We investigate the natural displacement ventilation of a space connected to a body of warm fluid through high- and low-level vents. The space is subject to discrete periodic gusts of wind entering at high level from a cold exterior. The cold exterior air entering the space produces buoyancy differences between the space and the body of warm fluid, driving a ventilation flow. Initially we examine the case of a series of identical gusts of wind modelled as turbulent buoyant thermals. New laboratory experiments show that an approximately two-layer stratification is established and the height of the interface is quasi-steady if the period between thermals is much less than the draining time of the space but longer than the fall time of individual thermals. Experiments also show that the interface height depends on the average buoyancy flux associated with the wind gusts, the time between thermals as well as the geometric properties of the vents. This contrasts with the case of a continuous source of buoyancy where the interface height depends only on the geometric properties of the vents and is independent of the buoyancy flux. We develop a quasi-steady two-layer model of the flow based on the classical theory of turbulent thermals and show that it is consistent with our new experimental data. We generalize the model to explore the sensitivity of the results to temporal variations in the size of thermals. We then extend the model to explore the effects of longer interval times between successive thermals and find a two-layer stratification still develops but that the interface height now varies cyclically in time. We then discuss the implications of these results for the ventilation of a shopping mall subject to gusts of wind.

We consider the steady motion of disks of various thicknesses in a weakly viscous flow, in the case where the angle of incidence (defined as that between the disk axis and its velocity) is small. We derive the structure of the steady flow past the body and the associated hydrodynamic force and torque through a weakly nonlinear expansion of the flow with respect to . When buoyancy drives the body motion, we obtain a solution corresponding to an oblique path with a non-zero incidence by requiring the torque to vanish and the hydrodynamic and net buoyancy forces to balance each other. This oblique solution is shown to arise through a bifurcation at a critical Reynolds number which does not depend upon the body-to-fluid density ratio and is distinct from the critical Reynolds number corresponding to the steady bifurcation of the flow past the body held fixed with . We then apply the same approach to the related problem of a sphere that weakly rotates about an axis perpendicular to its path and show that an oblique path sets in at a critical Reynolds number slightly lower than , in agreement with available numerical studies.

We investigate experimentally the characteristics of the flow field that develops at low Reynolds numbers () around a sharp corner bounded by channel walls. Two-dimensional planar velocity fields are obtained using particle image velocimetry (PIV) conducted in a towing tank filled with a silicone oil of high viscosity. We find that, in the vicinity of the corner, the steady-state flow patterns bear the signature of a three-dimensional secondary flow, characterized by counter-rotating pairs of streamwise vortical structures and identified by the presence of non-vanishing transverse velocities (). These results are compared to numerical solutions of the incompressible flow as well as to predictions obtained, for a similar geometry, from an asymptotic expansion solution (Guglielmini et al., J. Fluid Mech., vol. 668, 2011, pp. 33–57). Furthermore, we discuss the influence of both Reynolds number and aspect ratio of the channel cross-section on the resulting secondary flows. This work represents, to the best of our knowledge, the first experimental characterization of the three-dimensional flow features arising in a pressure-driven flow near a corner at low Reynolds number.

This paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

Interaction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier–Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of – equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock–boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

The mean electromotive force (EMF) associated with exponentially growing perturbations of an Euler flow with elliptic streamlines in a rotating frame of reference is studied. We are motivated by the possibility of dynamo action triggered by tidal deformation of astrophysical objects such as accretion discs, stars or planets. Ellipticity of the flow models such tidal deformations in the simplest way. Using analytical techniques developed by Lebovitz & Zweibel (Astrophys. J., vol. 609, 2004, pp. 301–312) in the limit of small elliptic (tidal) deformations, we find the EMF associated with each resonant instability described by Mizerski & Bajer (J. Fluid Mech., vol. 632, 2009, pp. 401–430), and for arbitrary ellipticity the EMF associated with unstable horizontal modes. Mixed resonance between unstable hydrodynamic and magnetic modes and resonance between unstable and oscillatory horizontal modes both lead to a non-vanishing mean EMF which grows exponentially in time. The essential conclusion is that interactions between unstable eigenmodes with the same wave-vector can lead to a non-vanishing mean EMF, without any need for viscous or magnetic dissipation. This applies generally (and not only to the elliptic instabilities considered here).

An improved version of the immersed boundary (IB) method for simulating an initially circular or elliptic flexible ring pinned at one point in a uniform flow has been developed. The boundary of the ring consists of a flexible filament with tension and bending stiffness. A penalty method derived from fluid compressibility was used to ensure the conservation of the internal volume of the flexible ring. At , two different flapping modes were identified by varying the tension coefficient for a fixed bending stiffness, or by changing the bending coefficient for a fixed tension coefficient. The optimal tension and bending coefficients that minimize the drag force of the flexible ring were found. Visualization of the vorticity field showed that the two flapping modes correspond to different vortex shedding patterns. We observed the hysteresis property of the flexible ring, which exhibits bistable states over a range of flow velocities depending on the initial inclination angle, i.e. one is a stationary stable state and the other a self-sustained periodically flapping state. The Reynolds number range of the bistability region and the flapping amplitude were determined for various aspect ratios . For , the hysteresis region arises at the highest Reynolds number and the flapping amplitude in the self-sustained flapping state is minimized. A new bistability phenomenon was observed: for certain aspect ratios, two periodically flapping states coexist with different amplitudes in a particular Reynolds number range, instead of the presence of a stationary stable state and a periodically flapping state.

Nonlinear interactions between free-surface waves of the same wave speed and wind are studied by extending the linear resonant theory of Miles (J. Fluid Mech., vol. 3, 1957, pp. 185–204). A nonlinear interaction can occur when the steepness of a primary three-dimensional wave, which propagates obliquely to the wind direction, becomes of the order of the cube of the density ratio of air to water. If a secondary wave of smaller amplitude is also an oblique wave, the nonlinear critical-layer interaction between the primary and secondary fluctuations in air generates a difference mode whose wavenumbers are equal to the differences between the primary and secondary values. In addition, the nonlinear interaction in the critical layer between the primary and difference modes induces a parametric-growth effect on the secondary surface wave, if the frequency of the primary wave is higher than that of the secondary wave. The primary wave remains linear during this ‘ mode critical-layer interaction’ stage between two free-surface waves and a nonlinearly generated mode. The evolution of the secondary-wave amplitude is governed by an integro-differential equation and that of the difference mode is determined by an integral equation. Both inviscid and viscous numerical results show that the nonlinear growth rates become much larger than the linear growth rates. Effect of viscosity is shown to delay the onset of the nonlinear growth. The growth of the secondary and difference modes is more effectively enhanced when the signs of propagation angles of the primary and secondary waves are opposite than when they are equal. The mode interaction can occur when wave steepnesses are very small. The nonlinear interaction is entirely confined to a thin critical layer, and the perturbations outside the critical layer are governed by linear equations. It is shown that the initial nonlinear growth of a free-surface wave could be governed by a mode–mode interaction in air.

A promising mechanism for generating a finite-time singularity in the incompressible Euler equations is the stretching of vortex filaments. Here, we argue that interacting vortex filaments cannot generate a singularity by analysing the asymptotic dynamics of their collapse. We use the separation of the dynamics of the filament shape, from that of its core, to derive constraints that must be satisfied for a singular solution to remain self-consistent uniformly in time. Our only assumption is that the length scales characterizing filament shape obey scaling laws set by the dimension of circulation as the singularity is approached. The core radius necessarily evolves on a different length scale. We show that a self-similar ansatz for the filament shapes cannot induce singular stretching, due to the logarithmic prefactor in the self-interaction term for the filaments. More generally, there is an antagonistic relationship between the stretching rate of the filaments and the requirement that the radius of curvature of filament shape obeys the dimensional scaling laws. This suggests that it is unlikely that solutions in which the core radii vanish sufficiently fast to maintain the filament approximation exist.

Over the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as . In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modelling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on the mean velocity in flow subject to control. In contrast to the traditional approach that relies on numerical simulations, we determine the turbulent viscosity from the second-order statistics of the linearized model driven by white-in-time stochastic forcing. The spatial power spectrum of the forcing is selected to ensure that the linearized model for uncontrolled flow reproduces the turbulent energy spectrum. The resulting correction to the turbulent mean velocity induced by small-amplitude wall movements is then used to identify the optimal frequency of drag-reducing oscillations. In addition, the control net efficiency and the turbulent flow structures that we obtain agree well with the results of numerical simulations and experiments. This demonstrates the predictive power of our model-based approach to controlling turbulent flows and is expected to pave the way for successful flow control at higher Reynolds numbers than currently possible.

Rigorous bounds on heat transport are derived for thermal convection between stress-free horizontal plates. For three-dimensional Rayleigh–Bénard convection at infinite Prandtl number (), the Nusselt number () is bounded according to where is the standard Rayleigh number. For convection driven by a uniform steady internal heat source between isothermal boundaries, the spatially and temporally averaged (non-dimensional) temperature is bounded from below by in three dimensions at infinite and by in two dimensions at arbitrary , where is the heat Rayleigh number proportional to the injected flux.

The canonical case of a vortex ring interacting with a solid surface orthogonal to its symmetry axis exhibits a variety of intricate behaviours, including stretching of the primary vortex ring and generation of secondary vorticity, which illustrate key features of vortex interactions with boundaries. Replacing the solid boundary with a permeable screen allows for new behaviour by relaxing the no-through-flow condition, and can provide a useful analogue for the interaction of large-scale vortices with permeable structures or closely spaced obstructions. The present investigation considers the interaction of experimentally generated vortex rings with a thin permeable screen. The vortex rings were generated using a piston-in-cylinder mechanism using piston stroke-to-diameter ratios () of 1.0 and 3.0 (nominal) with jet Reynolds numbers () of 3000 and 6000 (nominal). Planar laser-induced fluorescence and digital particle image velocimetry (DPIV) were used to study the interaction with wire-mesh screens having surface open-area ratios () in the range 0.44–0.79. Solid surfaces () and free vortex rings () were also included as special cases. Measurement of the vortex trajectories showed expansion of the vortex ring diameter as it approached the boundary and generation of secondary vorticity similar to the case of a solid boundary, but the primary vortex diameter then began to contract towards the symmetry axis as the flow permeated the screen and reorganized into a transmitted vortex downstream. The trajectories were highly dependent on , with little change in the incident ring trajectory for . Measurement of the hydrodynamic impulse and kinetic energy using DPIV showed that the change between the average upstream and downstream values of these quantities also depended primarily on , with a slight decrease in the relative change as and/or were increased. The kinetic energy dissipation () was much more sensitive to , with a strongly nonlinear dependence, while the decrease in impulse () was nearly linear in . A simple model is proposed to relate and in terms of bulk flow parameters. The model incorporates the decrease in flow velocity during the interaction due to the drag force exerted by the screen on the flow.

Experiments are conducted to examine the mechanisms behind the coupling between corner separation and separation away from the corner when holding a high-Mach-number normal shock in a rectangular channel. The ensuing shock wave interaction with the boundary layer on the wind tunnel floor and in the corners was studied using laser Doppler anemometry, Pitot probe traverses, pressure sensitive paint and flow visualization. The primary mechanism explaining the link between the corner separation size and the other areas of separation appears to be the generation of compression waves at the corner, which act to smear the adverse pressure gradient imposed upon other parts of the flow. Experimental results indicate that the alteration of the -region, which occurs in the supersonic portion of the shock wave/boundary layer interaction (SBLI), is more important than the generation of any blockage in the subsonic region downstream of the shock wave.

In this paper we present a set of wave flume experiments for a solitary wave reflecting off a vertical wall. A particle tracking velocimetry (PTV) technique is used to measure free-surface velocity and the velocity field in the vicinity of the moving contact line. We observe that the free surface undergoes the so-called rolling motion as the contact line moves up and down the vertical wall, and fluid particles on the free surface almost always flow toward the wall except at the end of the reflection process. As the contact line descends along the wall, wall boundary layer flows move in a downward direction and therefore the boundary layer acts like a conduit through which the surface-rolling-induced flow escapes from the meniscus. However, during the last phase of the reflection process flow reversal occurs inside the wall boundary layer. An approximate analytical solution is developed to explain the flow reversal feature. Very good agreement between the approximate theory and measured data is obtained. Because of the flow reversal, boundary layer flows collide with the surface-rolling-induced flows. The collision gives rise to a jet ejecting from the meniscus into the water body, which later evolves into a small eddy. It is noticed that the fluid particles in different regions such as the free stream, the free-surface boundary layer and the wall boundary layer, can be transported to other regions by passing through the meniscus.

We use LVDSMC (low-variance deviational Monte Carlo) simulations to calculate, under linearized conditions, the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term, as in the case of homogeneous volumetric heating. Both the hard-sphere gas and the BGK model of the Boltzmann equation, for which slip/jump coefficients are not functions of temperature, are considered. The temperature jump relation and jump coefficient determined here are closely linked to the general jump relations for time-dependent problems that have yet to be systematically treated in the literature; as a result, they are different from those corresponding to the well-known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

The present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

The three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

In strongly stratified fluids, an axisymmetric vertical columnar vortex is unstable because of a spontaneous radiation of internal waves. The growth rate of this radiative instability is strongly reduced in the presence of a cyclonic background rotation and is smaller than the growth rate of the centrifugal instability for anticyclonic rotation, so it is generally expected to affect vortices in geophysical flows only if the Rossby number is large (where is the angular velocity of the vortex). However, we show here that an anticyclonic Rankine vortex with low Rossby number in the range , which is centrifugally stable, is unstable to the radiative instability when the azimuthal wavenumber is larger than 2. Its growth rate for is comparable to the values reported in non-rotating stratified fluids. In the case of continuous vortex profiles, this new radiative instability is shown to occur if the potential vorticity of the base flow has a sufficiently steep radial profile. The most unstable azimuthal wavenumber is inversely proportional to the steepness of the vorticity jump. The properties and mechanism of the instability are explained by asymptotic analyses for large wavenumbers.

We consider the flow which develops when two separate spaces maintained at different temperatures, both in excess of the exterior temperature, are connected through high and low level openings to a central atrium in which there is negligible heat load but which can naturally ventilate through high and low level openings to the exterior. We show that with a small temperature contrast between the spaces or large openings from the atrium to the exterior, upflow displacement ventilation develops in each of the spaces, with air entering from the atrium at low level and exiting at high level. However, with a larger temperature contrast between the spaces or small openings between the atrium and the exterior, a convective circulation develops between the spaces, with upflow in the warmer space and downflow in the colder space. Exterior air, which may enter the atrium at low level, flows into the warmer space along with the air from the colder space. At high level, air flows back into the atrium from the warmer space, and then either vents from the building or flows into the colder space. In this convection dominated flow regime, the colder space is a net heat sink, whereas with the upward displacement ventilation, this space acts as a net heat source. This can have significant implications for energy usage and on the build up of contaminants in each of the spaces. We also show that in both steady flow regimes, the air at mid-level in the atrium is unventilated and stagnant. We discuss the relevance of our model for controlled natural ventilation in large public buildings such as shopping malls where individual shops often maintain temperatures independently of the central atrium-space.

The dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid–fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier–Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.