house DPIV system. A turbulent streamwise vortex was generated by a half delta wing, with 44 cm chord length and 60° sweep angle, mounted at 30° angle of attack. Reynolds number based on chord length was 65 000. Laser sheets oriented perpendicular to the flow direction were positioned 1, 3.5, and 7 chord lengths downstream of the wing trailing edge. Instantaneous vortex centres were identified in order to track vortex meandering as well as for better quantification of turbulence levels in the vortex core. Mean and fluctuating turbulence terms in the mean streamwise vorticity transport equation along with turbulent kinetic energy dissipation and production were evaluated relative to an inertial reference frame as well as relative to a vortex-centred frame. The results of this analysis highlight the importance of this near-wake region to the downstream evolution of the trailing vortices. There is a high degree of dissipation as well as streamwise vorticity convection in the very near wake which decreases rapidly with increasing distance from the trailing edge.

The instability of a forced, circular shear layer in a rotating fluid has been studied experimentally and numerically. The experiments were performed with a shallow layer of water in a parabolic tank, in which it is possible to apply radial pumping and to model a geophysical beta-effect. A shear layer was produced by a secondary rotation of the central part of the parabolic vessel. In most experiments, the shear layer takes on the appearance of a sequence of vortices, the number of which decreases with increasing strength of the shear. A beta-effect may prevent the formation of a steady vortex chain. Continuous pumping of fluid from the periphery to the centre or vice versa leads to an azimuthal velocity field corresponding to a point vortex. This azimuthal flow appears to stabilize the shear flow if it is opposite to the inner rotation, and to be destabilizing otherwise.

The numerical investigations consist of the solution of the quasi-geostrophic equation in a geometry similar to the experimental situation and with a term modelling the experimental forcing. Though the numerical computations are based on a two-dimensional model, they capture the essential features of the instability and the resulting vortex structures.

We investigate the influence of the ellipticity of a columnar vortex in a rotating environment on its linear stability to three-dimensional perturbations. As a model of the basic-state vorticity distribution, we employ the Stuart steady-state solution of the Euler equations. In the presence of background rotation, an anticyclonic vortex column is shown to be strongly destabilized to three-dimensional perturbations when background rotation is weak, while rapid rotation strongly stabilizes both anticyclonic and cyclonic columns, as might be expected on the basis of the Taylor–Proudman theorem. We demonstrate that there exist three distinct forms of three-dimensional instability to which strong anticyclonic vortices are subject. One form consists of a Coriolis force modified form of the ‘elliptical’ instability, which is dominant for vortex columns whose cross-sections are strongly elliptical. This mode was recently discussed by Potylitsin & Peltier (1998) and Leblanc & Cambon (1998). The second form of instability may be understood to constitute a three-dimensional inertial (centrifugal) mode, which becomes the dominant mechanism of instability as the ellipticity of the vortex column decreases. Also evident in the Stuart model of the vorticity distribution is a third ‘hyperbolic’ mode of instability that is focused on the stagnation point that exists between adjacent vortex cores. Although this short-wavelength cross-stream mode is much less important in the spectrum of the Stuart model than it is in the case of a true homogeneous mixing layer, it nevertheless does exist even though its presence has remained undetected in most previous analyses of the stability of the Stuart solution.

Plane and axisymmetric (radial), horizontal laminar jet flows, produced by natural convection on a horizontal finite plate acting as a heat dipole, are considered at large distances from the plate. It is shown that physically acceptable self-similar solutions of the boundary-layer equations, which include buoyancy effects, exist in certain Prandtl-number regimes, i.e. 0.5<Pr[les ]1.470588 for plane, and Pr>1 for axisymmetric flow. In the plane flow case, the eigenvalues of the self-similar solutions are independent of the Prandtl number and can be determined from a momentum balance, whereas in the axisymmetric case the eigenvalues depend on the Prandtl number and are to be determined as part of the solution of the eigenvalue problem. For Prandtl numbers equal to, or smaller than, the lower limiting values of 0.5 and 1 for plane and axisymmetric flow, respectively, the far flow field is a non-buoyant jet, for which self-similar solutions of the boundary-layer equations are also provided. Furthermore it is shown that self-similar solutions of the full Navier–Stokes equations for axisymmetric flow, with the velocity varying as 1/r, exist for arbitrary values of the Prandtl number.

Comparisons with finite-element solutions of the full Navier–Stokes equations show that the self-similar boundary-layer solutions are asymptotically approached as the plate Grashof number tends to infinity, whereas the self-similar solution to the full Navier–Stokes equations is applicable, for a given value of the Prandtl number, only to one particular, finite value of the Grashof number.

In the Appendices second-order boundary-layer solutions are given, and uniformly valid composite expansions are constructed; asymptotic expansions for large values of the lateral coordinate are performed to study the decay of the self-similar boundary-layer flows; and the stability of the jets is investigated using transient numerical solutions of the Navier–Stokes equations.

The resonant scattering of low-mode progressive edge waves by small-amplitude longshore periodic depth perturbations superposed on a plane beach has recently been investigated using the shallow water equations (Chen & Guza 1998). Coupled evolution equations describing the variations of edge wave amplitudes over a finite-size patch of undulating bathymetry were developed. Here similar evolution equations are derived using the full linear equations, removing the shallow water restriction of small (2N + 1)θ, where N is the maximum mode number considered and θ is the unperturbed planar beach slope angle. The present results confirm the shallow water solutions for vanishingly small (2N + 1)θ and allow simple corrections to the shallow water results for small but finite (2N + 1)θ. Additionally, multi-wave scattering cases occurring only when (2N + 1)θ = O(1) are identified, and detailed descriptions are given for the case involving modes 0, 1, and 2 that occurs only on a steep beach with θ = π/12.

Analytical expressions are derived for the velocity vector, the stress components and the viscosity function in fully developed channel and pipe flow of Phan-Thien–Tanner (PTT) fluids; both the linearized and the exponential forms of the PTT equation are considered. The solution shows that the wall shear stress of a PTT fluid is substantially smaller than the corresponding value for a Newtonian or upper-convected Maxwell fluid, with implications for comparing predicted and measured values in a non-dimensional form.

The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ijS˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.

A nonlinear feedback control strategy for delaying the onset and eliminating the subcritical nature of long-wavelength Marangoni–Bénard convection is investigated based on an evolution equation. A control temperature is applied to the lower wall in a gas–liquid layer otherwise heated uniformly from below. It is shown that, if the interface deflection is assumed to be known via sensing as a function of both horizontal coordinates and time, a control temperature with a cubic-order polynomial dependence on the deflection is capable of delaying the onset as well as eliminating the subcritical instability altogether, at least on the basis of a weakly nonlinear analysis. The analytical results are supported by direct numerical simulations. The control coefficients required for stabilization are O(1) for both delaying onset indefinitely and eliminating subcritical instability. In order to discuss the effects of control, a review is made of the dependence of the weakly nonlinear subcritical solutions without control upon the various governing parameters.

A simple criterion is derived for determining the sign of the pseudomomentum of neutral modes in shallow water systems. The sign of the pseudomomentum is determined by the gradient of the dispersion curve on a wavenumber vs. phase-speed plane: a mode has pseudomomentum with the opposite sign to that of the gradient of the dispersion curve. In most cases, the sign of the pseudomomentum is also determined only from the value of its phase speed: the pseudomomentum of a mode is positive if its phase speed is faster than the velocity of the basic flow at any point and vice versa, but with a few exceptions.

The evolution of a single hairpin vortex-like structure in the mean turbulent field of a low-Reynolds-number channel flow is studied by direct numerical simulation. The structure of the initial three-dimensional vortex is extracted from the two-point spatial correlation of the velocity field by linear stochastic estimation given a second-quadrant ejection event vector. Initial vortices having vorticity that is weak relative to the mean vorticity evolve gradually into omega-shaped vortices that persist for long times and decay slowly. As reported in Zhou, Adrian & Balachandar (1996), initial vortices that exceed a threshold strength relative to the mean flow generate new hairpin vortices upstream of the primary vortex. The detailed mechanisms for this upstream process are determined, and they are generally similar to the mechanisms proposed by Smith et al. (1991), with some notable differences in the details. It has also been found that new hairpins generate downstream of the primary hairpin, thereby forming, together with the upstream hairpins, a coherent packet of hairpins that propagate coherently. This is consistent with the experimental observations of Meinhart & Adrian (1995). The possibility of autogeneration above a critical threshold implies that hairpin vortices in fully turbulent fields may occur singly, but they more often occur in packets. The hairpins also generate quasi-streamwise vortices to the side of the primary hairpin legs. This mechanism bears many similarities to the mechanisms found by Brooke & Hanratty (1993) and Bernard, Thomas & Handler (1993). It provides a means by which new quasi-streamwise vortices, and, subsequently, new hairpin vortices can populate the near-wall layer.

Convection in a vertical magnetic field occurs in narrow cells in the physically relevant limit where the Chandrasekhar number Q becomes large, corresponding to a strong field or small diffusion. This allows asymptotic solutions to be developed for fully nonlinear convection, requiring only the solution of a nonlinear boundary value problem. Solutions for steady and oscillatory magnetoconvection are obtained, with different scalings. In the steady case, the heat flux and the fluid velocity are found at leading order in the asymptotic expansion and the vertical velocity scales as Q1/6. In the oscillatory case, where it is necessary to continue to second order, the vertical velocity is of order Q1/3 and the frequency of the oscillations is always greater than that predicted by linear theory. The heat flux does not depend on either the wavenumber or the planform.