Mesovortices in the eyewall region of a hurricane are intriguing elements of the hurricane engine. In-situ measurements of them are sparse, however, and our understanding of their overall role in the physics of a hurricane is incomplete. To further understand their dynamics an experimental apparatus using a homogeneous fluid (water) has been constructed to emulate the lower tropospheric flow of the hurricane eye/eyewall region.

For experimental configurations possessing a central aspect ratio less than unity, a primary and secondary circulation similar to the in flow layer of an intense hurricane, and a similar radius-to-width ratio of the curvilinear shear layer bordering the eye and eyewall region, the flow supports two primary quasi-steady vortices and secondary intermittent vortices. The vortices form through Kelvin–Helmholtz instability of the curvilinear shear layer bordering the slowly upwelling fluid in the centre and the converging fluid from the periphery. The primary vortices are maintained by convergence of circulation from the periphery and merger of secondary vortices spawned along the shear layer.

The horizontal flow field is measured using a particle image velocimeter. Despite the relatively strong secondary circulation through the parent vortex the horizontal flow is found to be approximately uniform in the direction parallel to the rotation axis. The peak tangential velocity is found to occur in the mesovortices and is roughly 50% greater than the parent vortex that supports them. The measurements provide insight into recent observations of excessive wind damage in landfalling storms and support the hypothesis that intense storms contain coherent vortex structures in the eyewall region with higher horizontal wind speeds locally than the parent hurricane.

The mixing produced by a turbulent buoyant plume with finite mass flux in a room is examined analytically and numerically. The entrainment of ambient fluid into the ascending buoyant plume leads to a return flow in the room which carries fluid downwards from the top of the room. The cycling of ambient fluid through the buoyant plume and the return flow causes the density to become uniform and gradually evolve towards that of the source fluid. As a result the buoyancy flux associated with the input fluid decreases and the plume motion becomes dominated by the source momentum flux. We develop an asymptotic model of the mixing using buoyant plume theory for a momentum-dominated flow. This provides an analytical description of the evolution of the density in the room which is in excellent accord with a full numerical simulation, and provides an improved description of the experimental filling-box data originally presented by Baines & Turner (1969).

We present a numerical study of the downstream evolution (mechanical and thermal) of vortex-jet cores whose velocity and temperature fields far from the axis match a family of inviscid and non-conducting vortices. The far-velocity field is rotational, except for a particular case which corresponds to the well-known Long's vortex. The evolution of the vortex core depends on both the conditions at a certain upstream station, characterized by the dimensionless value of the velocity at the axis, and a dimensionless swirling parameter L defined as the ratio of the values of the azimuthal and axial velocities outside the vortex core. This numerical study, based on the quasi-cylindrical approximation (QC) of the Navier–Stokes equations, determines the conditions under which the vortex evolution proceeds smoothly, eventually reaching an asymptotic self-similar behaviour as described in the literature (Fernández-Feria, Fernández de la Mora & Barrero 1995; Herrada, Pérez-Saborid & Barrero 1999), or breaks in a non-slender solution (vortex breakdown). In particular, the critical value L = Lb(a) beyond which vortex breakdown occurs downstream is a function of a dimensionless parameter a characterizing the axial momentum of the vortex jet at an initial upstream station. It is found numerically that for very large values of a this vortex breakdown criterion tends to an asymptote which is precisely the value L = L* predicted by the self-similar analysis, and beyond which a self-similar structure of the vortex core does not exist. In addition, the computation of the total temperature field provides useful information on the physical mechanisms responsible for the thermal separation phenomenon observed in Ranque–Hilsch tubes and other swirling jet devices. In particular, the mechanical work of viscous forces which gives rise to an intense loss of kinetic energy during the initial stages of the evolution has been identified as the physical mechanism responsible for thermal separation.

The nonlinear dynamics exhibited by a planar layer of precessing fluid is examined as a canonical example of a strained rotating flow. The simple basic flow, Ubasic = −YXˆ+(X−2εZ)Yˆ in a frame rotating at εXˆ, consists of sheared circular streamlines (where ε measures the shearing) which are linearly unstable through the pairwise resonance of two inertial waves in a fashion similar to elliptical flow. Direct numerical simulation shows that the weakly nonlinear regime is quickly disrupted by further instabilities which lead to a multitude of co-existing solution branches, some of which represent chaotic flows. All these solutions remain within O(ε) (in an energy norm) of Ubasic so that energy is not apparently withdrawn from the fluid's underlying rotation. Further increases in the precession rate cause the flow to branch-switch randomly between these now quasi-stable states so that a new form of ‘slow’ dynamics emerges. The implication of this and the fact that these instabilities can nevertheless be classed as ‘strong’ is discussed from the perspective of the closely related problem of the precessing Earth and laboratory models thereof.

Direct numerical simulation of two turbulent boundary layer flows has been performed. The boundary layers are both subject to a strong adverse pressure gradient. In one case a separation bubble is created while in the other the boundary layer is everywhere attached. The data from the simulations are used to investigate scaling laws near the wall, a crucial concept in turbulence models. Theoretical work concerning the inner region in a boundary layer under an adverse pressure gradient is reviewed and extended to the case of separation. Excellent agreement between theory and data from the direct numerical simulation is found in the viscous sub-layer, while a qualitative agreement is obtained for the overlap region.

In the EVOLVE concept for a nuclear fusion blanket a pool boiling scenario has been proposed where a number of permanent vertical vapour channels are formed in a horizontal layer of liquid lithium. Similar situations occur during laser beam welding where a relatively long vapour capillary is observed. The present analysis focuses on the flow of the electrically conducting liquid phase in the presence of a strong uniform horizontal magnetic field. The cross-section of vapour channels is circular if surface tension dominates magnetic forces. In the opposite case a stretching of the liquid–vapour interface along magnetic field lines is observed and contours become possible where a major part of the interface is straight and aligned with the field. For strong magnetic fields the liquid flow exhibits several distinct subregions. Most of the liquid domain is occupied by inviscid cores. These are separated from each other by parallel layers that spread along the field lines which are tangential to the vapour channel. In one core, which is located between two parallel layers, the flow direction is preferentially oriented along magnetic field lines, while in the other cores the flow is perpendicular to the field.

The short-wave stability properties of a Batchelor vortex are used to explain the intrinsic resistance of vortices to turbulent diffusion. We show that turbulence produced within the vortex core has to overcome a stabilizing ‘dispersion buffer’, where energy of the perturbations is dispersed by inertial waves without interfering with the mean flow, before they can reach the periphery of the vortex. While angular momentum is maintained by this mechanism, the difference in energy extraction by turbulence from the axial and tangential velocity fields due to a lack of alignment between the mean and turbulent strain tensors, a typical effect of flow rotation or curvature, leads to stabilization through a progressive damping of the axial shear in the vortex core. We show that the efficiency of these stabilizing mechanisms depends on the swirl number, the ratio between the maximum tangential velocity and the axial velocity difference. If the swirl parameter is low enough, turbulence is able to reach the vortex periphery and a small circulation overshoot develops, leading to weak diffusion of angular momentum outward.

Two parallel Gaussian vortices of circulations Γ1 and Γ2 radii a1 and a2, separated by a distance b may become unstable by the elliptical instability due the elliptic deformation of their cores. The goal of the paper is to analyse this occurrence theoretically in a general framework. An explicit formula for the temporal growth rate of the elliptical instability in each vortex is obtained as a function of the above global parameters of the system, the Reynolds number Γ1/v and the non-dimensionalized axial wavenumber kzb of the perturbation. This formula is based on a known asymptotic expression for the local instability growth rate at an elliptical stagnation point which depends on the local characteristics of the elliptical flow and the inclination angle of the local perturbation wavevector at this point. The elliptical flow characteristics are estimated by considering each Gaussian vortex alone in a weak uniform external strain field whose properties are provided by a point vortex modelling of the vortex pair. The inclination angle is obtained from the dispersion relation for the Gaussian vortex normal modes and the local expression near each vortex centre for the two helical modes of azimuthal wavenumber m = 1 and m = −1 which constitute the elliptical instability global mode. Both the final formula and the hypotheses made for its derivation are tested and validated by direct numerical simulations and large-eddy simulations.

We consider the slow motion of viscous fluid completely filling a rectangular container. The motion is generated by the combined action of differential wall temperatures and the linear motion of the lid. If the relevant Reynolds and Péclet numbers and the lid speed are all small enough, the velocity field will be governed by an inhomogeneous biharmonic equation. In this approximation the temperature field, unaffected by the fluid motion, drives, at least in part, the fluid velocity field. Of interest here are the relative effects of buoyancy and lid motion. It is shown that the field, suitably scaled, depends on the dimensionless depth and lid speed alone. The mixed convection problem is solved for two pairs of wall heating protocols by sequentially solving, by an eigenfunction expansion method, up to four biharmonic problems. We present streamline patterns and quantitative data on the relative effects of lid motion on the buoyancy-driven fields in these containers.

The motion of a lamina of high aspect ratio suspended in a Newtonian fluid was studied experimentally and numerically. The damped oscillations for one rotational degree of freedom showed strong nonlinear fluid–structure interactions, mainly caused by the vortex structures forming at the lamina tips. The numerical results were obtained by a fully implicit Navier–Stokes solver, using partitioned coupling of the equations of motion of the fluid and suspended structure. Computations were carried out for different grid levels and time steps, providing information on the accuracy of the numerical results. For the fluid domain, a Langrangian–Eulerian finite-volume method was applied in order to solve the two-dimensional Navier–Stokes equation on grids moving with the oscillating lamina. The elastic motion of the lamina was computed as that of a torsion spring pendulum. The computed time traces of the angular position are in close agreement with corresponding experimental results. An equivalent empirical model which accounted for the fluid moments by empirical coefficients was much less successful in predicting the experimentally observed behaviour.

This paper presents a general two-dimensional model for rotating barotropic flows over topography. The model incorporates in a vorticity–stream function formulation both inviscid topography effects, associated with stretching and squeezing of fluid columns enforced by their motion over variable topography, and viscous effects, due to the Ekman boundary layer at the solid bottom. From the present formulation, conventional two-dimensional models can be recovered. The model is tested by means of laboratory experiments on homogeneous vortices encountering irregular topographies. The experimental observations are then compared with the corresponding numerical simulations based on the general model. The results suggest that such a formulation incorporates both inviscid and viscous topography effects correctly.

The process of nonlinear geostrophic adjustment in the presence of a boundary (i.e. in a half-plane bounded by a rigid wall) is examined in the framework of a rotating shallow water model, using an asymptotic multiple-time-scale theory based on the assumed smallness of the Rossby number ε. The spatial scale is of the order of the Rossby scale. Different initial states are considered: periodic, ‘step’-like, and localized. In all cases the initial perturbation is split in a unique way into slow and fast components evolving with characteristic time scales f−1 and (εf)−1, respectively. The slow component is not influenced by the fast one, at least for times t [les ] (fε)−1, and remains close to geostrophic balance. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance and Kelvin waves confined near the boundary.

The theory provides simple formulae allowing us to construct the initial profile of the Kelvin wave, given arbitrary initial conditions. With increasing time, the Kelvin wave profile gradually distorts due to nonlinear-wave self-interaction, the distortion being described by the equation of a simple wave. The presence of Kelvin waves does not prevent the fast–slow splitting, in spite of the fact that the frequency gap between the Kelvin waves and slow motion is absent. The possibility of such splitting is explained by the special structure of the Kelvin waves in each case considered.

The slow motion on time scales t [les ] (εf)−1 is governed by the well-known quasigeostrophic potential vorticity equation for the elevation. The theory provides an algorithm to determine initial slow and fast fields, and the boundary conditions to any order in ε. For the periodic and step-like initial conditions, the slow component behaves in the usual way, conserving mass, energy and enstrophy. In the case of a localized initial disturbance the total mass of the lowest-order slow component is not conserved, and conservation of the total mass is provided by the first-order slow correction and the Kelvin wave.

On longer time scales t [les ] (ε2f)−1 the slow motion obeys the so-called modified quasi-geostrophic potential vorticity (QGPV) equation. The theory provides initial and boundary conditions for this equation. This modified equation coincides exactly with the ‘improved’ QGPV equation, derived by Reznik, Zeitlin & Ben Jelloul (2001), in the step-like and localized cases. In the periodic case this equation contains an additional term due to the Kelvin-wave self-interaction, this term depending on the initial Kelvin wave profile.

The sound generated by a circular cylinder in a flow at low Mach numbers is investigated by direct solution of the two-dimensional unsteady compressible Navier–Stokes equations. Results show that sound pressure waves are generated primarily by vortex shedding from the cylinder surface into its wake. When a vortex is shed from one side of the cylinder, a negative pressure pulse is generated from that side whereas a positive pressure pulse is generated from the other side; alternate vortex shedding from the upper and lower sides of the cylinder produces negative and positive pulses alternately and thus produces sound pressure waves on both sides. The dipolar nature of the generated sound is confirmed; lift dipole dominates the sound field. The Doppler effect is shown to play an important role at finite Mach numbers. The direct solutions are also compared with the solutions obtained by Curle's acoustic analogy. The results show that Curle's solution describes well not only the generation mechanism of the sound but also the propagation process if we take the Doppler effect into consideration.

Laboratory experiments on the flow of negatively buoyant two-dimensional plumes adjacent to a wall in a density-stratified environment are described. The flow passes through several stages, from an inertial jet to a buoyant plume, to a neutrally buoyant jet, and then a negatively buoyant plume when it overshoots its equilibrium density. This fluid then ‘springs back’ and eventually occupies an intermediate range of heights. The flow is primarily characterized by the initial value of the buoyancy number, B0 = Q0N3/g′02, where Q0 is the initial volume flux per unit width, g′0 is the initial buoyancy and N is the buoyancy frequency of the environment. Scaled with the initial equilibrium depth D of the in flowing fluid, the maximum depth of penetration increases with B0, as does the width of the initial down flow, which is observed to increase very slowly with distance downward. Observations are made of the profiles of flow into and away from the plume as a function of height. Various properties of the flow are compared with predictions from the ‘standard’ two-dimensional entraining plume model, and this shows generally consistent agreement, although there are differences in magnitudes and in details. This flow constrasts with flows down gentle slopes into stratified environments, where two-way exchange of fluid occurs.

The stability of two-layer thermal convection in high-Prandtl-number fluids is investigated using laboratory experiments and marginal stability analysis. The two fluids have different densities and viscosities but there is no surface tension and chemical diffusion at the interface is so slow that it is negligible. The density stratification is stable. A wide range of viscosity and layer depth ratios is studied. The onset of convection can be either stationary or oscillatory depending on the buoyancy number B, the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly: when B is lower than a critical value (a function of the viscosity and layer depth ratios), the oscillatory regime develops, with a deformed interface and convective patterns oscillating over the whole tank depth; when B is larger than this critical value, the stratified regime develops, with a flat interface and layers convecting separately. Experiments agree well with the marginal stability results. At low Rayleigh number, characteristic time and length scales are well-predicted by the linear theory. At higher Rayleigh number, the linear theory still determines which convective regime will start first, using local values of the Rayleigh and buoyancy numbers, and which regime will persist, using global values of these parameters.

The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the physicomathematical model of a distribution of potential singularities and, in particular, the flow singularities at the ends of the wetted regions are represented by sinks. A conformal transformation of the flow field is adopted and the unknown intensities of the discontinuities are found by an optimization procedure, together with the solution of the nonlinear free-surface problem. The flow separation at a sideslip is also considered.

Experiments have been conducted to investigate turbulent mixing and the dynamics of outer fluid interfaces, i.e. the interfaces between mixed fluid and pure ambient fluid. A novel six-foot-diameter octagonal-tank flow facility was developed to enable the optical imaging of fluid interfaces above the mixing transition, corresponding to fully developed turbulence. Approximately 10003 whole-field three-dimensional space– time measurements of the concentration field were recorded using laser-induced- fluorescence digital-imaging techniques in turbulent jets at a Reynolds number of Re ∼ 20 000, Schmidt number of Sc ∼ 2000, and downstream distance of ∼ 500 nozzle diameters. Multiple large-scale regions of spatially nearly uniform-concentration fluid are evident in instantaneous visualizations, in agreement with previous findings above the mixing transition. The ensemble-averaged probability density function of concentration is found to exhibit linear dependence over a wide range of concentration thresholds. This can be accounted for in terms of the dynamics of large-scale well- mixed regions. Visualization of the three-dimensional space–time concentration field indicates that molecular mixing of entrained pure ambient fluid is dynamically initiated and accomplished in the vicinity of the unsteady large scales. Examination of the outer interfaces shows that they are dynamically confined primarily near the instantaneous large-scale boundaries of the flow. This behaviour is quantified in terms of the probability density of the location of the outer interfaces relative to the flow centreline and the probability of pure ambient fluid as a function of distance from the centreline. The current measurements show that the dynamics of outer interfaces above the mixing transition is significantly different from the behaviour below the transition, where previous studies have shown that unmixed ambient fluid can extend across a wide range of transverse locations in the flow interior. The present observations of dynamical confinement of the outer interfaces to the unsteady large scales, and considerations of entrainment, suggest that the mechanism responsible for this behaviour must be the coupling of large-scale flow dynamics with the presence of small-scale structures internal to the large-scale structures, above the mixing transition. The dynamics and structure of the outer interfaces across the entire range of space–time scales are quantified in terms of a distribution of generalized level-crossing scales. The outer-interface behaviour determines the mixing efficiency of the flow, i.e. fraction of mixed fluid. The present findings indicate that the large-scale dynamics of the outer interfaces above the mixing transition provides the dominant contribution to the mixing efficiency. This suggests a new way to quantify the mixing efficiency of turbulent flows at high Reynolds numbers.