The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ($\unicode[STIX]{x1D6E4}=\text{major:minor axis ratio}$) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to $Re\lesssim 400$; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes $\widehat{\text{A}}$ and $\widehat{\text{B}}$, become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode $\widehat{\text{A}}$ persists for all incident angles investigated here, mode $\widehat{\text{B}}$ is found only to be unstable for incident angles up to $10^{\circ }$. Surprisingly, for $1.8\lesssim \unicode[STIX]{x1D6E4}\lesssim 2.9$, the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.

We study the dewetting of a porous plate withdrawn from a liquid bath. The contact angle is fixed to zero and the flow is assumed to be almost parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a stationary moving contact line with zero contact angle below a critical value of the capillary number η U/γ. Above this value, no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, which reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal (3/2 power law), provided the capillary length is much larger than the square root of the porous-medium permeability. In addition, it is shown that the classical lubrication equation leads not only to the well-known Landau–Levich–Derjaguin films, but also to a family of films for which thickness is not imposed by the problem parameters.

According to parallel-flow theory based on the Orr–Sommerfeld equation, a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there exist a non-zero Reynolds number below which disturbances cannot extract net energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism using the minimal composite theory and the properties of adjoints, following Govindarajan & Narasimha (Theor. Comput. Fluid Dyn. vol. 19, 2005, p. 229) resolves the issue by yielding a non-zero critical Reynolds number for co-flowing streams of any velocity ratio. The critical Reynolds number for the total disturbance kinetic energy is found to be close to 30 for all velocity ratios in the range from zero to unity.

The structure of a trailing vortex from a wing undergoing small amplitude, low frequency heaving motion is investigated using space–time representations determined from stereo particle image velocimetry. The evolution of the vortex shows large fluctuations of axial velocity deficit and circulation during the oscillation cycle. Correspondingly, large variations of swirl ratio occur and onset of pronounced azimuthal vorticity arises. At a given cross-section of the vortex, the pattern of azimuthal vorticity moves around its axis in an ordered fashion as both it and the pattern of velocity defect increase in magnitude and scale. When the swirl ratio attains its minimum value during the oscillation cycle, and this value lies below the theoretically established critical threshold for amplification of azimuthal modes, the magnitude and scale of the pattern of azimuthal vorticity is maximized. Subsequent increase of the swirl ratio yields attenuation of the azimuthal vorticity. Onset of pronounced azimuthal vorticity when the swirl ratio decreases involves rapid amplification, then disruption, of axial vorticity fluctuation.

We perform an experimental study of turbulent Rayleigh–Bénard convection up to very high Rayleigh number, $10^{8}<Ra<10^{14}$, in a cylindrical aspect ratio one cell, 30 cm in height, filled with cryogenic helium gas. We monitor temperature fluctuations in the convective flow with four small (0.2 mm) sensors positioned in pairs 1.5 cm from the sidewalls and 2.5 cm vertically apart and symmetrically around the mid-height of the cell. Based on one-point and two-point correlations of the temperature fluctuations, we determine different types of Reynolds numbers, $\mathit{Re}$, associated with the large-scale circulation (LSC). We observe a transition between two types of $\mathit{Re}(\mathit{Ra})$ scaling around $\mathit{Ra}=10^{10}{-}10^{11}$, which is accompanied by a scaling change of the skewness of the probability distribution functions (PDFs) of the temperature fluctuations. The $\mathit{Re}(\mathit{Ra})$ dependencies measured near the sidewall at Prandtl number $\mathit{Pr}\sim 1$ are consistent with the $\mathit{Ra}^{4/9}\mathit{Pr}^{-2/3}$ scaling above the transition, while for $\mathit{Ra}<10^{10}$, the $\mathit{Re}(\mathit{Ra})$ dependencies are steeper. It seems likely that this change in $\mathit{Re}(\mathit{Ra})$ scaling is linked to the previously reported change in the Nusselt number $\mathit{Nu}(\mathit{Ra})$ scaling. This behaviour is in agreement with independent cryogenic laboratory experiments with $\mathit{Pr}\sim 1$, but markedly different from the $\mathit{Re}$ scaling obtained in water experiments ($\mathit{Pr}\sim 3.3{-}5.6$). We discuss the results in comparison with different versions of the Grossmann–Lohse theory.

In this paper, we formulate the dynamic equations of radial and surface modes for a cylindrical cavitation bubble subject to a prescribed uniform rectilinear vortex flow. The potential flow in the bulk volume of the external flow is modelled using the general mode decomposition approach. The stability of surface modes is investigated under linear analysis. The effects of confinement due to a limited flow domain in a water tunnel and viscosity at the bubble surface are evaluated, which can be fairly neglected for the cylindrical cavitation bubbles discussed. Our model is capable of predicting the developments of surface modes, which agrees well with experimental observations reported in the literature. We derive the Mathieu structure in the dynamic equation of the surface oscillation and the associated instability condition of the surface mode oscillations. The numerical results confirm that the Mathieu-type instability controls the stability diagrams and the emergence of surface modes under specific radial oscillation.

We use analytical and numerical approaches to investigate head-on collisions between two self-propelled drops described as a phase separated binary mixture. Each drop is driven by chemical reactions that isotropically produce or consume the concentration of a third chemical component, which affects the surface tension of the drop. The isotropic distribution of the concentration field is destabilized by motion of the drop, which is created by the Marangoni flow from the concentration-dependent surface tension. This symmetry-breaking self-propulsion is distinct from other self-propulsion mechanisms due to its intrinsic polarity of squirmers and self-phoretic motion; there is a bifurcation point below which the drop is stationary and above which it moves spontaneously. When two drops are moving in the opposite direction along the same axis, their interactions arise from hydrodynamics and concentration overlap. We found that two drops exhibit either an elastic collision or fusion, depending on the distance from their bifurcation point, which may be controlled, for example, by viscosity. An elastic collision occurs when there is a balance between dissipation and the injection of energy by chemical reactions. We derive the reduced equations for the collision between two drops and analyse the contributions from the two interactions. The concentration-mediated interaction is found to dominate the hydrodynamic interaction for a head-on collision.

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.

Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

This work investigates intensive vortices, which are characterised by the existence of a converging radial flow that significantly intensifies the flow rotation. Evolution and amplification of the vorticity present in the flow play important roles in the formation of the vortex. When rotation in the flow becomes sufficiently strong (this implies the validity of the strong swirl approximation, which has been developed in a series of publications since the 1950s) the previous analysis of the author and the present work determine that further amplification of vorticity is moderated by interactions of vorticity and velocity. This imposes physical constraints on the flow, resulting in the so-called compensating regime, where the radial distribution of the axial vorticity is characterised by the $4/ 3$ and $3/ 2$ power laws. This asymptotic treatment of a strong swirl is based on vorticity equations and involves higher-order terms. This treatment incorporates multi-scale analysis indicating downstream relaxation of the flow to the compensating regime. The present work also investigates and takes into account viscous and transient effects. One of the main points of this work is the applicability of the power laws of the compensating regime to intermediate regions in large atmospheric vortices, such as tropical cyclones and tornadoes.

The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study.

The dynamics of radiative, near-limit, stretched premixed flames was investigated analytically and numerically, with emphasis on pulsating stability for sub-unity Lewis numbers. The analysis includes both flame stretch and order-unity heat loss, and yields a dispersion equation for the stability of radiative stretched flames subjected to symmetrical and asymmetrical perturbations. The dispersion equation reduces to that of the classical thermo-diffusional stability analysis of Sivashinsky in the limit of small heat loss, small stretch rate, and infinite flame separation distance. Results show that sub-limit flames are stable near both radiation and stretch extinction limits, and that oscillation occurs only at moderate flame stretch rates. The unstable regime and the stability diagram were obtained. Numerical simulation with detailed chemical kinetics and transport models yielded results that are in good agreement with theory. The present work also provides a satisfactory explanation of the experimental results obtained in microgravity.