The flow between two rotating disks (radius to heigh ratio of 20.9), enclosed by a rotating cylinder, is investigated experimentally in the cases of both co- and counter-rotation. This flow gives rise to a large gallery of instability patterns. A regime diagram of these patterns is presented in the (Reb,Ret)-plane, where Reb,t is the Reynolds number associated with each disk. The co-rotation case and the weak counter-rotation case are very similar to the rotor–stator case, both for the basic flow and the instability patterns: the basic flow consists of two boundary layers near each disk and the instability patterns are the axisymmetric vortices and the positive spirals described in the rotor–stator experiments of Gauthier, Gondret & Rabaud (1999), Schouveiler, Le Gal & Chauve (2001), and the numerical study of Serre, Crespo del Arco & Bontoux (2001). The counter-rotation case with higher rotation ratio is more complex: above a given rotation ratio, the recirculation flow becomes organized into a two-cell structure with the appearance of a stagnation circle on the slower disk. A new kind of instability pattern is observed, called negative spirals. Measurements of the main characteristics of this pattern are presented, including growth times, critical modes and phase velocities.

This paper describes an experimental study of the manipulation of a fully developed turbulent channel flow through large-scale streamwise vortices originated by vortex generator jets distributed along the wall in the spanwise direction. Apart from the interest in flow management itself, an important aim of the research is to observe the response of the flow to external perturbations as a technique for investigating the structure of turbulence. Considerable mean and fluctuating skin friction reductions, locally as high as 30% and 50% respectively, were measured for an optimal forcing flow intensity. Mean and fluctuating velocity profiles are also greatly modified by the manipulating large-scale vortices; in particular, attenuation of the turbulence intensity was measured. Moreover the flow manipulation caused an increase in longitudinal coherence of the wall organized motions, accompanied by a reduced frequency of burst events, demonstrated by a reduction of the velocity time derivative PDFs and by an higher intermittency. A strong transversal periodic organization of the flow field was observed, including some typical behaviours in each of the periodic boxes originated by the interaction of the vortex pairs. Results are interpreted and discussed in terms of management of the near-wall turbulent structures and with reference to the wall turbulence regeneration mechanisms suggested in the literature.

We propose a new generalized model to describe deformations of the mobile interface separating two immiscible liquids in a porous medium. The densities and the viscosities of the fluids can have any value. The horizontal size of the interface is much greater than the vertical size of the domain. Unlike the classical theory, the new model describes gravitational non-equilibrium processes, including the Rayleigh–Taylor instability which appears in the form of a negative apparent diffusion parameter. Several flow regimes are established depending on the ratio between gravity and the elastic fluid/medium forces, and between the vertical and horizontal flow rates. The model is used to analyse the evolution of the interface during the free spreading of one liquid over another. This is characterized by the presence of interface degeneration points. The explicit solution to the problem of oil and water flow towards a well is presented as an application to oil reservoirs.

We present some preliminary results from using large-eddy simulation to compute the late wake of a sphere towed at constant speed through a non-stratified and a uniformly stratified fluid. The wake is computed in each case for two values of the Reynolds number: Re = 104, which is comparable to that used in laboratory experiments, and Re = 105. An important aspect of the simulation is the use of an iterative procedure to relax the initial turbulence field so that the normal and shear turbulent stresses are properly correlated and the turbulent production and dissipation are in equilibrium. For the lower Reynolds number our results compare well with existing laboratory experimental results. For the higher Reynolds number we find that even though the turbulence is more developed and the wake contains finer structure, most of the similarity properties of the wake are unchanged compared with those observed at the lower Reynolds number.

The influence of the coherent structures on grid/subgrid-scale (GS/SGS) interactions in free shear layers is analysed through the application of a top-hat filter to several plane jet direct numerical simulations (DNS). The Reynolds number based on the plane jet inlet slot width is Reh = 3000. The study deals with energy containing (Kelvin–Helmholtz) and inertial range (streamwise) vortices, from the far field of the turbulent plane jet. The most intense kinetic energy exchanges between GS and SGS occur near these structures and not randomly in the space. The GS kinetic energy is dominated by GS advection and GS pressure/velocity interactions which appear located next to the Kelvin–Helmholtz rollers. Surprisingly, GS/SGS transfer is not very well correlated with the coherent vortices and GS/SGS diffusion plays an important role in the local dynamics of both GS and SGS kinetic energy. The so-called ‘local equilibrium assumption’ holds globally but not locally as most viscous dissipation of SGS kinetic energy takes place within the vortex cores whereas forward and backward GS/SGS transfer occurs at quite different locations. Finally, it was shown that SGS kinetic energy advection may be locally large as compared to the other terms of the SGS kinetic energy transport equation.

In this paper, we study the transverse vortex-induced vibrations of a cylinder with no structural restoring force (k = 0). In terms of the conventionally used normalized flow velocity, U*, the present experiments correspond to an infinite value (where U* = U/fND, fN = natural frequency, D = diameter). A reduction of mass ratios m* (mass/displaced mass) from the classically studied values of order m* = 100, down to m* = 1, yields negligible oscillations. However, a further reduction in mass exhibits a surprising result: large-amplitude vigorous vibrations suddenly appear for values of mass less than a critical mass ratio, m*crit = 0.54. The classical assumption, since the work of den Hartog (1934), has been that resonant large-amplitude oscillations exist only over a narrow range of velocities, around U*∼5, where the vortex shedding frequency is comparable with the natural frequency. However, in the present study, we demonstrate that, so long as the body’s mass is below this critical value, the regime of normalized velocities (U*) for resonant oscillations is infinitely wide, beginning at around U*∼5 and extending to U*→∞. This result is in precise accordance with the predictions put forward by Govardhan & Williamson (2000), based on elastically mounted vibration studies (where k > 0). We deduce a condition under which this unusual concept of an infinitely wide regime of resonance will occur in any generic vortex-induced vibration system.

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

We formulate a bounding principle for the heat transport in Rayleigh–Bénard convection with fixed heat flux through the boundaries. The heat transport, as measured by a conventional Nusselt number, is inversely proportional to the temperature drop across the layer and is bounded above according to Nu [les ] cRˆ1/3, where c < 0.42 is an absolute constant and Rˆ = αγβh4/(νκ) is the ‘effective’ Rayleigh number, the non-dimensional forcing scale set by the imposed heat flux κβ. The relation among the parameter Rˆ, the Nusselt number, and the conventional Rayleigh number defined in terms of the temperature drop across the layer, is NuRa = Rˆ, yielding the bound Nu [les ] c3/2Ra1/2.

The effects of a sidewall with finite thermal conductivity on confined turbulent thermal convection has been investigated using direct numerical simulation. The study is motivated by the observation that the heat flowing through the lateral wall is not always negligible in the low-aspect-ratio cells of several recent experiments. The extra heat flux modifies the temperature boundary conditions of the flow and therefore the convective heat transfer. It has been found that, for usual sidewall thicknesses, the heat travelling from the hot to the cold plates directly through the sidewall is negligible owing to the additional heat exchanged at the lateral fluid/wall interface. In contrast, the modified temperature boundary conditions alter the mean flow yielding significant Nusselt number corrections which, in the low Rayleigh number range, can change the exponent of the Nu vs. Ra power law by 10%.

Both a weakly nonlinear analytic theory and direct numerical simulation are used to document processes involved during the spin-up of a rotating stratified fluid driven by wind-stress forcing for time periods less than a homogeneous spin-up time. The strength of the wind forcing, characterized by the Rossby number ε, is small enough (i.e. ε[Lt ]1) that a regular perturbation expansion in ε can be performed yet large enough (more specifically, ε∝E1/2, where E is the Ekman number) that higher-order effects of vertical diffusion and horizontal advection of momentum/density are comparable in magnitude. Cases of strong stratification, where the Burger number S is equal to one, with zero heat flux at the upper boundary are considered. The Ekman transport calculated to O(ε) decreases with increasing absolute vorticity. In contrast to nonlinear barotropic spin-up, vortex stretching in the interior is predominantly linear, as vertical advection negates stretching of interior relative vorticity, yet is driven by Ekman pumping modified by nonlinearity. As vertical vorticity is generated during the spin-up of the fluid, the vertical vorticity feeds back on the Ekman pumping/suction, enhancing pumping and vortex squashing while reducing suction and vortex stretching. This feedback mechanism causes anticyclonic vorticity to grow more rapidly than cyclonic vorticity. Strict application of the zero-heat-flux boundary condition leads to the growth of a diffusive thermal boundary layer E−1/4 times thicker than the Ekman layer embedded within it. In the Ekman layer, vertical diffusion of heat balances horizontal advection of temperature by extracting heat from the thermal boundary layer beneath. The flux of heat extracted from the top of the thermal boundary layer by this mechanism is proportional to the product of the Ekman transport and the horizontal gradient of the temperature at the surface. The cooling caused by this heat flux generates density inversions and intensifies lateral density gradients where the wind-stress curl is negative. These thermal gradients make the potential vorticity strongly negative, conditioning the fluid for ensuing symmetric instability which greatly modifies the spin-up process.

A theoretical analysis was carried out to study the formation and propagation of a weak shock wave in a gas with longitudinal temperature gradients. An equation describing the formation and propagation of a weak shock wave through a non-uniform medium in the absence of energy dissipation was derived. An approximate analytical solution to the one-dimensional wave propagation equation is established. With this, the thermal gradient effects on the shock-wave Mach number and speed were investigated and the results were compared to earlier experiments. Numerical solutions for the same problem using Euler’s equations have also been obtained and compared to the analytical results. The analysis shows that the time of shock-wave formation from the initial disturbance, for mild temperature gradients, is independent of the gradient. The shock wave forms at a longer axial distance from the initial disturbance when the temperature gradient is positive whereas the opposite is true for a negative temperature gradient.

We present exact solutions for suspended sediment transport under one-dimensional dam-break flow, both over a dry bed and into a small depth of tail water. We explicitly calculate the suspended sediment concentration, including erosion and deposition, and investigate the effect of varying the erosional and depositional models employed. These solutions order insight into sediment transport processes under floods or sheet flow events, and we also discuss their application as test-bed solutions for the validation of numerical models.

The scattering of acoustic waves by compact three-dimensional axisymmetric vortices is studied using direct numerical simulation in the case where the incoming wave is aligned with the symmetry axis and the direction of propagation of the vortices. The cases of scattering by Hill’s spherical vortex and Gaussian vortex rings are examined, and results are compared with predictions obtained by matched asymptotic expansions and the Born approximation. Good agreement is obtained for long waves, with the Born approximation usually giving better predictions, especially as the difference in scale between vortex and incoming waves decreases and as the Mach number of the flow increases. An improved version of the Born approximation which takes into account higher-order effects in Mach number gives the best agreement.

In classical WKB theory the only way wave energy density, as a surrogate for wave action density, can increase or decrease along a ray is as a result of the ray focusing or widening. This occurs when the group velocity is divergent. There are particular regions, however, where the wave can resonantly exchange action with another wave mode with approximately the same wavenumbers; a situation known as Landau–Zener transition, mode conversion, linear (adiabatic) resonance, etc. This effect invalidates locally the underlying assumption of WKB theory that no scattering of energy occurs between WKB wave modes. In this paper this effect is investigated theoretically for free long baroclinic Rossby waves in a two-layer planetary geostrophic model of the ocean with a purely zonal topography, here taken as a Gaussian ridge. The waves are excited along the east coast by an unspecified wavemaker at a fixed frequency ω. In the computation considered, mode conversion is found to occur principally near the ridge’s top and on the eastern flank. The predictions of mode conversion theory are tested against the results of direct numerical simulations. This shows excellent agreement, both for the locations of mode conversion points, and for the amplitude of the transmitted and converted WKB wave modes.

A hydrophilic or a hydrophobic long rigid solid plate of finite width, forming a meniscus with a liquid in a uniform gravitational field is considered. The one-dimensional meniscus with prescribed heights of the triple point from the far-field liquid surface is investigated analytically using the Young–Laplace equation. It is found that for a hydrophilic plate, the vertical force necessary to break the meniscus during removal of the plate from the liquid is larger than the force necessary to break the meniscus during submersion of the plate into the liquid. Furthermore, the capillary force on the plate reaches a maximum before the meniscus collapses during removal, but no maximum exists before collapse during submersion. The reverse is true when the plate is hydrophobic. The study is then extended to investigate the interaction force between two plates, each forming a meniscus with the liquid. The elevations of the plates from the far-field liquid surface are prescribed, in contrast to earlier studies where interaction between long cylinders floating under self weight was considered. Here, the menisci are determined exactly using the Young–Laplace equation. It is shown that for prescribed plate elevations, there can be at most two possible pairs of menisci between them. Each pair bifurcates from a meniscus that is determined by the elevations of the plates and the gap between them. Furthermore, as known for solids floating under self-weight, the horizontal component of the interaction force is attractive for similar menisci (e.g. when the two plates are equally displaced in or out of the liquid), and repulsive when they form opposite menisci. It is shown that if the two menisci are of the same type, but not similar (e.g. one plate is pushed more into the liquid than the other), then the force is attractive at long distances, and may be repulsive at shorter distances with a stable equilibrium at a finite distance between the plates, depending on the elevations of the plates. Such interaction can be between two hydrophilic or two hydrophobic plates or between a hydrophilic and a hydrophobic plate.

An analysis is presented of the flow in a layer of liquid whose surface tension varies under the action of a moving surface heat flux distribution chosen to model the spread of a flame over the liquid. Subject to this heat flux, the surface temperature increases from the ambient temperature of the liquid, far upstream, to its vaporization temperature at a moving vaporization front, and stays constant at this value downstream of the vaporization front. The speed of the front is determined by a condition of regularity of the temperature. Three different regimes are found which correspond to the uniform, pulsating and pseudo-uniform regimes of flame spread observed experimentally when the ambient temperature of the liquid, or the strength of the surface heat flux, is decreased. The first and third of these are stationary regimes of high and low front speed, and the second is an oscillatory regime featuring long phases of low speed and short pulses of high speed. An asymptotic description is given of the flow relative to the moving vaporization front in the stationary regime of low speed, which includes a long recirculation eddy ahead of the front and a small region around the front that controls its speed. An explanation of the mechanism of oscillation is proposed based on the interplay between the quasi-steady response of this small controlling region and the delay introduced by the recirculating flow.

The lift forces on rigid spheres entrained in a vortex and a linear shear flow are computed using a direct numerical simulation. The sphere Reynolds number is in the range 10 to 100. The lift coefficient in a vortex is shown to be nearly two orders of magnitude higher than that in a shear flow. The inviscid mechanism is shown to be inadequate to account for the enhanced lift force. The effect of free rotation of the sphere is also shown to be too small to account for the enhanced lift force. Flow structure around the sphere is studied to explain the generation of the strong lift force in a vortex.

The spatial evolution of small-amplitude unsteady disturbances of an axisymmetric swirling jet is examined theoretically. The slow axial divergence of the jet mean flow is accounted for by using the method of multiple scales and a consistent solution for both the mean flow and unsteady disturbance is derived. Previous work by Lu & Lele (1999) has considered the leading-order analysis, in which the modal eigenvalues are determined from locally parallel theory, but the key feature of our analysis is the solution of the next-order secularity condition for the axial variation of the wave-envelope amplitude.

The swirling jet profile sustains two types of instability waves: the Kelvin–Helmholtz instability associated with axial shear, and a centrifugal instability which arises due to a decrease in circulation with radial distance. The evolution of the disturbance axial wavenumber and envelope amplitude with downstream distance is calculated. Numerical results show that the growth of the centrifugal mode is significantly curtailed as a result of a rapidly decaying envelope amplitude. The shear instability is significantly more amplified by the addition of swirl.

The general solution for the disturbance envelope amplitude breaks down at so-called turning points. This is found to occur for a series of neutral propagating modes. A rescaling in the vicinity of the turning point shows that the amplitude in this region is governed by a parabolic cylinder equation. The modal amplitude is seen to decay very significantly through this turning point, even though the mode is neutral to leading order.