We use a newly developed set of interface conditions to revisit the problem of an evaporating thin liquid film. In particular, instead of the conventional Hertz–Knudsen–Langmuir equation for the evaporation mass flux, we impose a more general equation expressing the balance of configurational momentum. This balance, which supplements the conventional conditions enforcing the balances of mass, momentum and energy on the film surface, arises from a consideration of configurational forces within a thermodynamical framework. We study the influence of two newly introduced terms on the evolution of the liquid film. One of these terms accounts for the transport of energy within the liquid–vapour interface. The other term, which we refer to as the effective pressure, accounts for vapour recoil. Both new terms are found to be stabilizing. Furthermore, the effective pressure is found to affect a time-dependent base state of the evaporating film and to be an important factor in applications involving liquid films with thicknesses of one or two monolayers. Specifically, we demonstrate that consideration of the effective pressure makes it possible to observe the influence of the van der Waals interactions on film evolution close to the instant of rupture. Dimensional considerations indicate that one of the most significant influences of these effects occurs for molten metals.

The stability of thermally stratified plane Couette flow of visco-elastic liquids, with respect to disturbances of small amplitude, is considered. It is found that an initial state of finite elastic stress is necessary for elasticity to effect stability. The critical Rayleigh number of the flow is shown to be decreased for all non-zero rates-of-strain. This greater instability is due solely to the variations of the apparent viscosity with shear rate. In this way, the presence of elasticity can be said to have a destabilizing effect on the flow.

An oblique detonation wave in two-phase kerosene–air mixtures over a wedge is numerically studied for the first time. The features of initiation and stabilisation of the two-phase oblique detonation are emphasised, and they are different from those in previous studies on single-phase gaseous detonation. The gas–droplet reacting flow system is solved by means of a hybrid Eulerian–Lagrangian method. The two-way coupling for the interphase interactions is carefully considered using a particle-in-cell model. For discretisation of the governing equations of the gas phase, a WENO-CU6 scheme (Hu et al., J. Comput. Phys., vol. 229 (23), 2010, pp. 8952–8965) and a sixth-order compact scheme are employed for the convective terms and the diffusive terms, respectively. The inflow parameters are chosen properly from real flight conditions. The fuel vapour, droplets and their mixture are taken as the fuel in homogeneous streams with a stoichiometric ratio, respectively. The effects of evaporating droplets and initial droplet size on the initiation, transition from oblique shock to detonation and stabilisation are elucidated. The two-phase oblique detonation wave is stabilised from the oblique shock wave induced by the wedge. As the mass flow rate of droplets increases, a shift from a smooth transition with a curved shock to an abrupt one with a multi-wave point is found, and the initiation length of the oblique detonation increases, which is associated with the increase of the transition pressure. By increasing the initial droplet size, a smooth transition pattern is observed, even if the equivalence ratio remains constant, and the transition pressure decreases. The factor responsible is incomplete evaporation before the detonation fronts, which results in a complicated flame structure, including regimes of formation of oblique detonation, evaporative cooling of droplets and post-detonation reaction.

The Honji instability is studied using direct numerical simulations of sinusoidal oscillatory flow around a circular cylinder. The three-dimensional Navier–Stokes equations are solved by a finite element method at a relatively small value of the Keulegan–Carpenter number KC. The generation and subsequent development of Honji vortices are discussed over a range of frequency parameters by means of flow visualization. It is found that the spacing between Honji vortices is only weakly dependent on the frequency of oscillation, but is strongly correlated to KC because it is the terms within the governing equation containing KC that dominate the three-dimensional features of the flow. An empirical relationship between KC and the spacing between neighbouring vortices is proposed. The three-dimensional steady streaming structure within the vortices is identified and it is found that at high frequencies the steady streaming is two-dimensional although the instantaneous flow structure is itself fully three-dimensional.

For the first time, a physical mechanism is identified to explain the phase lag term in Powell’s impinging feedback loop equation (Powell, J. Acoust. Soc. Am., vol. 83 (2), 1988, pp. 515–533). Ultra-high-speed schlieren reveals a previously unseen periodic transient shock in the wall jet region of underexpanded impinging flows. The motion of this shock appears to be responsible for the production of the acoustic waves corresponding to the impingement tone. It is suggested that the delay between the inception of the shock and the formation of the acoustic wave explains the phase lag in the aeroacoustic feedback process. This suggestion is quantitatively supported through an assessment of Powell’s feedback equation, using high-resolution particle image velocimetry and acoustic measurements.

The flow of a two-dimensional viscous film falling from the edge of an inclined plane exhibits a distinctive set of phenomena which, in various combinations, have been referred to as the teapot effect. This paper makes plain that three basic mechanisms are at the root of these phenomena: deflection of the liquid sheet by hydrodynamic forces, contact-angle hysteresis, and multiple steady states that give rise to a purely hydrodynamic hysteresis. The evidence is drawn from Galerkin/finite-element analysis of the Navier-Stokes system, matched to a one-dimensional asymptotic approximation of the sheet flow downstream, and is corroborated experimentally by flow visualization and measurements of free-surface profiles and contact line position. The results indicate that the Gibbs inequality condition quantifies the inhibiting effect of sharp edges on spreading of static contact lines, even in the presence of flow nearby. The branchings, turning points, and isolas of families of solutions in parameter space explain abrupt flow transitions observed experimentally, and illuminate the stability of predicted flow states.

European Mechanics Colloquium number 119 was held at Imperial College on 16–18 July 1979, when the subject of vortex shedding from bodies in unidirectional flow and oscillatory flow, was discussed. A wide range of experimental work was presented including low-Reynolds-number flows around circular cylinders, the influence of disturbances on bluff body flow, the measurement of fluctuating forces and the influence of oscillations of the stream. About a third of the 33 papers presented concentrated on theoretical aspects and the majority of these were concerned with the ‘method of discrete vortices’.

Wave propagation in one-dimensional erodible-bed channels is discussed by using the shallow-water approximation for the fluid and a continuity equation for the bed. In addition to gravity waves, a third wave, which gives the velocity of propagation of a bed disturbance, is found. An appropriate dimensional analysis yields the quasi-steady approximation for the complete shallow-water equations.

The well-known linear stability analysis of free-surface flows is extended to include the erodibility of the bed. The critical Froude number Fc above which the free-surface of the fluid may become unstable is obtained. It is shown that erodibility increases the stability of the free surface, in qualitative agreement with previous experiments if qb > qs, qb and qs being respectively the contact-bed discharge and suspended-material discharge. The stability theory is also used to discuss coupled beds and surface waves. From it, five different configurations have been obtained: a sinusoidal wave pattern moving downstream, a transition zone and antidunes moving upstream, moving downstream and stationary. These bed forms are in agreement with experimental results; hence shallow-water theory seems to give a reasonable explanation of the boundary instability.

It is shown that the quasi-steady approximation and Kennedy's (1963) stability analysis will be in agreement if (kh)2 [Lt ] 1, where k is the wave number, and h is the depth of the water. When the phase shift δ is introduced in the quasi-steady approximation, the five bed patterns derived from the full equations are found again.

This paper reports an experimental investigation of pressure-driven flow through models of porous media. Each model porous medium is a square array of circular acrylic rods oriented across the flow in a rectangular channel. The solid volume fraction φ of the arrays ranged from 0.01 to 0.49. Three boundary conditions were studied. In the first boundary condition, the model porous medium was installed on the lower wall of the channel only and was bounded by a free zone. In the second and third boundary conditions, porous media of equal and unequal φ were arranged on the lower and upper channel walls so that the two media touched (second boundary condition), and did not touch (third boundary condition). Using water as the working fluid, the Reynolds number was kept low so that inertia was not a factor. Particle image velocimetry was used to obtain detailed velocity measurements in the streamwise-transverse plane of the test section. The velocity data were used to study the effects of φ and the different boundary conditions on the flow through and over the porous medium, and at the interface. For the first boundary condition, it was observed that at φ = 0.22, flow inside the porous medium was essentially zero, and the slip velocity at the porous medium and free zone interface decayed with permeability. In the second and third boundary conditions, flow communication between the porous media was observed to be dependent on the combinations of φ used, and the trends of the slip velocities at the interface between the two porous media obtained for that boundary condition were indicative of complicated interfacial flow.

The trapping of short-period gravity waves by islands and seamounts has been studied by Chambers (1965) and by Longuet-Higgins (1967). It was shown by the latter that in the absence of rotation, or when the wave frequency σ is large compared with the Coriolis parameter f, these waves cannot be perfectly trapped; some energy must always leak away to infinity. Very long-period oscillations in the presence of a sloping shelf surrounding an island, with σ [Lt ] f, have been studied by Mysak (1967) and Rhines (1967, 1969). Here perfect trapping is possible. However, as pointed out in Longuet-Higgins (1968), the rotation itself exerts a strong trapping effect not only when |σ| [Lt ] f, but also whenever a |σ| < f. It seems not to have been noticed that this effect is capable of trapping waves round an island in an ocean of uniform depth, in the absence of any shelf or sloping region offshore.

The existence of such waves is demonstrated for a circular island in § 1 of the present paper. It is shown that the waves exist only when the azimuthal wave-number n is at least 1. The waves always progress round the island in a clockwise sense in the northern hemisphere. At large distances r from the island, the wave amplitude decays exponentially, but this exponential trapping occurs only if the radius a of the island exceeds the critical value (n(n − 1)gh)½/f. When n = 1, this critical radius is zero, so that in theory the waves exist for any island of non-zero radius.

The application of these results to the ocean is discussed in § 2. Except possibly for baroclinic motions, it appears that only the waves corresponding to n = 1 could exist in fact, and that their frequency would be nearly equal to the inertial frequency f. It is unlikely that f could be regarded as constant over a sufficiently wide area for the model to apply without qualification. Nevertheless, the oscillations may be regarded as the local adjustment of the pressure field to inertial currents in the neighbourhood of the island. It is possible that the peak at about 0·73 c.p.d. in the spectrum of sea-level at Oahu, as found by Miyata & Groves (1968), can be interpreted in this way.

In the present study, the experimental set-up of Ganesh et al. (J. Fluid Mech., vol. 802, 2016, pp. 37–78) is used to examine the dynamics of a shedding cavity by examining the vapour production rate of the natural cavity and determining how minimal injection of non-condensable gas can substantially alter the vapour production rate, the resulting cavity flow and the cavity shedding process. The influence of the dissolved gas content on the shedding natural cavity flow is also examined. High-speed visual imaging and cinemagraphic X-ray densitometry were used to observe the void fraction dynamics of the cavity flow. Non-condensable gas is injected across the span of the cavity flow at two locations: immediately downstream of the cavity detachment location at the apex of the wedge or further downstream into mid-cavity. The gas injected near the apex is found to increase the pressure near the suction peak, which resulted in the suppression of vapour formation. Hence, the injection of gas could result in a substantial net reduction in the overall cavity void fraction. Injection at the mid-cavity did less to suppress the vapour production and resulted in less significant modification of both the mean cavity pressure and net volume fraction. Changes in the cavity void fraction, in turn, altered the dynamics of the bubbly shock formation. Variation of the dissolved gas content alone (i.e. without injection) did not significantly change the cavity dynamics.

The effect of pressure gradients on the stability of creeping flows of Newtonian fluids in channels lined with an incompressible and impermeable neo-Hookean material is examined in this work. Three different configurations are considered: (i) pressure-driven flow between a rigid wall and a wall lined with a neo-Hookean material; (ii) pressure-driven flow between neo-Hookean-lined walls; and (iii) combined Couette–Poiseuille flow between a rigid wall and a neo-Hookean-lined wall. In each case, a first normal stress difference whose magnitude depends on depth arises in the base state for the solid, and linear stability analysis reveals that this leads to a short-wave instability which is removed by the presence of interfacial tension. For sufficiently thick solids, low-wavenumber modes become unstable first as the applied strain increases above a critical value, whereas for sufficiently thin solids, high-wavenumber modes becomes unstable first. Comparison of the dimensionless critical strains shows that configurations (i) and (ii) are more difficult to destabilize than Couette flow past a neo-Hookean solid. For configuration (iii), the nonlinear elasticity of the solid leads to two physically distinct critical conditions, in contrast to what happens when a linear elastic material is used. The mechanisms underlying the behaviour of the critical strains are explained through an analysis of the interfacial boundary conditions.

Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid heated from beneath were calculated using Galerkin's method. Both systems with insulated and with conducting lateral boundaries were investigated for radius-to-depth ratios of 1, 2·25, 2·55 and 2·66. Flows bounded by a conducting lateral boundary were found to be unstable for Rayleigh numbers greater than 1·1 times the critical value. The cell size was found to be an increasing function of the Rayleigh number.

The initial multi-mode interfacial velocity and density perturbations present at the onset of a small-Atwood-number, incompressible, miscible Rayleigh–Taylor instability- driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuating velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh–Taylor instability-induced turbulence are discussed.

We present the first laboratory evidence of internal gravity wave tunnelling through weakly stratified fluid patches and we derive analytic theories for energy transmission by the waves in two distinct circumstances. In one, the computed transmission coefficient is directly analogous to the textbook calculation for quantum tunnelling of a free electron incident upon a potential barrier. In the other, we consider the partial reflection and transmission of internal waves through a mixed region bounded by discontinuities in the density profile. The results reveal a linear resonance between vertically propagating internal waves and interfacial waves that exist on either flank of the mixing region. The resonance permits perfect transmission of internal waves that would otherwise strongly reflect from the weakly stratified region. We discuss a specific application of our results to deep convective storm-generated internal waves that tunnel through the mesosphere to the ionosphere.

One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.

A new multiscale simulation methodology is introduced to facilitate computationally efficient simulations of high Reynolds number turbulence seen in wall-bounded flows. The scale splitting methodology uses traditional large eddy simulation (LES) with a wall model to simulate the larger scales which are subsequently enriched using a space–time compatible kinematic simulation. Computational feasibility and robustness of the methodology are investigated using two idealized problems that emulate turbulence within the planetary boundary layer (PBL), and a finite Reynolds number channel flow problem which serves to validate the methodology against direct numerical simulation. The space–time correlations and spectra generated using enriched LES show excellent agreement with LES conducted at high resolution for all three problems; thereby demonstrating the potential of this approach for high resolution PBL simulations with a drastic reduction in the computational costs when compared to the conventional approach.

An experimental investigation of transition phenomena in non-steady boundary layers of sinusoidally oscillating flows was conducted, and the effect of various parameters on the transition process was observed.

The manner in which transition occurs appears to be related to a dimensionless grouping designated as the non-steady Reynolds number, (Re)NS = LΔU/2πvν. When this number exceeds a certain critical value, transition begins with turbulent bursts appearing periodically at the frequency of the free stream oscillation; these are preceded by instability waves having the appearance of a Tollmien-Schlichting instability. The transition Reynolds number depends, in this case, only on the amplitude of the free stream oscillations and not on their frequency, at least to the first order. Below a critical value of this parameter, transition occurs at a relatively constant Reynolds number which appears independent of the amplitude and frequency of the oscillation, at least over the range tested.

When the bursts appear periodically, their development appears to occur in two succeeding phases: an initial or ‘creative’ phase marked by a sequential appearance of turbulence upstream and rapid development and a latter or ‘convective’ phase marked by turbulent spots having relatively constant leading and trailing edge velocities.

The dimensionless amplitude, ΔU/U∞, of the imposed oscillations was varied from 0.014 to 0.29 while the oscillation frequencies extended from 4.5 to 62c/s. Pressure gradients imposed on the flat plate model during the course of the study are given by dCp/dx = − 0.004/ft., −0.081/ft. and 0.045/ft. where Cp = 2p/ρU2∞ and x is the distance (ft.) along the plate.

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor is measured as a function of the Reynolds number . From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the – curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.