We study the collapse of a transient cavity of air in water created by the impact of a solid body. Experimentally, we characterize the dynamics of the cavity from its creation (t = 0) until it collapses (t = τ) in the limit where inertia dominates viscous and capillary effects. Theoretically, we find in this regime an approximate analytical solution which describes the time evolution of the shape of the cavity. This theoretical solution predicts the existence of two different types of cavities that we also observe experimentally.

We report on an experimental and theoretical study of the transient flows which develop as a naturally ventilated room adjusts from one temperature to another. We focus on a room heated from below by a uniform heat source, with both high- and low-level ventilation openings. Depending on the initial temperature of the room relative to (i) the final equilibrium temperature and (ii) the exterior temperature, three different modes of ventilation may develop. First, if the room temperature lies between the exterior and the equilibrium temperature, the interior remains well-mixed and gradually heats up to the equilibrium temperature. Secondly, if the room is initially warmer than the equilibrium temperature, then a thermal stratification develops in which the upper layer of originally hot air is displaced upwards by a lower layer of relatively cool inflowing air. At the interface, some mixing occurs owing to the effects of penetrative convection. Thirdly, if the room is initially cooler than the exterior, then on opening the vents, the original air is displaced downwards and a layer of ambient air deepens from above. As this lower layer drains, it is eventually heated to the ambient temperature, and is then able to mix into the overlying layer of external air, and the room becomes well-mixed. For each case, we present new laboratory experiments and compare these with some new quantitative models of the transient flows. We conclude by considering the implications of our work for natural ventilation of large auditoria.

Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

Low-frequency noise sources in heated single-stream jets were identified by cross-correlating turbulent density fluctuations ρ′ with the far-field sound pressure fluctuations p′. The turbulent density fluctuations were measured by a molecular Rayleigh-scattering technique. For a fixed jet velocity Uj, the normalized correlation coefficient 〈ρ′; p′〉/(ρ′rmsp′rms is found to increase progressively with an increase in the plume temperature (subscript rms stands for root-mean-square). The result indicates an improvement of the noise radiation efficiency with heating. Directly measured noise spectra from fixed velocity jets with increasing temperature ratio show confusing trends. However, if such spectra are normalized by theplume density, then a consistent trend of increasing noise level with increased plume temperature emerges. The increased noise is the most prominent at the low-frequency end, consistent with the correlation data. The effect of increasing jet velocity keeping the plume temperature constant was also studied. The correlation coefficients were found to improve significantly with velocity; a result consistent with prior observation from unheated jets. Additional findings on the time-averaged density variations and the changes in the air density fluctuations with increasing plume temperature are also discussed.

While energy efficiency is important, the adoption of energy-efficient ventilation systems still requires the provision of acceptable indoor air quality. Many low-energy systems, such as displacement or natural ventilation, rely on temperature stratification within the interior environment, always extracting the warmest air from the top of the room. Understanding buoyancy-driven convection in a confined ventilated space is key to understanding the flow that develops with many of these modern low-energy ventilation schemes. In this work we study the transport of an initially uniformly distributed passive contaminant in a displacement-ventilated space. Representing a heat source as an ideal sourced of buoyancy, analytical and numerical models are developed that allow us to compare the average efficiency of contaminant removal between traditional mixing and modern low-energy systems. A set of small-scale analogue laboratory experiments was also conducted to further validate our analytical and numerical solutions.

We find that on average traditional and low-energy ventilation methods are similar with regard to pollutant flushing efficiency. This is because the concentration being extracted from the system at any given time is approximately the same for both systems. However, very different vertical concentration gradients exist. For the low-energy system, a peak in contaminant concentration occurs at the temperature interface that is established within the space. This interface is typically designed to sit at some intermediate height in the space. Since this peak does not coincide with the extraction point, displacement ventilation does not offer the same benefits for pollutant flushing as it does for buoyancy removal.

A tethered cylinder may be considered an extension of the widely studied problem of a hydro-elastically mounted cylinder. Here we numerically investigate the flow past a positively buoyant tethered cylinder for a range of mass ratios and tether length ratios at a Reynolds number Re = 200. The results are found to be qualitatively similar to related experimental work performed at significantly higher Reynolds numbers. Two important findings are related in this paper. First, we find that the action of the tethered cylinder oscillating at an angle to the flow induces a mean lift coefficient. Second, a critical mass ratio (m*crit) is found below which large-amplitude oscillations are noted, similar to that previously reported for the case of a hydro-elastically mounted cylinder. For short tether lengths, (m*crit) is significantly greater than that found for a hydro-elastically mounted cylinder. As the tether length increases, the (m*crit) decreases and asymptotes to that of a hydro-elastically mounted cylinder as the tether length approaches infinity.

The vortex clusters in the turbulent outer region of rough- and smooth-walled channels, and their associated velocity structures, are compared using data from numerical experiments at friction Reynolds numbers Reτ ≤ 674. The results indicate that the roughness of the wall does not affect their properties, particularly the existence of wall-detached and wall-attached populations, and the self-similar size distribution of the latter. The average flow field conditioned to the attached clusters reveals similar conical structures of low streamwise velocity for the rough- and smooth-walled cases, which eventually grow into the global modes previously identified from spectral analysis. We conclude that the vortex clusters of the turbulent outer region either originate away from the wall, or quickly forget their origin, in agreement with Townsend's similarity hypothesis.

This paper presents the first numerical investigation via direct numerical simulation of the tone noise phenomenon occurring in the flow past laminar airfoils. This phenomenon corresponds to the radiation of discrete acoustic tones in some specific flow conditions, and has received much attention since the 1970s, and several experimental studies have been carried out to identify and understand the underlying physical mechanisms. However, several points remain to be clarified in order to provide a complete explanation of its origin. The flow around a two-dimensional NACA0012 airfoil is considered in order to have a deeper understanding of the tone noise phenomenon. Consistently with previous experimental studies, it is shown that depending on the Reynolds number and angle of attack, two different types of acoustic spectrum are observed: one which exhibits a broadband contribution with a dominant frequency together with a sequence of regularly spaced discrete frequencies, while the other one is only characterized by a simple broadband contribution. The first configuration is typical of the tone noise phenomenon. The present work shows that in this case, the mean flow on the pressure side of the airfoil exhibits a separation bubble near the trailing edge and the main tone frequency is close to the most amplified frequency of the boundary layer. The mechanism proposed in previous works for the main tone generation – which implies the existence of a separation bubble at the pressure side – is therefore validated by numerical simulation. On the other hand, the analysis of the suction side boundary layer reveals that there is no separation and that the most amplified frequency is different from the main tonal one. However, the suction side boundary layer is highly receptive to the tone frequency. Finally, an original explanation for the existence of the secondary discrete frequencies observed in the radiated pressure spectrum is given. They are associated to a bifurcation of the airfoil wake from a symmetric to a non-symmetric vortex pattern. A possible explanation for the existence of this bifurcation is the interaction between the disturbances which are the most amplified by the suction side boundary layer and those originating in the forcing of the suction side flow by the main tone noise mechanism.

The generation and evolution of two-dimensional bores in water of uniform depth and on sloping beaches are simulated through numerical solution of the Euler equations using the smoothed particle hydrodynamics (SPH) method, wherein particles are followed in Lagrangian fashion, avoiding the need for computational grids. In water of uniform depth, a piston wavemaker produces cyclically breaking bores in the Froude number range 1.37–1.82, which were shown to move at time-averaged speeds in very good agreement with the requirements of global mass and momentum conservation. A single Strouhal number for the breaking period was discovered. Complex repetitive splashing patterns are observed and described, involving forward jet formation growth, impact and ricochet, and similarly, backward jet formation and impact. Observed consequences were the creation of vortical regions of both signs, dipole creation through pairing, large-scale transport of surface water downward and high tangential scouring velocities on the bed, which are quantified. These bores are further allowed to rise on linear slopes to the shoreline, where they are seen to collapse into a tongue-like flow resembling dam-break evolution.

This essentially inviscid calculation is able to reproduce the development of a highly vortical flow in excellent agreement with experimental observations and theoretical concepts. The turbulent flow behaviour is partially described by the numerical solution.

Numerical simulation of a compressible mixing layer past an axisymmetric trailing edge is carried out for a Reynolds number based on the diameter of the trailing edge approximately equal to 2.9 × 106. The free-stream Mach number at separation is equal to 2.46, which corresponds to experiments and leads to high levels of compressibility. The present work focuses on the evolution of the turbulence field through extra strain rates and on the unsteady features of the annular shear layer. Both time-averaged and instantaneous data are used to obtain further insight into the dynamics of the flow. An investigation of the time-averaged flow field reveals an important shear-layer growth rate in its initial stage and a strong anisotropy of the turbulent field. The convection velocity of the vortices is found to be somewhat higher than the estimated isentropic value. This corroborates findings on the domination of the supersonic mode in planar supersonic/subsonic mixing layers. The development of the shear layer leads to a rapid decrease of the anisotropy until the onset of streamline realignment with the axis. Due to the increase of the axisymmetric constraints, an adverse pressure gradient originates from the change in streamline curvature. This recompression is found to slow down the eddy convection. The foot shock pattern features several convected shocks emanating from the upper side of the vortices, which merge into a recompression shock in the free stream. Then, the flow accelerates and the compressibility levels quickly drop in the turbulent developing wake. Some evidence of the existence of large-scale structures in the near wake is found through the domination of the azimuthal mode m = 1 for a Strouhal number based on trailing-edge diameter equal to 0.26.

Accelerated flow past a NACA 0015 aerofoil is investigated experimentally and computationally for Reynolds number Re = 7968 at an angle of attack α = 30°. Experiments are conducted in a specially designed piston-driven water tunnel capable of producing free-stream velocity with different ramp-type accelerations, and the DPIV technique is used to measure the resulting flow field past the aerofoil. Computations are also performed for other published data on flow past an NACA 0015 aerofoil in the range 5200 ≤ Re ≤ 35000, at different angles of attack. One of the motivations is to see if the salient features of the flow captured experimentally can be reproduced numerically. These computations to solve the incompressible Navier–Stokes equation are performed using high-accuracy compact schemes. Load and moment coefficient variations with time are obtained by solving the Poisson equation for the total pressure in the flow field. Results have also been analysed using the proper orthogonal decomposition technique to understand better the evolving vorticity field and its dependence on Reynolds number and angle of attack. An energy-based stability analysis is performed to understand unsteady flow separation.

We conduct experiments on gravitational phase separation of binary immiscible fluids using an oil–water mixture and study how the volumetric and viscosity ratios of the two phases control the separation process. First, we change the volumetric fraction of the two phases. We find that the initial phase separation rate depends strongly on the volumetric ratio of the two phases, and can be modelled by a buoyancy-driven permeable flow using the Blake–Kozeny–Carman permeability formula. Next, we change the viscosity ratios of the two fluids, and we find that there are two distinct regimes with different styles of phase separation. Small viscosity ratio (<100) cases are characterized by a sharp lower boundary and a vertically homogeneous mixture layer. On the other hand, high viscosity ratio (>100) cases are characterized by a diffuse lower boundary and a large vertical gradient of porosity. A polyhedral foam structure develops at the top of the mixture layer which is slow to rupture and to transform into a uniform oil layer. These differences can be interpreted to arise from a faster coalescence rate relative to the separation rate at high viscosity ratios. We simultaneously measured electrical resistivity in order to monitor the temporal change of the mean porosity in the mixture layer. The measurements were found to be consistent with the visual observation.

Wing pitch reversal, the rapid change of angle of attack near stroke transition, represents a difference between hovering with flapping wings and with a continuously rotating blade (e.g. helicopter flight). Although insects have the musculature to control the wing pitch during flight, we show here that aerodynamic and wing inertia forces are sufficient to pitch the wing without the aid of the muscles. We study the passive nature of wing pitching in several observed wing kinematics, including the wing motion of a tethered dragonfly, Libellula pulchella, hovering fruitfly, hovering hawkmoth and simplified dragonfly hovering kinematics. To determine whether the pitching is passive, we calculate rotational power about the torsion axis owing to aerodynamic and wing inertial forces. This is done using both direct numerical simulations and quasi-steady fluid force models. We find that, in all the cases studied here, the net rotational power is negative, signifying that the fluid force assists rather than resists the wing pitching. To further understand the generality of these results, we use the quasi-steady force model to analyse the effect of the components of the fluid forces at pitch reversal, and predict the conditions under which the wing pitch reversal is passive. These results suggest the pitching motion of the wings can be passive in insect flight.

The theory of weak turbulence developed for wind-driven waves in theoretical works and in recent extensive numerical studies concludes that non-dimensional features of self-similar wave growth (i.e. wave energy and characteristic frequency) have to be scaled by internal wave-field properties (fluxes of energy, momentum or wave action) rather than by external attributes (e.g. wind speed) which have been widely adopted since the 1960s. Based on the hypothesis of dominant nonlinear transfer, an asymptotic weakly turbulent relation for the total energy ϵ and a characteristic wave frequency ω* was derived The self-similarity parameter αss was found in the numerical duration-limited experiments and was shown to be naturally varying in a relatively narrow range, being dependent on the energy growth rate only.

In this work, the analytical and numerical conclusions are further verified by means of known field dependencies for wave energy growth and peak frequency downshift. A comprehensive set of more than 20 such dependencies, obtained over almost 50 years of field observations, is analysed. The estimates give αss very close to the numerical values. They demonstrate that the weakly turbulent law has a general value and describes the wave evolution well, apart from the earliest and full wave development stages when nonlinear transfer competes with wave input and dissipation.

Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a χ2/3k−1 enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation χ in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes.

We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing χ in the limit Re → ∞. Our proposal is supported by high Reynolds number simulations which confirm that χ decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy 〈ω2〉/2 in the inertial range as Re increases. Together with the mathematical analysis of vanishing χ, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum χ2/3k−1 with 〈ω2〉 k−1 (ln Re)−1).

The number of periodic arrangements of point vortices – point vortex streets – in two-dimensional fluid flow that are stationary is known to be finite for a generic choice of vortex circulations. When all circulations are the same in absolute value, however, stationary vortex street configurations have been associated with the zeros of certain trigonometric polynomials containing free complex parameters. The presence of these parameters may prove useful in constructing point vortex models of shear layers and wakes. In this paper it is shown that such a continuum of stationary configurations exists in a much wider class of point vortex street systems. The circulations may take on many values, not just two, providing increased flexibility in the modelling context. A simple method for computing these configurations is derived. The effects of symmetries on the solution polynomials are described, and illustrated with examples. In addition, novel translating vortex street configurations are found having arbitrary translation velocity and containing free parameters for vortex circulations ±1 and also for vortex circulations +1, −2.

We consider the behaviour of solutions to the nonlinear shallow-water equations which describe wave runup on a plane beach, concentrating on the behaviour at and just behind the moving shoreline. We develop regular series expansions for the hydrodynamic variables behind the shoreline, which are valid for any smooth initial condition for the waveform. We then develop asymptotic descriptions of the shoreline motion under localized initial conditions, in particular a localized Gaussian waveform: we obtain estimates for the maximum runup and drawdown of the wave, for its maximum velocities and the forces it is able to exert on objects in its path, and for the conditions under which such a wave breaks down. We show how these results may be extended to include initial velocity conditions and initial waveforms which may be approximated as the sum of several Gaussians. Finally, we relate these results tentatively to the observed behaviour of a tsunami.

A combined experimental and numerical approach is used to extract information on the kinetics of ion evaporation from the region of high electric field around the tip of a Taylor cone of the neutral solvent propylene carbonate (PC) mixed with two ionic liquids. On the numerical side, the electric field on the surface of the liquid is computed in the absence of evaporation by solving the electrohydrodynamic problem in this region within the framework of the leaky dielectric model. These computations justify the approximate (2% max error) scaling Emax = β Ek for the maximum electric field on the surface, with Ek = γ1/2 ϵ0−2/3 (K/Q)1/6 for 0.111 < K < 0.888 S m−1 and a numerical value of β ≈ 0.76. Here γ is the surface tension of PC, ϵ0 is the electrical permittivity of vacuum, and K and Q are the liquid electrical conductivity and flow rate. On the experimental side, 16 different propylene carbonate solutions with either of the ionic liquids 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4) or EMI-bis(trifluoro-methylsulfonyl)imide (EMI-Im) are electrosprayed in a vacuum from a single Taylor cone, and their emissions of charged drops and ions are analysed by time-of-flight mass spectrometry at varying liquid flow rates Q. The sprays contain exclusively drops at large Q, both for small and for large electrical conductivities K, but enter a mixed ion–drop regime at sufficiently large K and small Q. Interestingly, the mixtures containing 10% and 15% (vol) EMI-Im exhibit no measurable ion currents at high Q, but approach a purely ionic regime (almost no drops) at small Q. The charge/mass ratio for the drops produced in these two mixtures increases continuously with decreasing Q, and gets very close to ionic values. Measured ion currents are represented versus computed maximum electric fields Emax on the liquid surface to infer ion evaporation kinetics. Comparison of measured ion currents with predictions from ion evaporation theory yields an anomalously low activation energy (~1.1 eV). This paradox appears to be due to alteration of the pure conj–eet electric field in the scaling laws used for the pure cone–jet regime, due to the substantial ion current density arising even when the ion current is relatively small. Elimination of this interference would require future ion current measurements in the 10–100 pA level. The electrical propulsion characteristics of the emissions from these liquids are determined and found to be excellent, particularly for 10% and 15% (vol) EMI-Im.

The objective of this investigation is to give experimental support to recent direct numerical simulation (DNS) results which demonstrated that in bypass transition the flow first breaks down to turbulence on the low-speed streaks (or so-called negative jets) that are lifted up towards the boundary-layer edge region. In order to do this, wall-normal profiles of the streamwise fluctuation velocity are presented in terms of maximum positive and negative values over a range of turbulence intensities (1.3–6%) and Reynolds numbers for zero pressure gradient flow upstream of, and including, transition onset. For all turbulence intensities considered, it was found that the peak negative fluctuation velocity increased in magnitude above the peak positive fluctuations and their positions relative to the wall shifted as transition onset approached; the peak negative value moved towards the boundary-layer edge and the peak positive value moved toward the wall. An experimental measure of the penetration depth (PD) of free-stream disturbances into the boundary layer has been gained through the use of the skewness function. The penetration depth (measured from the boundary-layer edge) scales as PD ∝ (ω Rexτw)−0.3), where ω is the frequency of the largest eddies in the free stream, Rex is the Reynolds number of the flow based on the streamwise distance from the leading edge and τw is the wall shear stress. The parameter dependence demonstrated by this scaling compares favourably with recent solutions to the Orr–Sommerfeld equation on the penetration depth of disturbances into the boundary layer. The findings illustrate the importance of negative fluctuation velocities in the transition process, giving experimental support to suggestions from recent DNS predictions that the breakdown to turbulence is initiated on the low-speed regions of the flow in the upper portion of the boundary layer. The representation of pre-transitional disturbances in time-averaged form is shown to be inadequate in elucidating which disturbances grow to cause the breakdown to turbulence.

A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.