Building upon the recent experimentally verified modelling of turbulent plumes which are subject to decreases in their source strength (Scase et al., J. Fluid Mech., vol. 563, 2006b, p. 443), we consider the complementary case where the plume's source strength is increased. We consider the effect of increasing the source strength of an established plume and we also compare time-dependent plume model predictions for the behaviour of a starting plume to those of Turner (J. Fluid Mech., vol. 13, 1962, p. 356).

Unlike the decreasing source strength problems considered previously, the relevant solution to the time-dependent plume equations is not a simple similarity solution. However, scaling laws are demonstrated which are shown to be applicable across a large number of orders of magnitude of source strength increase. It is shown that an established plume that is subjected to an increase in its source strength supports a self-similar ‘pulse’ structure propagating upwards. For a point source plume, in pure plume balance, subjected to an increase in the source buoyancy flux F0, the rise height of this pulse in terms of time t scales as t3/4 while the vertical extent of the pulse scales as t1/4. The volume of the pulse is shown to scale as t9/4. For plumes in pure plume balance that emanate from a distributed source it is shown that the same scaling laws apply far from the source, demonstrating an analogous convergence to pure plume balance as that which is well known in steady plumes. These scaling law predictions are compared to implicit large eddy simulations of the buoyancy increase problem and are shown to be in good agreement.

We also compare the predictions of the time-dependent model to a starting plume in the limit where the source buoyancy flux is discontinuously increased from zero. The conventional model for a starting plume is well approximated by a rising turbulent, entraining, buoyant vortex ring which is fed from below by a ‘steady’ plume. However, the time-dependent plume equations have been defined for top-hat profiles assuming only horizontal entrainment. Therefore, this system cannot model either the internal dynamics of the starting plume's head or the extra entrainment of ambient fluid into the head due to the turbulent boundary of the vortex ring-like cap. We show that the lack of entrainment of ambient fluid through the head of the starting plume means that the time-dependent plume equations overestimate the rise height of a starting plume with time. However, by modifying the entrainment coefficient appropriately, we see that realistic predictions consistent with experiment can be attained.

Stereoscopic three-component particle image velocimetry (3C-PIV) measurements have been made in a turbulent round jet to investigate the spatio-temporal correlations that are the origin of aerodynamic noise. Restricting attention to subsonic, isothermal jets, measurements were taken in a water flow experiment where, for the same Reynolds number and nozzle size, the shortest time scale of the dynamically important turbulent structures is more than an order of magnitude greater that in equivalent airflow experiments, greatly facilitating time-resolved PIV measurements. Results obtained (for a jet nozzle diameter and velocity of 40 mm and $1~\text{m}~\text{s}^{-1}$, giving $\mathit{Re}=4\times 10^{4}$) show that, on the basis of both single-point statistics and two-point quantities (correlation functions, integral length scales) the present incompressible flow data are in excellent agreement with published compressible, subsonic airflow measurements. The 3C-PIV data are first compared to higher-spatial-resolution 2C-PIV data and observed to be in good agreement, although some deterioration in quality for higher-order correlations caused by high-frequency noise in the 3C-PIV data is noted. A filter method to correct for this is proposed, based on proper orthogonal decomposition (POD) of the 3C-PIV data. The corrected data are then used to construct correlation maps at the second- and fourth-order level for all velocity components. The present data are in accordance with existing hot-wire measurements, but provide significantly more detailed information on correlation components than has previously been available. The measured relative magnitudes of various components of the two-point fourth-order turbulence correlation coefficient ($R_{ij,kl}$) – the fundamental building block for free shear flow aerodynamic noise sources – are presented and represent a valuable source of validation data for acoustic source modelling. The relationship between fourth-order and second-order velocity correlations is also examined, based on an assumption of a quasi-Gaussian nearly normal p.d.f. for the velocity fluctuations. The present results indicate that this approximation shows reasonable agreement for the measured relative magnitudes of several correlation components; however, areas of discrepancy are identified, indicating the need for work on alternative models such as the shell turbulence concept of Afsar (Eur. J. Mech. (B/Fluids), vol. 31, 2012, pp. 129–139).

A linear analysis of the free oscillations of captive drops or bubbles is discussed. The drop is surrounded by an immiscible liquid or gas and undergoes rotation as a rigid body in the presence of gravity. Using spectral analytical methods, we provide a general formulation for both elliptic and hyperbolic oscillation regimes of the frequency spectrum, for any combination of the Weber and Bond numbers. The method uses a Green function to reduce the inviscid Navier–Stokes equations and boundary conditions to an eigenvalue problem. Both the Green function and normal velocities at the interface are expanded in the orthogonal functional space generated by the Sturm–Liouville problem associated to the interface equation. The effect on the vibration modes of the density and geometrical parameters of the captive drop and surrounding medium is analysed. We present a complete analysis of the low-frequency spectra in the elliptic regime of a set of floating liquid zones and captive drops for a continuous range of Weber and Bond numbers. It is shown that, depending on the geometrical parameters of the system, the elliptic vibration spectrum presents a sui generis modal interaction for low wavenumbers and certain ranges of Weber number.

Flow around a high-speed rotating circular cylinder for $Re\leqslant 500$ is investigated numerically. The Reynolds number is defined as $UD/\unicode[STIX]{x1D708}$ with $U$, $D$ and $\unicode[STIX]{x1D708}$ being the free-stream flow velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. The aim of this study is to investigate the effect of a high rotation rate on the wake flow for a range of Reynolds numbers. Simulations are performed for Reynolds numbers of 100, 150, 200, 250 and 500 and a wide range of rotation rates from 1.6 to 6 with an increment of 0.2. Rotation rate is the ratio of the rotational speed of the cylinder surface to the incoming fluid velocity. A systematic study is performed to investigate the effect of rotation rate on the flow transition to different flow regimes. It is found that there is a transition from a two-dimensional vortex shedding mode to no vortex shedding mode when the rotation rate is increased beyond a critical value for Reynolds numbers between 100 and 200. Further increase in rotation rate results in a transition to three-dimensional flow which is characterized by the presence of finger-shaped (FV) vortices that elongate in the wake of the cylinder and very weak ring-shaped vortices (RV) that wrap the surface of the cylinder. The no vortex shedding mode is not observed at Reynolds numbers greater than or equal to 250 since the flow remains three-dimensional. As the rotation rate is increased further, the occurrence frequency and size of the ring-shaped vortices increases and the flow is dominated by RVs. The RVs become bigger in size and the flow becomes chaotic with increasing rotation rate. A detailed analysis of the flow structures shows that the vortices always exist in pairs and the strength of separated shear layers increases with the increase of rotation rate. A map of flow regimes on a plane of Reynolds number and rotation rate is presented.

In this paper the pressure field during the early development of turbulent vortex rings at two Reynolds numbers is determined using temporally resolved two-dimensional and stereoscopic particle image velocimetry (PIV). The pressure gradient terms are obtained by solving the incompressible Euler equation so that the drag coefficients of the vortex rings can be evaluated. Maxworthy (J. Fluid Mech., vol. 64, 1974, pp. 227–239) and Glezer & Coles (J. Fluid Mech., vol. 211, 1990, pp. 243–283) each developed models to describe the long-term physics of turbulent vortex rings: the former developed a semi-empirical model which permits loss of impulse via the shedding of vorticity into the wake whereas the latter developed a similarity model based on invariance of the hydrodynamic impulse. Maxworthy’s model implies that a significant correction to the similarity solution is required to account for the drag on the vortex ring bubble. We show that during the early development of the turbulent vortex rings the drag is very small and the similarity scaling can basically be retained.

The effects of spanwise rotation on the channel flow across a symmetric sudden expansion are investigated using direct numerical simulation. Four rotation regimes are considered with the same Reynolds number $\mathit{Re}=5000$ and expansion ratio $\mathit{Er}=3/2$. Upstream from the expansion, inflow turbulent conditions are generated realistically for each rotation rate through a very simple and efficient technique of recycling without the need for any precursor calculation. As the rotation is increased, the flow becomes progressively asymmetric with stabilization (destabilization) effects on the cyclonic (anticyclonic) side, respectively. These rotation effects, already present in the upstream channel, lead further downstream to an increase (reduction) of the separation size behind the cyclonic (anticyclonic) step. In the cyclonic separation, the free-shear layer created behind the step corner leads to the formation of large-scale spanwise vortices that become increasingly two-dimensional as the rotation is increased. Conversely, in the anticyclonic region, the turbulent structures in the separated layer are more elongated in the streamwise direction and also more active in promoting reattachment. For the highest rotation rate, a secondary separation is observed further downstream in the anticyclonic region, leading to the establishment of an elongated recirculation bubble that deflects the main flow towards the cyclonic wall. The highest level of turbulent kinetic energy is obtained at high rotation near the cyclonic reattachment in a region where stabilization effects are expected. The phenomenological model of absolute vortex stretching is found to be useful in understanding how the rotation influences the dynamics in the various regions of the flow.

Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.

Non-ideal gases refer to deformable substances in which the speed of sound can decrease following an isentropic compression. This may occur near a phase transition such as the liquid–vapour critical point due to long-range molecular interactions. Isentropes can then become locally concave in the pressure/specific-volume phase diagram (e.g. Bethe–Zel’dovich–Thompson (BZT) gases). Following the pioneering work of Bethe (Tech. Rep. 545, Office of Scientific Research and Development, 1942) on shocks in non-ideal gases, this paper explores the refraction properties of stable compression shocks in non-reacting but arbitrary substances featuring a positive isobaric volume expansivity. A small-perturbation analysis is carried out to obtain analytical expressions for the thermo-acoustic properties of the refracted field normal to the shock front. Three new regimes are discovered: (i) an extensive but selective (in upstream Mach numbers) amplification of the entropy mode (hundreds of times larger than those of a corresponding ideal gas); (ii) discontinuous (in upstream Mach numbers) refraction properties following the appearance of non-admissible portions of the shock adiabats; (iii) the emergence of a phase shift for the generated acoustic modes and therefore the existence of conditions for which the perturbed shock does not produce any acoustic field (i.e. ‘quiet’ shocks, to contrast with the spontaneous D’yakov–Kontorovich acoustic emission expected in 2D or 3D). In the context of multidimensional flows, and compressible turbulence in particular, these results demonstrate a variety of pathways by which a supplied amount of energy (in the form of an entropy, vortical or acoustic mode) can be redistributed in the form of other entropy, acoustic and vortical modes in a manner that is simply not achievable in ideal gases. These findings are relevant for turbines and compressors operating close to the liquid–vapour critical point (e.g. organic Rankine cycle expanders, supercritical $\text{CO}_{2}$ compressors), astrophysical flows modelled as continuum media with exotic equations of state (e.g. the early Universe) or Bose–Einstein condensates with small but finite temperature effects.

Using high-resolution particle image velocimetry, we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor–Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\times 10^{9}$. The extracted angular velocity profiles follow a log law more closely than the azimuthal velocity profiles due to the strong curvature of this ${\it\eta}=0.5$ set-up. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted $3/7$ scaling for the classical turbulent regime, which is much more pronounced than for the well-explored ${\it\eta}=0.71$ case, for which the ultimate regime sets in at much lower Taylor number. By measuring at varying axial positions, roll structures are found for counter-rotation while no clear coherent structures are seen for pure inner cylinder rotation. In addition, turbulent plumes coming from the inner and outer cylinders are investigated. For pure inner cylinder rotation, the plumes in the radial velocity move away from the inner cylinder, while the plumes in the azimuthal velocity mainly move away from the outer cylinder. For counter-rotation, the mean radial flow in the roll structures strongly affects the direction and intensity of the turbulent plumes. Furthermore, it is experimentally confirmed that, in regions where plumes are emitted, boundary layer profiles with a logarithmic signature are created.

The linear instability mechanisms of horizontal convection in a rectangular cavity forced by a horizontal buoyancy gradient along its surface are investigated using local and global stability analyses for a Prandtl number equal to unity. The results show that the stability of the base flow, a steady circulation characterized by a narrow descending plume and a broad upwelling region, depends on the Rayleigh number, $Ra$. For free-slip boundary conditions at a critical value of $Ra\approx 2\times 10^{7}$, the steady base flow becomes unstable to three-dimensional perturbations, characterized by counter-rotating vortices originating within the plume region. A Wentzel–Kramers–Brillouin (WKB) method applied along closed streamlines demonstrates that this instability is of a Rayleigh–Taylor type and can be used to accurately reconstruct the global instability mode. In the case of no-slip boundary conditions, the base flow also becomes unstable to a self-sustained two-dimensional instability whose critical Rayleigh number is $Ra\approx 1.7\times 10^{8}$. Beyond this critical $Ra$, two-dimensional equilibrium stationary states of the Navier–Stokes equations are computed using the selective frequency damping method. The two-dimensional onset of instability is shown to be characterized by a family of modes also originating within the plume. A local spatio-temporal stability analysis shows that the flow becomes absolutely unstable at the origin of the plume. Taken together, these results illustrate the mechanisms behind the onset of turbulence that has been observed in horizontal convection.

Motivated by the reopening mechanics of strongly collapsed airways, we study the steady propagation of an air finger through a collapsed oil-filled channel with a single compliant wall. In a previous study using fully compliant elastic tubes, a ‘pointed’ air finger was found to propagate at high speed and low pressure, which, if clinically accessible, offers the potential for rapid reopening of highly collapsed airways with minimal tissue damage (Heap & Juel Phys. Fluids, vol. 20 (8), 2008, 081702). The mechanism underlying the selection of that pointed finger, however, remained unexplained. In this paper, we identify the required selection mechanism by conducting an experimental study in a simpler geometry: a rigid rectangular Hele-Shaw channel with an elastic top boundary. The constitutive behaviour of this elasto-rigid channel is nonlinear and broadly similar to that of an elastic tube, but unlike the tube, the channel’s cross-section adopts self-similar shapes from the undeformed state to the point of first near wall contact. The ensuing simplification of the vessel geometry enables the systematic investigation of the reopening dynamics in terms of increasing initial collapse. We find that for low levels of initial collapse, a single centred symmetric finger propagates in the channel and its shape is set by the tip curvature. As the level of collapse increases, the channel cross-section develops a central region of near opposite wall contact, and the finger shape evolves smoothly towards a ‘flat-tipped’ finger whose geometry is set by the strong depth gradient near the channel walls. We show that the flat-tipped mode of reopening is analogous to the pointed finger observed in tubes. Its propagation is sustained by the vessel’s extreme cross-sectional profile at high collapse, while vessel compliance is necessary to stabilise it. A simple scaling argument based on the dissipated power reveals that this reopening mode is preferred at higher propagation speeds when it becomes favourable to displace the elastic channel wall rather than the viscous fluid.

In this study, the Bragg–Hawthorne equation (BHE) is extended in the context of a steady, inviscid and compressible fluid, thus leading to an assortment of partial differential equations that must be solved simultaneously. A solution is pursued by implementing a Rayleigh–Janzen expansion in the square of the reference Mach number. The corresponding formulation is subsequently used to derive a compressible approximation for the Trkalian model of the bidirectional vortex. The approximate solution is compared to a representative computational fluid dynamics simulation in order to validate the modelling assumptions under realistic conditions. The latter is found to exhibit an appreciable steepening of the axial velocity profile, which is accompanied by an axial dependence in the mantle location that is somewhat reminiscent of the radial shifting of mantles reported in some experimental trials and simulations. In this context, flows with a strong swirl intensity do not seem to be significantly affected by the introduction of compressibility. Rather, as the swirl intensity is reduced the effects of compressibility become more noticeable, especially in the axial and radial velocity components. It may also be realized that imparting a progressively larger swirl component stands to promote the axisymmetric distribution of flow field properties, and these include an implicit resistance to dilatational effects in the tangential direction. From a broader perspective, this study provides a viable approximation to the Trkalian motion associated with cyclonic flows, while serving as a limited proof of concept for the compressible Bragg–Hawthorne procedure applied to a steady, axisymmetric and inviscid fluid.

In the ocean, stratification and rotation allow for the existence of inertia–gravity waves. Instabilities of these waves, such as triadic resonant instability (TRI), may play a key role in the mixing process of the deep ocean. In an experimental set-up, we generate inertia–gravity waves which may become unstable depending on the background rotation and wave frequency. The instability produces secondary waves that match the spatial and temporal resonance conditions of TRI. The effect of rotation is introduced in a pre-existing theory and results in a prediction of the growth rate of TRI in the case of an infinite plane wave. The issue of finite size of the beam is then addressed using a simple model in which we show that the instability is enhanced in a given range of Coriolis parameter. Finally, we compare the experimental threshold of the instability with the model, and find good agreement except at higher rotation rate. At constant primary wave frequency, we analyse the evolution of the secondary wave characteristics with rotation. The appearance of unexpected sub-inertial secondary waves may be related to the discrepancy observed between predicted and experimental thresholds at higher rotation.

High-speed free-shear-flow turbulence, laden with droplets or particles, can radiate weaker pressure fluctuations than its unladen counterpart. In this study, Eulerian–Lagrangian simulations of high-speed temporally evolving shear layers laden with monodisperse, adiabatic, inertial particles are used to examine particle–turbulence interactions and their effect on radiated pressure fluctuations. An evolution equation for gas-phase pressure intensity is formulated for particle-laden flows, and local mechanisms of pressure changes are quantified over a range of Mach numbers and particle mass loadings. Particle–turbulence interactions alter the local pressure intensity directly via volume displacement (due to the flow of finite-size particles) and drag coupling (due to local slip velocity between phases), and indirectly through significant turbulence changes. The sound radiation intensity near subsonic mixing layers increases with mass loading, consistent with existing low Mach number theory. For supersonic flows, sound levels decrease with mass loading, consistent with trends observed in previous experiments. Particle-laden cases exhibit reduced turbulent kinetic energy compared to single-phase flow, providing one source of their sound changes; however, the subsonic flow does not support such an obvious source-to-sound decomposition to explain its sound intensity increase. Despite its decrease in turbulence intensity, the louder particle-laden subsonic flows show an increase in the magnitude and time-rate-of-change of fluid dilatation, providing a mechanism for its increased sound radiation. Contrasting this, the quieter supersonic particle-laden flows exhibit decreased gas-phase dilatation yet its time-rate-of-change is relatively insensitive to mass loading, supporting such a connection.