The three-dimensional structure and decay of a dipolar vortex in a linearly stratified fluid is investigated experimentally using a high-resolution three-dimensional scanning correlation image velocimetry system (SCIV). Comparisons with simple theoretical and numerical models are made for late times in the low-Froude-number regime. The relatively well-known stratified dipole, most of the time assumed to be quasi-two-dimensional, is revealed to have a complex three-dimensional vortex topology arising from its self-induced propagation. As the buoyancy scale $u/N$ approaches zero the dynamics of such a structure are dominated by the horizontal velocity field, whereas the diffusion is mainly vertical. The evolution is then governed by an effective Reynolds number, $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}$, based on vertical diffusion and horizontal advection. At early times this effective Reynolds number is large, horizontal advection terms dominate and a decrease of aspect ratio of the structure is observed until $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}$ reaches a critical value $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}^c \,{\sim}\, O(1)$, independent of the initial condition and associated with a horizontal advection–vertical diffusion balance. Thereafter the evolution becomes purely diffusive with decay time $\hbox{\it Re}_{\hbox{\scriptsize{\it eff}}}^c$.

We describe measurements of the surface slope and reconstruction of the interface shape during the spreading of an oleic acid film on the surface of a thin aqueous glycerol mixture. This experimental system closely mimics the behaviour of an insoluble surfactant film driven to spread on a thin viscous layer under the action of a tangential (Marangoni) surface stress. Refracted image Moiré topography is used to monitor the evolution of the surface slope over macroscopic distances, from which the time variant interface shape and advancing speed of the surfactant film are inferred. The interfacial profile exhibits a strong surface depression ahead of the surfactant source capped by an elevated rim at the surfactant leading edge. The surface slope and shape as well as the propagation characteristics of the advancing rim can be compared directly with theoretical predictions. The agreement is quite strong when the model allows for a small level of pre-existing surface contamination of the initial liquid layer. Comparison between theoretical and experimental profiles reveals the importance of the initial shear stress in determining the evolution in the film thickness and surfactant distribution. This initial stress appears to thin the underlying liquid support so drastically that the surfactant droplet behaves as a finite and not an infinite source, even though there is always an excess of surfactant present at the origin.

The stability of steady inviscid vortex pairs in equilibrium with a circular cylinder is studied by discretizing equations derived from contour dynamics. There are two families of vortices, one with a pair of counter-rotating vortices standing behind the cylinder, which may be thought of as desingularizing the Föppl point vortices, and the other with the vortices standing directly above and below the cylinder. Vortices in the first family are found to be neutrally stable with respect to symmetric perturbations. When asymmetric perturbations are included, there is a single unstable mode and a single asymptotically stable mode. Vortices above and below the cylinder have two modes of instability, one symmetric and the other asymmetric, and likewise two asymptotically stable modes.

The dynamics of a baroclinic vortex in a two-layer rotating stratified fluid is investigated. The vortex is produced by the classical geostrophic adjustment process, starting from an initial step in the layer interface. The experiments are performed on the 13m diameter Coriolis turntable, allowing investigation of inertial regimes, in which viscous friction effects are negligible. The velocity fields are measured in both layers by employing particle image velocimetry, thus providing a quantitative measure of the flow evolution.

The baroclinic instability occurs much later in time than the initial inertial oscillations. The growth occurs in a hydrostatic regime, with velocity being independent of height in each layer. This process is described well by linear stability theory for a quasi-geostrophic disk vortex, or by the classical model of Phillips (1954) empirically adapted to the circular geometry. This stability prediction from the quasi-geostrophic model remains relevant even for a large initial interfacial step. For strong cyclones, the instability grows roughly twice as fast as these predictions.

In the nonlinear stage of the instability, the initial vortex splits and reorganizes into vortex pairs propagating outward. These dipoles involve the interactions of positive and negative vortices, with components in the upper and in the lower layer. In the case of a large initial interface step, a clear asymmetry between anticyclones and cyclones is observed: the latter are more intense and compact, with a more barotropic structure.

Our results are compared with numerical simulations, using a two-layer isopycnal model. Data assimilation is used to initiate the model with the same perturbations as in the laboratory experiments, thus providing a quantitative test of the dynamics. Furthermore, data assimilation is used to extrapolate the measurements, yielding the interface position and potential vorticity fields.

Two conceptual frameworks for the origin of the streaky pattern in near-wall developed turbulent flows are compared. According to the framework that dominated the research over several decades, the pattern of streaks is dictated by the pattern of wall-normal motions via the lift-up mechanism. Various concepts within this framework describe the wall-normal motions as induced by longitudinal vortices, hairpin vortices, vortex packets, etc. According to the newly emerging conceptual framework, the combined action of lift-up of the mean profile, mean shear, and viscous diffusion has its own pattern-forming properties. The pattern of streaks is dictated by these linear effects to a much greater extent than by the pattern of the wall-normal motions. Numerical results supporting the new conceptual framework are presented. An approximate approach for calculating the streak spacing within the new framework is proposed. It is shown to have a significant predictive ability.

A theory for the transport of a tracer in flow dominated by turbulence and jets is developed and tested. Such a system can be taken as a model either for the stirring of true tracers in the atmosphere and ocean, or, less obviously, for the stirring of baroclinic potential vorticity by non-zonal flow in the ocean. The flow is generated by two-dimensional turbulence with a mean vorticity gradient ($\beta$) and forced randomly and isotropically at small scales. The tracer transported by the flow is forced by a mean tracer gradient that is arbitrarily oriented with respect to the mean vorticity gradient. Such a tracer can be decomposed into two independent tracers: one forced by a gradient that is parallel to the vorticity gradient (and so is stirred across jets), and another that is forced by a mean gradient that is perpendicular to the mean vorticity gradient (and so is stirred along jets). The turbulent transport of the tracer across jets has been discussed in previous research, and is well-described by mixing-length theory. Here it is shown that the transport of the tracer along the jets is described by shear dispersion, but with a diffusivity determined by the across-jet mixing. Even at only moderate levels of anisotropy, the along-jet transport is much larger than the corresponding across-jet transport, consistent, for example, with observations from surface floats in the Pacific.

An experimental study has been performed on the dynamics of a large turbulent buoyanthelium plume. Two-dimensional velocity fields were measured using particle image velocimetry (PIV) while helium mass fraction was determined by planar laser-induced fluorescence (PLIF). PIV and PLIF were performed simultaneously in order to obtain velocity and mass fraction data over a plane that encompassed the plume core, the near-field mixing zones and the surrounding air. The Rayleigh–Taylor instability at the base of the plume leads to the vortex that grows to dominate the flow. This process repeats in a cyclical manner. The temporally and spatially resolved data show a strong negative correlation between density and vertical velocity, as well as a strong 90° phase lag between peaks in the vertical and horizontal velocities throughout the flow field owing to large coherent structures associated with puffing of the turbulent plume. The joint velocity an mass fraction data are used to calculate Favre-averaged statistics in addition to Reynolds-(time) averaged statistics. Unexpectedly, the difference between both the Favre-averaged and Reynolds-averaged velocities and second-order turbulent statistics is less than the uncertainty in the data throughout the flow field. A simple analysis was performed to determine the expected differences between Favre and Reynolds statistics for flows with periodic fluctuations in which the density and velocity fields are perfectly correlated, but have the phase relations as suggested by the data. The analytical results agreewith the data, showing that the Favre and Reynolds statistics will be the same to lead order. The combination of observation and simple analysis suggests that for buoyancy-dominated flows in which it can be expected that density and velocity are strongly correlated,phase relations will result in only second-order differences between Favre- and Reynolds-averaged data in spite of strong fluctuations in both density and velocity.

The flow-induced Marangoni instability due to the presence of surfactant is examined for long-wavelength perturbations. A unified view of the underlying mechanisms is provided through revisiting both falling film and two-fluid Couette flow systems. The analysisis performed by inspecting the corresponding coupled set of evolution equations for the interface and surfactant concentration perturbations. While both systems appear to have very similar sets of equations consisting of base flows and Marangoni effects, the origins of stability/instability are identified and illustrated from a viewpoint of vorticity. The base flow rearranges the surfactant distribution and the induced Marangoni flow tends to stimulate the interface's growth. But this destabilizing effect is reduced by effects combining the interface travelling motions and the Marangoni recoil. The competition between these opposing effects determines the system stability, and is elucidated using equations in concert with observations from initial value problems. Moreover,a criterion for the onset of instability can be established in line with the same rationale. The present work not only furnishes a lucid way to clarify the instability mechanisms, but also complements previous studies. Extension to the weakly nonlinear regime is also discussed.

The near-field tip-vortex flow structure behind an oscillating NACA 0015 wing was investigated at ${\hbox {{\it Re}}}\,{=}\,1.86 \times 10^{5}$. For attached-flow and light-stall oscillations, a small hysteretic property existed between the pitch-up and pitch-down motion, and many of the vortex flow features were found to be qualitatively similar to those of a static wing. For deep-stall oscillations, the wing oscillations imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was less organized during pitch-down (as a result of leading-edge-vortex-induced massive flow separation) than during pitch-up. The tangential velocity, circulation and lift-induced drag increased progressively with the airfoil incidence, and had higher magnitudes during pitch-up than during pitch-down, while varying slightly with the downstream distance. The vortex size, however, was larger during pitch-down than during pitch-up. The axial flow was always wake-like during the deep-stall oscillation cycle. The normalized circulation within the inner region of the tip vortex also exhibited a self-similar structure, similar to that of a static wing, and was insensitive to the reduced frequency.

Slender-body theory is used to investigate the steady-state deformation and time-dependent evolution of an inviscid axisymmetric bubble in zero-Reynolds-number extensional flow, when insoluble surfactant is present on the bubble surface. The asymptotic solutions reveal steady ellipsoidal bubbles covered with surfactant, and, at increasing deformation, solutions distinguished by a cylindrical surfactant-free central part, with stagnant surfactant caps at the bubble endpoints. The bubble shapes are rounded near the endpoints, in contrast to the pointed shapes found for clean inviscid bubbles. Simple expressions are derived relating the capillary number $Q$ to the steady bubble slenderness ratio $\epsilon$. These show that there is a critical value $Q_c$ above which steady solutions no longer exist. Equations governing the time-evolution of a slender inviscid bubble with surfactant, valid for large capillary number, are also derived. Numerical solutions of the slender bubble equations for $Q\,{>}\,Q_c$ exhibit spindle shapes with tip-streaming filaments.

This investigation presents a unique and elaborate set of experiments relating the generation of noise to the evolution of large-scale turbulence structures within an ideally expanded, Mach 1.28, high-Reynolds-number $(1.03\,{\times}\,10^{6})$ jet. The results appear to indicate many similarities between the noise generation processes of high-speed low-Reynolds-number and high-speed high-Reynolds-number jets. Similar to the rapid changes observed in theregion of noise generation in low-Reynolds-number jets in previous experimental and computational work, a series of robust flow features formed approximately one convective time scale before noise emission and then rapidly disintegrated shortly before the estimated moment of noise emission. Coincident with the disintegration, a positive image intensity fluctuation formed at the jet centreline in a region that is immediately past the endof the potential core. This indicates mixed fluid had reached the jet core. These results are consistent with the formation of large-scale structures within the shear layer, which entrain ambient air into the jet, and their eventual interaction and disintegration apparently result in noise generation. These results are quite different from the evolution of the jet during prolonged periods that lacked significant sound emission. The observations presented in this work were made through the use of well-established technique that were brought together in an unconventional fashion. The sources of large-amplitude sound waves were estimated in time and three-dimensional space using a novel microphone array/beamforming algorithm while the noise-generation region of the mixing layer was simultaneously visualized on two orthogonal planes (one of which was temporally resolved). The flow images were conditionally sampled based on whether or not a sound wave wascreated within the region of the flow while it was being imaged and a series of images was compiled that was roughly phase-locked onto the moment of sound emission. Another set of images was gathered based on a lack of sound waves reaching the microphone array over several convective time scales. Proper orthogonal decomposition (POD) was then used tocreate a basis for the flow images and this basis was used to reconstruct the evolution of the jet.

Numerical simulations of Rayleigh–Bénard convection in a fluid layer heated from below between two rigid horizontal boundaries have been performed for Rayleigh numbers Ra up to 107, Prandtl numbers in the range between 0.7 and 60 and for aspect ratios $\Gamma$ up to 20. Periodic boundary conditions in the horizontal plane have been used. To a considerable extent, the evolution towards turbulent convection at high values of Ra is governed by processes exhibited by instabilities of steady or time periodic forms of convection at lower Rayleigh numbers. With increasing Ra, the properties of convection are increasingly determined by the thermal boundary layers. The role of mean flows which may be symmetric or antisymmetric with respect to the mid-plane of the layer is emphasized.

We have extended the procedure to find the exact solution of the Riemann problem in relativistic hydrodynamics to a particular case of relativistic magnetohydrodynamics in which the magnetic field of the initial states is tangential to the discontinuity and orthogonal to the flow velocity. The wave pattern produced after the break up of the initial discontinuity is analogous to the non-magnetic case and we show that the problem can be understood as a purely relativistic hydrodynamical problem with a modified equation of state. The new degree of freedom introduced by the non-zero component of the magnetic field results in interesting effects consisting in the change of the wave patterns for given initial thermodynamical states, in a similar way to the effects arising from the introduction of tangential velocities. Secondly, when the magnetic field dominates the thermodynamical pressure and energy, the wave speeds approach the speed of light, leading to fast shocks and fast and arbitrarily thin rarefaction waves. Our approach is the first non-trivial exact solution of a Riemann problem in relativistic magnetohydrodynamics and it can also be of great interest to test numerical codes against known analytical or exact solutions.

We establish transport relations for integrals over evolving fluid interfaces. These relations make it possible to localize integral balance laws over non-material interfaces separating fluid phases and, therefore, obtain associated interface conditions in differential form.

A mathematical model for the evolution of a thin film in an interior corner region is presented. The model is based on the idea that the film can be considered thin everywhere in the $\eta$-direction if viewed in the new coordinate system $\xi\,{=}\,x^2\,{-}\,y^2$, $\eta\,{=}\,2xy$. Lubrication theory is applied to the governing equations written in this coordinate system. The exact integration of the mass conservation equation for a no-slip boundary condition yields a single evolution equation, which is integrated numerically. The evolution of a thin film driven by surface tension and gravity is predicted as a function of the Bond number and successfully compared to laboratory experiments.