The motion of isothermal vapour in a permeable rock is governed by a nonlinear diffusion equation for the vapour pressure. We analyse vapour flow described by this equation in both bounded and unbounded domains. We then apply these solutions to describe the controls on the rate of vaporization of liquid invading a hot permeable rock. In an unbounded domain, we determine asymptotic similarity solutions describing the motion of vapour when it is either supplied to or removed from the reservoir. Owing to the compressibility, these solutions have the property that vapour surfaces migrate towards the isobar on which the vapour has the maximum speed.

In contrast, if vapour is supplied to or removed from a closed bounded system sufficiently slowly then the vapour density and pressure rapidly become approximately uniform. As more vapour is added, the mean pressure gradually increases and vapour surfaces become compressed. If liquid slowly invades a hot bounded porous layer and vaporizes, the vapour pressure becomes nearly uniform. As more liquid is added, the reservoir gradually becomes vapour saturated and the vaporization ceases.

In an open bounded system, with a constant rate of vapour injection, the flux of vapour across the reservoir becomes uniform. If liquid is injected slowly and vaporizes then again the vapour flux becomes spatially uniform. However, the vapour flux now increases slowly as the liquid invades further into the rock, as a result of the decreased resistance to vapour flow from the interface to the far boundary.

Employing a recently proposed ‘multi-wave interaction’ theory (Glazman 1992), inertial spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g. nonlinear inertia-gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

A modification to the O(Re)-accurate expression for the hydrodynamic force acting on a body in arbitrary time-dependent motion, determined by Lovalenti & Brady (1993), is presented. This simple modification captures the O(Re2) transient behaviour of the force, which has been recently shown to dominate at large time (Lawrence & Mei 1995), while maintaining the overall O(Re) accuracy.

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.

It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.

A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.

The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.

Results of experiments using a number of techniques to study the nature of convection in a mushy layer generated by directional solidification of aqueous ammonium chloride solutions are reported. The techniques include flow visualization using a dye tracing method to study convection within the mushy layer before and after the onset of plume convection, and X-ray tomography to measure the solid fraction of a growing mush. The principal results are as follows. (i) Prior to the onset of chimneys, there is no convective motion in the mush, in spite of the vigorous finger convection at the mush-liquid interface. (ii) When the plume convection is fully developed, the flow of fluid in the mush consists of a nearly uniform downward motion toward the bottom of the tank, horizontal motion along the bottom toward the chimneys, then upward plume motion through the chimneys in the liquid region above the mush. (iii) The solid fraction of a growing mush as determined by X-ray tomography shows a significant decrease toward the bottom of the tank after the chimneys are fully developed. As a result, the concomitant increase in the local permeability can be as much as 50%. Some of the results reported herein confirm theoretical predictions of Worster (1992) and Amberg & Homsey (1993). Others reveal phenomena not observed heretofore.

Recent observations of growing and collapsing bubbles in flows over axisymmetric headforms have revealed the complexity of the ‘micro-fluid-mechanics’ associated with these bubbles (van der Meulen & van Renesse 1989; Briancon-Marjollet et al. 1990; Ceccio & Brennen 1991). Among the complex features observed were the bubble-to-bubble and bubble-to-boundary-layer interactions which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests, though, were performed on small headform sizes. The focus of this research is to analyse the scaling effects of these phenomena due to variations in model size, Reynolds number and cavitation number. For this purpose, cavitating flows over Schiebe headforms of different sizes (5.08, 25.4 and 50.8 cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). The bubble dynamics captured using high-speed film and electrode sensors are presented along with the noise signals generated during the collapse of the cavities.

In the light of the complexity of the dynamics of the travelling bubbles and the important bubble/bubble interactions, it is clear that the spherical Rayleigh-Plesset analysis cannot reproduce many of the phenomena observed. For this purpose an unsteady numerical code was developed which uses travelling sources to model the interactions between the bubble (or bubbles) and the pressure gradients in the irrotational flow outside the boundary layer on the headform. The paper compares the results of this numerical code with the present experimental results and demonstrates good qualitative agreement between the two.

The stability of a binary liquid mixture heated from above is analysed. The heat transfer is driven by the imposed temperature difference between the horizontal bottom plate and the ambient gas. The mass flux in the layer is induced by the Soret effect. The gravitational effects are ignored, and the instability is driven by solutocapillarity and retarded by thermocapillarity. The interface is allowed to deform, and both the small-wavenumber and the Pearson-type instabilities are studied. Oscillatory instability can exist when the thermocapillary is destabilizing and the solutocapillarity is stabilizing.

Proteins in a biological membrane can be idealized as disks suspended in a thin viscous sheet surrounded by a fluid of lower viscosity (Saffman 1976). To determine the effect of hydrodynamic interactions on protein diffusivities in non-dilute suspensions, we numerically solve the Stokes equations of motion for a system of disks in a bounded periodic two-dimensional fluid using a multipole expansion technique. We consider both free suspensions, in which all the proteins are mobile, and fixed beds, in which a fraction of the proteins are fixed. For free suspensions, we determine both translational and rotational short-time self-diffusivities and the gradient diffusivity as a function of the area fraction of the disks. The translational self- and gradient diffusivities computed in this way grow logarithmically with the number of disks owing to Stokes paradox; to obtain finite values, we renormalize our simulation results by treating long-range interactions in terms of a membrane with an enhanced viscosity in contact with a low-viscosity three-dimensional fluid. The diffusivities in fixed beds require no such adjustment because, at non-dilute area fractions of disks, the Brinkman screening of hydrodynamic interactions is more important that the viscous drag due to the surrounding three-dimensional fluid in limiting the range of hydrodynamic interactions. The diffusivities are determined as functions of the area fractions of both mobile and fixed proteins. We compare our results for diffusivities with experimental measurements of long-time protein self-diffusivity after adjusting our short-time diffusivities calculations in an approximate way to account for effects of hindered diffusion due to volume exclusion, and find very good agreement between the two.

An asymptotic frequency-domain approach is used to describe the radiation from a supersonic swept propeller within the framework of linear acoustics. With this approach the radiation of singularities, their points of origin on the blades, and their relation to blade geometry and loading are easily obtained. In particular, it is shown that a swept propeller with a completely subsonic leading edge can still radiate singularities, if the leading edge is blunt, due to a supersonic edge effect at the blade tips. In addition, the radiation from a family of ‘critical’ swept-blade designs is shown to be more singular than that from a straight-bladed design. Numerical and asymptotic results for such designs show that the peak radiation is, typically, increased by 5–10 dB.

Steady-state two-phase flow in porous media was studied experimentally, using a model pore network of the chamber-and-throat type, etched in glass. The size of the network was sufficient to make end effects negligible. The capillary number, Ca, the flow-rate ratio, r, and the viscosity ratio, k, were changed systematically in a range that is of practical interest, whereas the wettability (moderate), the coalescence factor (high), and the geometrical and topological parameters of the porous medium were kept constant. Optical observations and macroscopic measurements were used to determine the flow regimes, and to calculate the corresponding relative permeabilities and fractional flow values. Four main flow regimes were observed and videorecorded, namely large-ganglion dynamics (LGD), small-ganglion dynamics (SGD), drop-traffic flow (DTF) and connected pathway flow (CPF). A map of the flow regimes is given in figure 3. The experimental demonstration that LGD, SGD and DTF prevail under flow conditions of practical interest, for which the widely held dogma presumes connected pathway flow, necessitates the drastic modification of that assumption. This is bound to have profound implications for the mathematical analysis and computer simulation of the process. The relative permeabilities are shown to correlate strongly with the flow regimes, figure 11. The relative permeability to oil (non-wetting fluid), kro, is minimal in the domain of LGD, and increases strongly as the flow mechanism changes from LGD to SGD to DTF to CPF. The relative permeability to water (wetting fluid), krw, is minimal in the domain of SGD; it increases moderately as the flow mechanism changes from SGD to LGD, whereas it increases strongly as the mechanism changes from SGD to DTF to CPF. Qualitative mechanistic explanations for these experimental results are proposed. The conventional relative permeabilities and the fractional flow of water, fw, are found to be strong functions not only of the water saturation, Sw, but also of Ca and k (with the wettability, the coalescence factor, and all the other parameters kept constant). These results imply that a fundamental reconsideration of fractional flow theory is warranted.

Faraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. Hysteresis occurs when both finite-amplitude solutions and the flat-surface solution are available. We derive a nonlinear model of Faraday resonance, extending the Lagrangian method of Miles (1976). The model is used to investigate hysteresis. The theoretical results are compared to previous experimental studies and to some new observations. It is found necessary to retain damping and forcing terms up to third-order in wave amplitude, and also the fifth-order conservative frequency shift, in order to achieve agreement with experiments. The latter fifth-order term was omitted from all previous studies of Faraday waves. The lower hysteresis boundary in forcing-frequency space is found in most cases to be defined by the lower boundary above which non-trivial stationary points exist. However, the stability of stationary points and the existence of limit cycles are also found to be factors in determining the lower hysteresis boundary. Our results also suggest an indirect method for estimating the coefficient of cubic damping, which is difficult to obtain either experimentally or theoretically.

A general theory for two-dimensional vortex interactions is developed from the observation that, under slowly changing external influences, an individual vortex evolves through a series of equilibrium states until such a state proves unstable. Once an unstable equilibrium state is reached, a relatively fast unsteady evolution ensues, typically involving another nearby vortex. During this fast unsteady evolution, a fraction of the original coherent circulation is lost to filamentary debris, and, remarkably, the flow reorganizes into a set of quasi-steady stable vortices.

The simplifying feature of the proposed theory is its use of adiabatic steadiness and marginal stability to determine the shapes and separation distance of vortices on the brink of an inelastic interaction. As a result, the parameter space for the inelastic interaction of nearby vortices is greatly reduced. In the case of two vortex patches, which is the focus of the present work, inelastic interactions depend only on a single parameter: the area ratio of the two vortices (taking the vorticity magnitude inside each to be equal). Without invoking adiabatic steadiness and marginal stability, one would have to contend with the additional parameters of vortex separation and shape, and the latter is actually an infinitude of parameters.

Spanwise scale changes of the streamwise vortical structure in a plane forced mixing layer have been investigated through direct measurements. Detailed three-dimensional phase-averaged measurements were obtained of the spanwise and streamwise vorticity in a forced mixing layer undergoing three spanwise roller pairings. A two-stream mixing layer with a velocity ratio (U2/U1) of 0.6 and laminar initial boundary layers was generated in a mixing-layer wind tunnel. Acoustic forcing, consisting of a fundamental roll-up frequency and its first, second and third subharmonics, was used to phase-lock the initial development and the first three pairings of the spanwise rollers. Although the overall spanwise scale remained unchanged through the first two roller pairings, some (cyclic) ‘readjustment’ of the weaker streamwise structures was observed. The overall spanwise scale doubled during the third roller pairing. For the first time, one of the proposed mechanisms for the scale change has been identified and its details measured directly. The weakest (positive) streamwise vortex is split into two and displaced by stronger neighbouring (negative) vortices. These two vortices (of the same sign) then merge together, thus doubling the spanwise scale and circulation of the resulting streamwise vortical structure.

Statistical analysis was performed for interpreting the dissipation correlations in turbulent wall-bounded flows. The fundamental issues related to the formulation of the closure assumptions are discussed. Using the two-point correlation technique, a distinction is made between the homogeneous and inhomogeneous parts of the dissipation tensor. It is shown that the inhomogeneous part contributes half of the dissipation rate at the wall and vanishes remote from the wall region. The structure of an analytically derived equation was analysed utilizing the results of direct numerical simulations of turbulent channel flow at low Reynolds number.

The unsteady spreading of an insoluble monolayer containing a fixed mass of surface-active material over the initially horizontal free surface of a viscous fluid layer is investigated. A flow driving the spreading is induced by gradients in surface tension, which arise from the nonuniform surfactant distribution. Distinct phases in the flow's dynamics are distinguished by a time T = H02/v, where H0 is the fluid depth and v its viscosity. For times t [Lt ] T, i.e. before the lower boundary has any significant influence on the flow, a laminar sub-surface boundary-layer flow is generated. The effects of gravity, capillarity, surface diffusion or surface contamination may be weak enough for the flow to drive a substantial unsteady displacement of the free surface, upward behind the monolayer's leading edge and downward towards its centre. Similarity solutions are identified describing the spreading of a localized planar monolayer strip (which spreads like t1/2) or an axisymmetric drop (which spreads like t3/8); using the Prandtl transformation, the associated boundary-layer problems are solved numerically. Quasi-steady sub-layers are shown to exist at the centre and at the leading edge of the monolayer; that due to surface contamination, for example, may eventually grow to dominate the flow, in which case spreading proceeds like t3/4. Once t = O(T), vorticity created at the free surface has diffused down to the lower boundary and the flow changes character, slowing appreciably. The dynamics of this stage are modelled by reducing the problem to a single nonlinear diffusion equation. For a spreading monolayer strip or drop, the transition from an inertia-dominated (boundary-layer) flow to a viscosity-dominated (thin-film) flow is predicted to be largely complete once t ≈ 85 T.

We present an integro-differential equation model which, combined with experimental measurements of an oscillating free surface jet, calculates dynamic surface tension and elongational viscosity of a fluid. Our model builds upon previous models due to Rayleigh and Bohr in that it self-consistently incorporates the effects of viscosity and gravity. Further, surface tension and viscosity are allowed to be non-constant. The principal result of this paper is a technique for the measurement of surface tension of newly forming surfaces on the millisecond timescale relevant for agricultural spray mixtures. Coincidentally, our model independently yields the elongational viscosity of the fluid, although our present experimental apparatus limits the accuracy of measurement of this material property.

In this paper we take measurements from physical jet experiments and implement our inverse model to deduce these material properties. The model is first benchmarked against standard techniques on a well-characterized fluid with constant surface tension and Newtonian viscosity. We then apply our method to an agricultural spray mixture, with non-constant surface tension and non-Newtonian rheology. We measure (i) the rapid decay of surface tension from the newly formed surface (aged less than a millisecond) to the much lower equilibrium value, and (ii) the rate dependence of elongational viscosity.