The stationary meniscus of an evaporating, perfectly wetting system exhibits an apparent contact angle Θ which vanishes with the applied temperature difference ΔT, and is maintained for ΔT > 0 by a small-scale flow driven by evaporation. Existing theory predicts Θ and the heat flow q∗ from the contact region as the solution of a free-boundary problem. Though that theory admits the possibility that Θ and q∗ are determined at the same scale, we show that, in practice, a separation of scales gives the theory an inner and outer structure; Θ is determined within an inner region contributing a negligible fraction of the total evaporation, but q∗ is determined at larger scales by conduction across an outer liquid wedge subtending an angle Θ. The existence of a contact angle can thus be assumed for computing the heat flow; the problems for Θ and q∗ decouple. We analyse the inner problem to derive a formula for Θ as a function of ΔT and material properties; the formula agrees closely with numerical solutions of the existing theory. Though microphysics must be included in the model of the inner region to resolve a singularity in the hydrodynamic equations, Θ is insensitive to microphysical detail because the singularity is weak. Our analysis shows that Θ is determined chiefly by the capillary number Ca = μlVl/σ based on surface tension σ, liquid viscosity μl and a velocity scale Vl set by evaporation kinetics. To illustrate this result of our asymptotic analysis, we show that computed angles lie close to the curve Θ = 2.2Ca1/4; a small scatter of ±15% about that curve is the only hint that Θ depends on microphysics. To test our scaling relation, we use film profiles measured by Kim (1994) to determine experimental values of Θ and Ca; these are the first such values to be published for the evaporating meniscus. Agreement between theory and experiment is adequate; the difference is less than ±40% for 9 of 15 points, while the scatter within experimental values is ±25%.

The concentric, two-phase flow of two immiscible fluids in a tube of sinusoidally varying cross-section is studied. This geometry is often used as a model to study the onset of different flow regimes in packed beds. Neglecting gravitational effects, the model equations depend on five dimensionless parameters: the Reynolds and Weber numbers, and the ratios of density, viscosity and volume of the two fluids. Two more dimensionless numbers describe the shape of the solid wall: the constriction ratio and the ratio of its maximum radius to its period. In addition to the effect of the Weber number, which depends on both the fluid and the flow, the effect of the Ohnesorge number J has been examined as it characterizes the fluid alone. The governing equations are approximated using the pseudo-spectral methodology while the Arnoldi algorithm has been implemented for computing the most critical eigenvalues that correspond to axisymmetric disturbances. Stationary solutions are obtained for a wide parameter range, which may exhibit flow recirculation at the expanding portion of the tube. Extensive calculations are made for the dependence of the neutral stability boundaries on the various parameters. In most cases where the steady solution becomes unstable it does so through a Hopf bifurcation. Exceptions to this are cases where the viscosity ratio is O(10−3) and, then, the most unstable eigenvalue remains real. Generally, steady core–annular flow in this geometry is more susceptible to instability than in a straight tube and, in similar ranges of the parameters, it may be generated by different mechanisms. Decreasing the thickness of the annular fluid, inverse Weber number or the Ohnesorge number or the density of the core fluid stabilizes the flow. For stability reasons, the viscosity ratio must remain strictly below unity and it has an optimum value that maximizes the range of allowed Reynolds numbers.

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

The influence of initial flow conditions on the passive scalar field of a turbulent free jet issuing from the round nozzle is investigated in this paper by a review of the literature and a detailed experimental study. Two sets of distinctly different initial conditions are generated using two nozzle types: a smooth contraction and a long straight pipe. The present measurements of the passive scalar (temperature) field were conducted in a slightly heated air jet from each nozzle at a Reynolds number of 16 000 using identical experimental facilities and a single measurement technique. Significant differences between the flows from the two nozzles are revealed throughout the measured flow region which covers the axial range from 0 to 70 jet exit diameters. The study suggests that the differences observed in the statistics of the scalar field may be related to differences in the underlying turbulence structure of the jet in the near field. The present findings support the analytical result of George (1989) that the entire flow is influenced by the initial conditions, resulting in a variety of self-similar states in the far field.

Unsteady separation processes at large finite, Reynolds number, Re, are considered, as well as the possible relation to existing descriptions of boundary-layer separation in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow, believed to be relevant to bursting near the wall in a turbulent boundary layer. Bursting is known to be associated with streamwise vortex motion, but the vortex/wall interactions that drive the near-wall flow toward breakdown have not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices is used to assess the influence of sustained pumping action on the development of a viscous wall layer. The calculated solutions describe a three-dimensional flow at finite Re that is independent of the streamwise coordinate and consists of a crossflow plane motion, with a developing streamwise flow. The unsteady problem is constructed to mimic a typical cycle in turbulent wall layers and numerical solutions are obtained over a range of Re. Recirculating eddies develop rapidly in the near-wall flow, but these eddies are eventually bisected by alleyways which open up from the external flow region to the wall. At sufficiently high Re, an oscillation was found to develop in the streamwise vorticity field near the alleyways with a concurrent evolution of a local spiky behaviour in the wall shear. Above a critical value of Re, the oscillation grows rapidly in amplitude and eventually penetrates the external flow field, suggesting the onset of an unstable wall-layer breakdown. Local zones of severely retarded streamwise velocity are computed which are reminiscent of the low-speed streaks commonly observed in turbulent boundary layers. A number of other features also bear a resemblance to observed coherent structure in the turbulent wall layer.

Two-dimensional nonlinear sloshing of an incompressible fluid with irrotational flow in a rectangular tank is analysed by a modal theory. Infinite tank roof height and no overturning waves are assumed. The modal theory is based on an infinite-dimensional system of nonlinear ordinary differential equations coupling generalized coordinates of the free surface and fluid motion associated with the amplitude response of natural modes. This modal system is asymptotically reduced to an infinite-dimensional system of ordinary differential equations with fifth-order polynomial nonlinearity by assuming sufficiently small fluid motion relative to fluid depth and tank breadth. When introducing inter-modal ordering, the system can be detuned and truncated to describe resonant sloshing in different domains of the excitation period. Resonant sloshing due to surge and pitch sinusoidal excitation of the primary mode is considered. By assuming that each mode has only one main harmonic an adaptive procedure is proposed to describe direct and secondary resonant responses when Moiseyev-like relations do not agree with experiments, i.e. when the excitation amplitude is not very small, and the fluid depth is close to the critical depth or small. Adaptive procedures have been established for a wide range of excitation periods as long as the mean fluid depth h is larger than 0.24 times the tank breadth l. Steady-state results for wave elevation, horizontal force and pitch moment are experimentally validated except when heavy roof impact occurs. The analysis of small depth requires that many modes have primary order and that each mode may have more than one main harmonic. This is illustrated by an example for h/l = 0.173, where the previous model by Faltinsen et al. (2000) failed. The new model agrees well with experiments.

We present details of an experimental study of crystallization adjacent to a cooled boundary from an aqueous solution of potassium nitrate and sodium nitrate. This transparent system is typical of many ternary melts that do not form solid solutions, including examples in igneous petrology and metallurgy. We have measured the rates of advance of the front of crystallization and the eutectic front, behind which the system is completely solid. From careful measurements of the concentration and temperature fields, we have been able to infer the location of an internal phase boundary: the cotectic front separating a region in which only one component of the ternary system forms crystals from a region in which two components form crystals. Our experiments were conducted under conditions in which fluid flow is minimal, so that rates of crystallization are determined principally by the diffusive transport of heat. We have confirmed that the thicknesses of the various regions all grow in proportion to the square root of time, as is expected of diffusion-limited growth, and have determined the constants of proportionality for a range of different initial concentrations and boundary temperatures. We have found evidence to suggest that there may be a significant nucleation delay in the secondary and tertiary crystallization. Our measurements of concentration provide much more information about the ternary phase diagram than has hitherto been available.

A decaying compressible nearly homogeneous and nearly isotropic grid-generated turbulent flow has been set up in a large scale shock tube research facility. Experiments have been performed using instrumentation with spatial resolution of the order of 7 to 26 Kolmogorov viscous length scales. A variety of turbulence-generating grids provided a wide range of turbulence scales with bulk flow Mach numbers ranging from 0.3 to 0.6 and turbulent Reynolds numbers up to 700. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was also found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A possible mechanism responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid. Measurements of the time-dependent, three dimensional vorticity vectors were attempted for the first time with a 12-wire miniature probe. This also allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. It was found that the fluctuations of these quantities increase with increasing mean Mach number of the flow. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause.

A laboratory study has been performed to simulate intrusive flows generated by internal wave-breaking activity in the oceanic pycnocline. Two different cases were considered. In the first set of experiments a short-duration source of motion was modelled by creating a finite region of well-mixed fluid. The collapse of this region resulted in intrusive flows and internal waves in the pycnocline. Attention was focused on the formation and subsequent evolution of solitary ‘bulges’ in the intrusion. Detailed flow measurements have revealed that the weak motion inside these bulges (which contain well-mixed fluid from the source) is organized in a four-vortex structure. Numerical flow simulations provided important information about the dynamics of this four-cell structure: the outer cells are associated with baroclinic generation of vorticity, while the inner cells are characterized by a balance between the advective and the viscous terms in the vorticity equation.

In the second set of experiments continuous mixing was induced by a vertically oscillating, horizontal grid centred in the pycnocline. The mixed region collapses, thus forming an intrusive flow into the pycnocline and internal waves that propagate along the pycnocline at higher speed than the intrusion. It was found that the velocity of the intrusive flow is approximately constant and that its dynamics is controlled by an inertial–buoyancy balance. The parameters of the internal waves in both cases were compared with theory.

The linear and nonlinear growth of longitudinal vortices in a laminar boundary layer and the development of secondary instabilities are investigated theoretically and by experiment. As a prototype problem the natural convection flow along a constant-heat-flux inclined flat plate in water is chosen. Based upon the smallness of the plate's angle of inclination from the vertical, the largeness of the Grashof number, and the smallness of the vortex strength, a perturbation method is used to derive and solve a consistent set of governing equations for the linear, weakly nonlinear and the strongly nonlinear regimes which is asymptotically correct to first order. Liquid-crystal thermography based on wide-band liquid crystals is used to provide full-field, highly accurate wall temperature measurements and visualizations.

The spanwise periodic thickening and thinning of the boundary layer through a nonlinear, but steady, vortex growth is seen to be responsible for practically all of the increase of mean heat transfer values during the laminar–turbulent transition. Secondary instabilties in the form of sinuous and varicose unsteady wave modes and the steady merging of vortices are visualized but are seen to have only a minor additional influence on mean heat transfer.

A finite difference method based on the Euler equations is developed for computing waves and wave resistance due to different bottom topographies moving steadily at the critical velocity in shallow water. A two-dimensional symmetric and slowly varying bottom topography, as a forcing for wave generation, can be viewed as a combination of fore and aft parts. For a positive topography (a bump), the fore part is a forward-step forcing, which contributes to the generation of upstream-advancing solitary waves, whereas the aft part is a backward-step forcing to which a depressed water surface region and a trailing wavetrain are attributed. These two wave systems respectively radiate upstream and downstream without mutual interaction.

For a negative topography (a hollow), the fore part is a backward step and the aft part is a forward step. The downstream-radiating waves generated by the backward-step forcing at the fore part will interact with the upstream-running waves generated by the forward-step forcing at the aft. Therefore, the wave system generated by a negative topography is quite different from that by a positive topography. The generation period of solitary waves is slightly longer and the instantaneous drag fluctuation is skewed for a negative topography. When the length of the negative topography increases, the oscillation of the wave-resistance coefficient with time does not coincide with the period of solitary wave emission.

Finite-amplitude convection in the form of rolls and their stability with respect to infinitesimal disturbances is investigated in the case of boundaries of the horizontal fluid layer which exhibit a thermal conductivity comparable to that of the fluid. It is found that even when rolls represent the preferred mode at the onset of convection a transition to square cells may occur at slightly supercritical Rayleigh numbers. The phenomenon of inertial convection in low Prandtl number fluids appears to become more pronounced as the conductivity of the boundaries is reduced. Modulated convection rolls have also been found as solutions of the problem. But they appear to be unstable in general. Experimental observations have been made and are found in general agreement with the theoretical predictions.

The results of an experimental study of electrohydrodynamic convection in a liquid crystal are presented. Investigations concerned a small-aspect-ratio device so that finite geometry effects could be exploited to study the mechanisms by which complicated flows were organized. The results have been related to ideas on Shil'nikov dynamics and gluing bifurcations in low-dimensional dynamical systems.

We study the flow induced by random vibration of a solid boundary in an otherwise quiescent fluid. The analysis is motivated by experiments conducted under the low level and random effective acceleration field that is typical of a microgravity environment. When the boundary is planar and is being vibrated along its own plane, the variance of the velocity field decays as a power law of distance away from the boundary. If a low-frequency cut-off is introduced in the power spectrum of the boundary velocity, the variance decays exponentially for distances larger than a Stokes layer thickness based on the cut-off frequency. Vibration of a gently curved boundary results in steady streaming in the ensemble average of the tangential velocity. Its amplitude diverges logarithmically with distance away from the boundary, but asymptotes to a constant value instead if a low-frequency cut-off is considered. This steady component of the velocity is shown to depend logarithmically on the cut-off frequency. Finally, we consider the case of a periodically modulated solid boundary that is being randomly vibrated. We find steady streaming in the ensemble average of the first-order velocity, with flow extending up to a characteristic distance of the order of the boundary wavelength. The structure of the flow in the vicinity of the boundary depends strongly on the correlation time of the boundary velocity.

In recent experiments on the growth of localized disturbances in a Blasius boundary layer, Medeiros & Gaster (1999a, b) observed that the development of nonlinear effects depends markedly on the initial phase of their imposed disturbance. Here, a simple explanation of this phenomenon is proposed. Because the disturbance is localized in space and time, it has a spread of wavenumbers and frequencies: among these are components which can initiate a pair of resonant subharmonic waves with well-determined phase, which are then amplified by the familiar three-wave resonance mechanism. The amplitude attained after some time is strongly phase-dependent, consistent with the experimental observations.

We investigate the horizontal flow produced by source–sink forcing in a stably stratified fluid. The forcing jets are kept laminar and are placed along the boundary of a square domain. We find that the resultant flow patterns are extremely sensitive to the forcing geometry. The single dominant vortex pattern, interpreted as the result of inverse energy cascade of two-dimensional turbulence in our previous work (Boubnov, Dalziel & Linden 1994), turns out to be a special case. We show that some of the steady patterns resemble the eigenmodes of the Helmholtz equation as the inviscid vorticity equation. Although there are significant discrepancies in the streamfunction vs. vorticity relations between the observed flows and the analytical solutions, we identify the differences as a result of viscous diffusion of vorticity from the source flows. We also study the transition from forced to decaying flow. The flow assumes the properties of Stokes flow at quite large Reynolds number, indicating transformation into patterns with small advective acceleration.