Bubble interaction with turbulence has a number of applications in engineering processes and nature. The complex interplay between the vortical structures present in a turbulent flow and the bubbles drives their deformation dynamics, which may lead to bubble rupture under the appropriate conditions. Such a process includes nonlinear interaction among the turbulent eddies and between the eddies and the bubbles. Thus, the coupled evolution of a single vortex ring with a bubble represents an idealized scenario that can provide a framework to shed light on understanding such a common and complex mechanism. Jha & Govardhan (J. Fluid Mech., vol. 773, 2015, pp. 460–497) have performed elegant experiments generating controlled vortex rings and injecting bubbles of known volume. They have reported interesting results on the elongation process of the bubble and its impact on vortex dynamics.

In stably stratified and rotating fluids, an axisymmetric columnar vortex can be unstable to a special instability with an azimuthal wavenumber $m=1$ which bends and slices the vortex into pancake vortices (Gent & McWilliams Geophys. Astrophys. Fluid Dyn., vol. 35 (1–4), 1986, pp. 209–233). This bending instability, called the ‘Gent–McWilliams instability’ herein, is distinct from the shear, centrifugal or radiative instabilities. The goals of the paper are to better understand the origin and properties of this instability and to explain why it operates only in stratified rotating fluids. Both numerical and asymptotic stability analyses of several velocity profiles have been performed for wide ranges of Froude number $\mathit{Fr}_{h}={\it\Omega}_{0}/N$ and Rossby number $\mathit{Ro}=2{\it\Omega}_{0}/f$, where ${\it\Omega}_{0}$ is the angular velocity on the vortex axis, $N$ the Brunt–Väisälä frequency and $f$ the Coriolis parameter. Numerical analyses restricted to the centrifugally stable range show that the maximum growth rate of the Gent–McWilliams instability increases with $\mathit{Ro}$ and is independent of $\mathit{Fr}_{h}$ for $\mathit{Fr}_{h}\leqslant 1$. In contrast, when $\mathit{Fr}_{h}>1$, the maximum growth rate decreases dramatically with $\mathit{Fr}_{h}$. Long axial wavelength asymptotic analyses for isolated vortices prove that the Gent–McWilliams instability is due to the destabilization of the long-wavelength bending mode by a critical layer at the radius $r_{c}$ where the angular velocity ${\it\Omega}$ is equal to the frequency ${\it\omega}$: ${\it\Omega}(r_{c})={\it\omega}$. A necessary and sufficient instability condition valid for long wavelengths, finite Rossby number and $\mathit{Fr}_{h}\leqslant 1$ is that the derivative of the vertical vorticity of the basic vortex is positive at $r_{c}$: ${\it\zeta}^{\prime }(r_{c})>0$. Such a critical layer $r_{c}$ exists for finite Rossby and Froude numbers because the real part of the frequency of the long-wavelength bending mode is positive instead of being negative as in a homogeneous non-rotating fluid ($\mathit{Ro}=\mathit{Fr}_{h}=\infty$). When $\mathit{Fr}_{h}>1$, the instability condition ${\it\zeta}^{\prime }(r_{c})>0$ is necessary but not sufficient because the destabilizing effect of the critical layer $r_{c}$ is strongly reduced by a second stabilizing critical layer $r_{c2}$ existing at the radius where the angular velocity is equal to the Brunt–Väisälä frequency. For non-isolated vortices, numerical results show that only finite axial wavenumbers are unstable to the Gent–McWilliams instability.

The hydrodynamic oscillations of a cyclone separator – in particular the precessing vortex core (PVC) phenomena – are investigated by measuring their radiated sound spectra. Strong coherence was observed between internal flow oscillations measured via hot wire anemometry and the external acoustic field measured via microphone. This means that the oscillations can be characterised by using acoustics as a proxy. The oscillations cause narrow-band noise, referred to as cyclone hum. System characterisation by dimensional analysis used velocity and length scales of the vortex core region as scaling parameters. The relevant non-dimensional parameters are a Strouhal number for the cyclone hum centre frequency, a Reynolds number, a geometry based swirl number and numerous geometric scales defining the shape of the device. Cyclones with multiple sizes of inlets and outlets were tested at different flow rates using external microphones to detect the cyclone hum. The results produce an excellent collapse of the data, yielding a simple relationship for Strouhal number as a function of swirl number and the outlet diameter ratio. The non-invasive method of examining oscillations that is presented in this paper could be applied to other swirling systems.

The statistics of the velocity gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by $\unicode[STIX]{x1D63C}$. Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the $Q$ field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.

This article contains numerical and theoretical results on the circular and polygonal hydraulic jumps in the framework of inertial lubrication theory. The free surface and velocity fields are computed along with cross-sections of the vorticity and pressure, in agreement with experimental data. The forces that drive and resist the instability are identified with the radial shear force, the azimuthal surface tension and the hydrostatic azimuthal force, in addition to a nonlinear term in the radial coordinate. Periodic solutions are obtained from the first orders of a perturbation theory by considering azimuthal symmetries. The thresholds of the instability are defined at closed jumps for discontinuous solutions and at one-sided hydraulic jumps for continuous curves that conserve fluid mass density.

The active flapping motions of fish and cetaceans generate both propulsive and manoeuvring forces. The tail fin motions of the majority of fish can essentially be viewed as a combined pitch-and-heave motion. Downstream bodies are strongly influenced by the vortices shed from an upstream body. To investigate the interactions between flexible bodies and vortices, the present study examined tandem flexible flags in a viscous flow by using an improved version of the immersed boundary method. The upstream flag underwent passive flapping in a uniform flow while the downstream flag flapped according to a prescribed pitching and heaving motion of the leading edge. The influences of the active flapping motion on the system dynamics were examined in detail, including the frequency, the phase angle, the bending coefficient and the amplitudes of the pitching and heaving motion. The variation of the drag coefficient of the downstream flag was explored together with the instantaneous vorticity contours and the body shapes. Both the slalom mode and the interception mode were identified according to the vortex–flexible body interactions, corresponding to the low- and high-drag situations, respectively. The underlying mechanism was discussed and compared with previous studies.

A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three time scales that respectively characterize the convective time scale, the large-scale magnetic evolution time scale and the large-scale thermal evolution time scale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large scale. For the order one magnetic Prandtl number model, the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the horizontal boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress & Soward (Phys. Rev. Lett., vol. 29, 1972, pp. 837–839), and provide a new theoretical framework for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.

The subject of this experimental study is the feedback effects due to tonal noise emission in a laminar separation bubble (LSB) formed on the suction side of an airfoil in low Reynolds number flows. Experiments were performed on a NACA 0012 airfoil for a range of chord-based Reynolds numbers $0.65\times 10^{5}\leqslant \mathit{Re}_{c}\leqslant 4.5\times 10^{5}$ at angle of attack ${\it\alpha}=2^{\circ }$, where laminar boundary layer separation is encountered on both sides of the airfoil. Simultaneous time-resolved, two-component particle image velocimetry (PIV) measurements, unsteady surface pressure and far-field acoustic pressure measurements were employed to characterize flow development and acoustic emissions. Amplification of disturbances in separated shear layers on both the suction and pressure sides of the airfoil leads to shear layer roll-up and shedding of vortices from separation bubbles. When the vortices do not break up upstream of the trailing edge, the passage of these structures over the trailing edge generates tonal noise. Acoustic feedback between the trailing edge noise source and the upstream separation bubble narrows the frequency band of amplified disturbances, effectively locking onto a particular frequency. Acoustic excitation further results in notable changes to the overall separation bubble characteristics. Roll-up vortices forming on the pressure side, where the bubble is located closer to the trailing edge, are shown to define the characteristic frequency of pressure fluctuations, thereby affecting the disturbance spectrum on the suction side. However, when the bubble on the pressure side is suppressed via boundary layer tripping, a weaker feedback effect is also observed on the suction side. The results give a detailed quantitative description of the observed phenomenon and provide a new outlook on the role of coherent structures in separation bubble dynamics and trailing edge noise generation.

The direct numerical simulation of an accelerating boundary layer over a rough wall has been carried out to investigate the coupling between the effects of roughness and strong free-stream acceleration. While the favourable pressure gradient is sufficient to achieve quasi-laminarization on a smooth wall, the flow reversion is prevented on a rough wall, and a higher friction coefficient, a faster increase of turbulence intensity compared to the free-stream velocity and more isotropic turbulence near the wall are observed. The logarithmic region of the mean-velocity profile presents an initial decrease in slope as in the smooth case, but soon recovers, as the fully rough regime is reached and a new overlap region is established. A strong coupling between the roughness and acceleration effects develops as roughness leads to more responsive turbulence and prevents the strong acceleration from stabilizing the turbulence, and the acceleration intensifies the velocity scale of the wake field (i.e. the near-wall spatial heterogeneity of the time-averaged velocity distribution). The combined effect is a ‘rougher’ surface as the flow accelerates. In addition, the link between the local values of the free stream and the near-wall velocity depends on the flow history; this explains the different flow responses observed in previous studies, in terms of friction coefficient, turbulent kinetic energy and Reynolds-stress anisotropy. This study elucidates the near-wall flow dynamics, which may be used to explain other non-canonical flows over rough walls.

Scaling of grid turbulence with a constant mean cross-stream temperature gradient is investigated using a combination of theoretical predictions and experimental data. A novel nanoscale temperature probe (T-NSTAP) was used to acquire temperature data. Conditions for self-similarity of the governing equations and the scalar spectrum are investigated, which reveals necessary conditions for the existence of a self-similar solution. These conditions provide a theoretical framework for scaling of the temperature spectrum as well as the temperature flux spectrum. One necessary condition, predicted by the theory, is that the characteristic length scale describing the scalar spectrum must vary as $\sqrt{t}$ in the case of a zero virtual origin for a self-similar solution to exist. As predicted by the similarity analysis, the data show the variance growing as a power law with streamwise position. When scaled with the similarity variable, as found through the theoretical analysis, the temperature spectra show a good collapse over all wavenumbers. A new method to determine the quality of the scaling was developed, comparing the coefficient of variation. The minimum coefficient of variation, and thus the best scaling, for the measured spectra agrees well with the similarity requirements. The theoretical work also reveals an additional requirement related to the scaling of the scalar flux spectrum.

We have investigated the properties of transverse sonic hydrogen jets in high-temperature supersonic crossflow at jet-to-crossflow momentum flux ratios $J$ between 0.3 and 5.0. The crossflow was held fixed at a Mach number of 2.4, 1400 K and 40 kPa. Schlieren and $\text{OH}^{\ast }$ chemiluminescence imaging were used to investigate the global flame structure, penetration and ignition points; $\text{OH}$ planar laser-induced fluorescence imaging over several planes was used to investigate the instantaneous reaction zone. It is found that $J$ indirectly controls many of the combustion processes. Two regimes for low (${<}1$) and high (${>}3$) $J$ are identified. At low $J$, the flame is lifted and stabilizes in the wake close to the wall possibly by autoignition after some partial premixing occurs; most of the heat release occurs at the wall in regions where $\text{OH}$ occurs over broad regions. At high $J$, the flame is anchored at the upstream recirculation region and remains attached to the wall within the boundary layer where $\text{OH}$ remains distributed over broad regions; a strong reacting shear layer exists where the flame is organized in thin layers. Stabilization occurs in the upstream recirculation region that forms as a consequence of the strong interaction between the bow shock, the jet and the boundary layer. In general, this interaction – which indirectly depends on $J$ because it controls the jet penetration – dominates the fluid dynamic processes and thus stabilization. As a result, the flow field may be characterized by a flame structure characteristic of multiple interacting combustion regimes, from (non-premixed) flamelets to (partially premixed) distributed reaction zones, thus requiring a description based on a multi-regime combustion formulation.

This paper presents spatially averaged temperature equations for modelling macro-scale heat transfer in periodic solid structures such as fin and tube arrays. The governing equations for the periodically developed heat transfer regime in isothermal solids are derived. It is shown that the appropriate macro-scale temperature in the periodically developed heat transfer regime is obtained by averaging the temperature with a specific weighting function which is adapted to the temperature decay rate. This matched weighting function allows the representation of the macro-scale interfacial heat transfer and thermal dispersion source by means of a spatially constant interfacial heat transfer coefficient and thermal dispersion vector, which both can be calculated from the periodic rescaled temperature on a unit cell of the solid structures. Moreover, it is proved that for small temperature decay rates, the matched weighting function yields the same macro-scale description as repeated volume averaging. The theoretical framework of this paper is applied to a case study, describing the heat transfer between a fluid and an array of solid cylinders at constant temperature.

Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly of bubbles is also analysed. The solutions are given by a conformal mapping from a multiply connected circular domain in an auxiliary complex plane to the fluid region exterior to the bubbles. In all cases the desired mapping is written explicitly in terms of certain special transcendental functions, known as the secondary Schottky–Klein prime functions. Taken together, the solutions reported here represent the complete set of solutions for steady bubbles and fingers in a horizontal Hele-Shaw channel when surface tension is neglected. All previous solutions under these assumptions are particular cases of the general solutions reported here. Other possible applications of the formalism described here are also discussed.

‘Preferential concentration’ (Squires & Eaton, Phys. Fluids, vol. A3, 1991, pp. 1169–1178) refers to the clustering of inertial particles in the high strain, low-rotation regions of turbulence. The ‘centrifuge mechanism’ of Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) appears to explain this phenomenon. In a recent paper, Bragg & Collins (New J. Phys., vol. 16, 2014, 055013) showed that the centrifuge mechanism is dominant only in the regime $St\ll 1$, where $St$ is the Stokes number based on the Kolmogorov time scale. Outside this regime, the centrifuge mechanism gives way to a non-local, path history symmetry breaking mechanism. However, despite the change in the clustering mechanism, the instantaneous particle positions continue to correlate with high strain, low-rotation regions of the turbulence. In this paper, we analyse the exact equation governing the radial distribution function and show how the non-local clustering mechanism is influenced by, but not dependent upon, the preferential sampling of the fluid velocity gradient tensor along the particle path histories in such a way as to generate a bias for clustering in high strain regions of the turbulence. We also show how the non-local mechanism still generates clustering, but without preferential concentration, in the limit where the time scales of the fluid velocity gradient tensor measured along the inertial particle trajectories approaches zero (such as white noise flows or for particles in turbulence settling under strong gravity). Finally, we use data from a direct numerical simulation of inertial particles suspended in Navier–Stokes turbulence to validate the arguments presented in this study.

The temporal and spatiotemporal stability of thermal plumes is investigated for laminar velocity and temperature profiles, under the Boussinesq approximation, in the far self-similar region as well as in the region close to a finite-size inlet. In the self-similar case, Prandtl and Grashof numbers are systematically varied, and azimuthal wavenumbers $m=0$, 1 and 2 are considered. In the temporal analysis, helical modes of $m=1$ are found to be dominant throughout the unstable parameter space, with few exceptions. Axisymmetric modes typically present smaller growth rates, but they may dominate at very low Prandtl and Grashof numbers. Double-helical modes of $m=2$ are unstable over a very restricted range of parameters. Only the helical $m=1$ mode is found to ever become absolutely unstable, whereas $m=0$ and $m=2$ modes are at most convectively unstable. In a temporal setting, an analysis of the perturbation energy growth identifies buoyancy- and shear-related mechanisms as the two potentially destabilizing flow ingredients. Buoyancy is demonstrated to be important at low Grashof numbers and long wavelengths, whereas classical shear mechanisms are dominant at high Grashof numbers and shorter wavelengths. The physical mechanism of destabilization through the effect of buoyancy is investigated, and an interpretation is proposed. In the near-source region, both axisymmetric and helical modes may be unstable in a temporal sense over a significant range of wavenumbers. However, absolute instability is again only found for helical $m=1$ modes.

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

The influence of viscosity contrast on buoyantly unstable miscible fluids in a porous medium is investigated through a linear stability analysis (LSA) as well as direct numerical simulations (DNS). The linear stability method implemented in this paper is based on an initial value approach, which helps to capture the onset of instability more accurately than the quasi-steady-state analysis. In the absence of displacement, we show that viscosity contrast delays the onset of instability in buoyantly unstable miscible fluids. Further, it is observed that by suitably choosing the viscosity contrast and injection velocity a gravitationally unstable miscible interface can be stabilized completely. Through LSA we draw a phase diagram, which shows three distinct stability regions in a parameter space spanned by the displacement velocity and the viscosity contrast. DNS are performed corresponding to parameters from each regime and the results obtained are in accordance with the linear stability results. Moreover, the conversion from one dimensionless formulation to another and its importance when comparing the different type of flow problem associated with each dimensionless formulation are discussed. We also calculate ${\it\epsilon}$-pseudo-spectra of the time dependent linearized operator to investigate the response to external excitation.

Tonal noise generated by airfoils at low to moderate Reynolds number is relevant for applications in, for example, small-scale wind turbines, fans and unmanned aerial vehicles. Coherent and convected vortical structures scattering at the trailing edge from the pressure or suction sides of the airfoil have been identified to be responsible for such tonal noise generation. Controversy remains on the respective significance of pressure- and suction-side events, along with their interaction for tonal noise generation. The present study surveys the regimes of tonal noise generation for low to moderate chord-based Reynolds number between $\mathit{Re}_{c}=0.3\times 10^{5}$ and $2.3\times 10^{5}$ and effective angle of attack between $0^{\circ }$ and $6.3^{\circ }$ for the NACA 0012 airfoil profile. Extensive acoustic measurements with smooth surface and with transition to turbulence forced by boundary layer tripping are presented. Results show that, at non-zero angle of attack, tonal noise generation is dominated by suction-side events at low Reynolds number and by pressure-side events at high Reynolds number. At smaller angle of attack, interaction between events on the two sides becomes increasingly important. Particle image velocimetry measurements complete the information on the flow field structure in the source region around the trailing edge. The influences of both angle of attack and Reynolds number on tonal noise generation are explained by changes in the mean flow topology, namely the presence and location of reverse flow regions on the two sides. Data gathered from experimental and numerical studies in the literature are reviewed and interpreted in view of the different regimes.

Stratified cocurrent flow of air and water was studied experimentally in a 5 cm diameter horizontal pipe. The velocity in the liquid phase was measured using planar particle image velocimetry, and the instantaneous interfacial profile was recorded using a separate camera. The resulting velocity fields extended from the pipe wall to the wavy interface. The principal aims of the study were to investigate the laminar–turbulent transition of the liquid phase in stratified gas–liquid flow, and to explore the interaction between the transition process and the interfacial waves. The boundaries of transition were determined in both the smooth and the wavy region. The occurrence of waves had the effect of increasing the Reynolds numbers at the end of transition. On the other hand, the transition to turbulence caused a change from the ‘2D small-amplitude’ to the ‘3D small-amplitude’ wave pattern, which were seen to correspond to the capillary–gravity and gravity–capillary solutions of the dispersion relationship respectively. In light of this, the flowmap of the wavy region was recast into Weber number–Froude number coordinates, which provided a physical interpretation of the interaction between the developing turbulence and the changing wave patterns.

Results are presented from a numerical and analytical study of negatively buoyant thermals. The numerical study consists of large-eddy simulations of thermal descent and spread. The thermals are initiated by a spherical perturbation in the homogeneous background potential temperature. Simulations covering various release heights, thermal radii and thermal buoyancies are carried out. The analysis involves matching similarity models of a thermal and an axisymmetric gravity current, hence describing the flow evolution in terms of the initial conditions and flow coefficients only. The simulations demonstrate that the flow transition through the impingement region is relatively smooth, the main flow adjustment being in the initial post-release phase of the thermal. Comparison of the simulations and the model enables determination of the coefficients, and validation of the similarity approach to predict the radial speed, reduced gravity and depth of the spreading flow on the ground. The predictions of reduced gravity and depth also depend on quantification of the increase in gravity-current volume due to entrainment, which is obtained from the simulations.