We calculate analytically the self-similar Stokes flow driven by an externally applied electric field in a multiple coaxial Taylor cone consisting of an arbitrary number of immiscible leaky-dielectric or dielectric fluids. The proposed conical solutions open new avenues for innovative technological applications, some of which are briefly discussed.

Direct numerical simulations (DNS) were carried out to investigate laminar-turbulent transition for a blunt (right) cone ($7^\circ$ half-angle) at Mach 5.9 and zero angle of attack. First, (linear) stability calculations were carried out by employing a high-order Navier–Stokes solver and using very small disturbance amplitudes in order to capture the linear disturbance development. Contrary to standard linear stability theory (LST) results, these investigations revealed a strong ‘linear’ instability in the entropy-layer region for a very short downstream distance for oblique disturbance waves with spatial growth rates far exceeding those of second-mode disturbances. This linear instability behaviour was not captured with conventional LST and/or the parabolized stability equations (PSE). Secondly, a nonlinear breakdown simulation was performed using high-fidelity DNS. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and complete laminar-turbulent transition in the entropy layer just upstream of the second-mode instability region.

The application of cavitation-induced shock waves generated at low driving frequencies, known as power ultrasound, is essential for a wide range of fields, such as sonochemistry, lithotripsy, nanomaterials, emulsions and casting, to name but a few. In this paper, we present measurements of the shock wave pressures emitted by cavitating bubbles in water, under ultrasonic excitation produced by an immersed probe oscillating at 24 kHz. A broad-spectrum fibre-optic hydrophone calibrated in the range of 1–30 MHz was used for this purpose. Spectral analysis of the data reveals a consistent resonance peak at a very narrow range of frequencies (3.27–3.43 MHz). Results were confirmed using real-time analysis of high-speed recordings. By eliminating other possible sources, we propose that this new peak might be associated with shock wave emissions from collapsing bubbles. Spatial maps obtained by collating individual shock wave pressures highlight the effect of pressure shielding with increasing input power, attributed to a cloud of bubbles surrounding the probe. This work contributes towards the elucidation of the key properties of cavitation-driven shock waves and the underlying mechanisms, essential in controlling the effectiveness of the external processing conditions on various physical, chemical and biological systems.

Instability and transition in the boundary layer on a slender cone ($60^{\circ }$ apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Görtler number. The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi (J. Fluid Mech., vol. 127, 1983, pp. 353–364) and considered as being due to a centrifugal instability.

We present experimentally obtained time-averaged vertical temperature profiles $\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio $\varGamma \equiv L:W:H = 10:1:1$ ($L$, $W$ and $H$ are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range $2 \times 10^{10} \lesssim {Ra} \lesssim 9 \times 10^{12}$. The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form $\theta (z/\lambda _c)$ with $\lambda _c$ being a $Ra$-dependent thickness of the cold thermal boundary layer (BL). The $\theta (z/\lambda _c)$-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the $\theta$ profiles scale with the hot thermal BL thickness $\lambda _h$, while in the upper layer, they again scale with $\lambda _c$. Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.

Liquid-infused surfaces (LISs) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid–liquid surface tension is small and/or grooves are wide, we observe travelling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves induce a roughness effect that increases drag. The generation mechanism of these waves is explained using the theory developed by Miles for gravity waves. Energy is transferred from the turbulent flow to the LIS provided that there is a negative curvature of the mean flow at the critical layer. Given the groove width, the Weber number and an estimate of the friction Reynolds number, we provide relations to determine whether a LIS behaves as a smooth or rough surface in a turbulent flow.

New analytical solutions for the one-dimensional steady-state compressible viscous adiabatic flow of an ideal gas through a conical nozzle or diffuser have been obtained. In order to analytically solve the problem, it is essential to determine the correct transformations of the variables and to identify the kinetic energy per unit of mass as the physical variable that appears in the final Abel ordinary differential equation.

A dimensionless representation is given of the new solution, which points out the fundamental role exerted by some dimensionless groups in problems where viscous power dissipation and variable flow areas are present simultaneously as driving factors of flow changes. Furthermore, a steady-state fluid dynamics analysis of the compressible viscous flows in conical nozzles and diffusers has been carried out to improve the physical interpretation of the solutions.

Finally, the thus determined analytical solutions have been validated for both subsonic and supersonic flows through a comparison with numerical solutions pertaining to the same ordinary differential equation. However, when the exact solution includes shocks, the time-asymptotic numerical solutions of the Euler equations for the quasi-one-dimensional unsteady-state gas dynamics are used for validation and the discretisation is performed by applying a finite volume technique.

The proposed analytical solutions are complementary to the Fanno and nozzle models that refer to a viscous adiabatic constant cross-section pipe flow and an inviscid adiabatic variable cross-section pipe flow, respectively, and extend the collection of the exact solutions of gas dynamics.

We report laboratory results on bubble plumes released from a point source into a homogeneous liquid environment of depth $H$ and rotation rate $\varOmega$. The gas phase is characterised by the non-dimensional slip velocity $u_N=u_s/(BH^{-1})^{1/3}$, where $u_s$ is the slip velocity of the dominant bubble species and $B$ is the source buoyancy flux. The effects of the background rotation are characterised by the Rossby number $Ro=(B\varOmega ^{-3})^{1/4}/H$. We study the regimes $0.06\lessapprox u_N\lessapprox 0.36$ and $0.03\lessapprox Ro\lessapprox 0.3$. We establish that, from $\varOmega t\approx 2.3$, the growth of the maximum plume width $b_{max}$ is slowed down compared to the non-rotating $t^{3/4}$ power law, where $t$ is the time. At $\varOmega t\approx {\rm \pi}$, the plume axis starts to tilt laterally and causes a slowdown of the rise of the height $h_c$ of the plume silhouette centroid from the $t^{3/4}$ power law. These critical times do not depend on $u_N$. After $\varOmega t \approx {\rm \pi}$, the slip velocity counteracts the effects of rotation such that $h_c$ rises faster for larger $u_N$. The subsequent onset of the anticyclonic plume precession causes the disintegration of the rising plume front into vertical columnar structures for $Ro\lessapprox 0.15$. Once the plume reaches the free surface, the subsurface lateral dispersion of bubbles is increased compared to the non-rotating case. However, background rotation suppresses the lateral dispersion of bubbles at the free surface. We find that, asymptotically, the surface area $A$ affected by the bubbles scales as $(B\varOmega ^{-1})^{1/2}t$, and the proportionality factor reduces with an increasing $u_N$.

Direct numerical simulations are used to study the impact of chemical modelling on the flame dynamics and the sound generated by three-dimensional, turbulent, premixed methane/air jet flames. The semi-global BFER mechanism from Franzelli et al. (Combust. Flame, vol. 159, issue 2, 2012, pp. 621–637) and the more complex skeletal COFFEE mechanism from Coffee (Combust. Flame, vol. 55, issue 2, 1984, pp. 161–170) are considered. A more wrinkled flame is observed at downstream locations when using the COFFEE mechanism, demonstrating stronger flame/turbulence interaction. This flame also has a significantly lower acoustic power even though it features more acoustic output at high frequencies. The former is shown to arise from lower fluctuations of the heat release rate, whilst the latter is caused by the COFFEE mechanism creating more wrinkled flame surfaces. These results suggest that the accurate simulation of the noise emitted by turbulent premixed flames requires a chemical mechanism that ensures two main features: the heat release rate profile is important for modelling the overall sound amplitude and low frequency acoustics, whilst the flame/turbulence interaction impacts the higher frequency sound.

Direct numerical simulations are performed to contrast turbulent boundary layers over a concave wall without and with free-stream turbulence. An adverse pressure gradient near the onset of curvature leads to a sharp decrease in skin friction and intermittent separation. The presence of free-stream turbulence reduces the probability of reverse flow, accelerates the recovery of the boundary layer in the downstream zero-pressure-gradient region, and leads to a sustained and appreciable increase in the skin friction. The forcing also promotes the amplification of coherent Görtler structures in the logarithmic layer of the curved-wall boundary layer. Statistically, the spanwise and wall-normal Reynolds stresses intensify and the radial distance between their peaks increases downstream as the Görtler structures expand. The Reynolds shear stress coefficient also increases in the logarithmic layer, in contrast to a decrease when a flat-plate boundary layer is exposed to free-stream turbulence. In addition, the more coherent and energetic roll motions in the forced flow promote mixing of free-stream and boundary-layer fluids, where the former is seen more often deep within the buffer layer.

In the present study particle dispersions (concentrations) through vortical interactions are experimentally investigated for a particle-laden upward jet, with a horizontal crossflow covering a vertical range partially near the jet exit (Reynolds numbers of 1170–5200). We focus on the influences of the dynamics of counter-rotating vortex pairs existing in the flow on changes in the particle dispersion patterns, depending on the velocity (jet/crossflow) ratio and particle Stokes number ($St = 0.01\text {--}27.42$). Without crossflow, there is no dominant vortical structure along the horizontal direction; thus, the particles are not dispersed significantly out of the jet core in most cases, except for the case with the highest particle inertia (i.e. $St$). With crossflow, on the other hand, counter-rotating vortex pairs appear above the jet exit and become stronger as the velocity ratio decreases. With a lower velocity ratio, the vortices are tilted more toward the leeward side and dissipate faster. Driven by the vortex pairs, the drag force acting on the particles becomes stronger and, thus, particles with $St < 1.0$ are dragged out of the jet core following the rotation of the vortices. Those with $St \simeq 1.0$ are concentrated between the vortex pairs before the vortices collapse. When $St \gg 1.0$, particles are simply transported by the inertial effect. Finally, we suggest different regimes for particle dispersion (concentration) as classified by the Stokes number and velocity ratio, and elucidate their mechanisms, which are further extended to empirical particle dispersion models.

Oscillatory motions of charged particles inside a liquid medium have been explored under the influence of an electric field emulating field-induced particle-laden fluid flows. The properties of the surrounding fluid are found to play key roles in the kinetics of such a particle aggregation process. While the weakly conducting or insulating liquids promote high-frequency oscillations of charged particles followed by a quick assemblage, the viscosity and relative permittivity of the liquid play significant roles in modulating the time scale. In fact, the origin of such motions in a multi-particle system is very similar to a system with a single charged particle wherein the particle gathers charge from one of the electrodes before moving towards the other of opposite polarity. Interestingly, in the multi-particle system, an unprecedented charge reversal is observed wherein a charged particle reverses its direction of motion after colliding with another particle of opposite polarity. Experiments together with simulations further reveal that, while the equal-sized particles undergo an electric field driven ‘elastic’ collision and show synchronized motions with nearly similar speeds of approach and separation, the motions of unequal-sized particles are rather non-uniform after undergoing an ‘inelastic’ collision. Importantly, the simulations with two-particle systems uncover the presence of counter-rotating vortices surrounding the charged particles. The results reported not only usher the genesis of the chain-like assemblage in the multi-particle systems but also open up the possibility of the generation of on-demand power-law liquid properties through ‘chaining’ or ‘layering’ of the charged particles.

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

On the basis of the generalized Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. They arise as stable stationary solutions of the governing equations and are particularly well suited for a dynamical systems analysis, where they manifest themselves as near-parabolic trajectories in phase space. We derive an analytic approximate expression for the jump length as a function of the Froude and effective Reynolds numbers, reflecting the fact that – along with inertia – gravity and viscous diffusion both contribute to the balance of forces that shape the jump. The stability of the jumps is confirmed by means of a numerical experiment and an analysis of the propagation and attenuation of small perturbations.

The net erosion-deposition rate of an avalanche is fundamental to its dynamics and in determining its growth or decay. Small-scale experiments are performed by releasing a given volume of yellow sand onto a stationary erodible red sand layer on a rough inclined plane. Depending on the erodible layer depth and the slope angle, the avalanche is found to either decay, grow, propagate steadily or rapidly shed grains to produce secondary avalanches. The use of different coloured sand with identical properties shows that a particle exchange occurs, which eventually results in a flow that is comprised entirely of particles from the stationary layer rather than the initial release. It is notoriously difficult to model the erosion and deposition processes in granular flows, but it is shown that a two-dimensional depth-averaged avalanche model, with a hysteretic basal friction law, can reproduce all of the observed behaviours. The results illustrate how a continuous exchange of particles with the substrate layer is fundamentally important to the propagation of such avalanches. An investigation into long distance propagation behaviour reveals that avalanches can reach a steady state, the size and speed of which are independent of the initially released volume. In certain conditions avalanches can grow to steady states that are significantly more massive than the flows from which they are originally formed. This paper demonstrates the importance of correctly including erosion-deposition in operational forecast models of snow avalanches and other geophysical mass flows.

We introduce a network (graph) theoretic community-based framework to extract vortical structures that serve the role of connectors for the vortical interactions in two- and three-dimensional isotropic turbulence. The present framework represents the vortical interactions on a network, where the vortical elements are viewed as the nodes and the vortical interactions are regarded as edges weighted by induced velocity. We identify closely interacting vortical elements as vortical network communities through community detection algorithms. The inter- and intra-community interactions are used to identify the communities which have the strongest and weakest interactions amongst them. These vortical communities are referred to as the connector and peripheral communities, respectively. We demonstrate the influence of the network-based structures to modify the dynamics of a collection of discrete point vortices. Taking advantage of the strong inter-community interactions, connector community can significantly modify the collective dynamics of vortices through the application of multiple impulse perturbations. We then apply the community-based framework to extract influential structures in isotropic turbulence. The connector and peripheral communities extracted from turbulent flows resemble shear-layer and vortex-core-like structures, respectively. The influence of the connector structures on the flow field and their neighbouring vortical structures is analysed by adding impulse perturbations to the connectors in direct numerical simulations. The findings are compared with the cases of perturbing the strongest vortex tube and shear-layer regions. We reveal that perturbing the connector structures enhances local turbulent mixing beyond what is achieved by the other cases.

The interaction between starting jets and a steady cross-flow with a zero-pressure-gradient, turbulent boundary layer is studied experimentally. A device typically used in flow control applications is employed as jets of compressed air are injected into the cross-flow through a rectangular high-aspect-ratio outlet. Investigating different velocity ratios between starting jets and cross-flow within the interval $r=u_{jet}/U_\infty =2.4, \ldots ,11$, we identify two regimes of different flow structure appearance, transferring the classification map applicable to parallel circular starting jets in cross-flow established by Sau & Mahesh (J. Fluid Mech., vol. 604, 2008, pp. 389–409). At $r<4$, the vorticity associated with the upstream part of the starting jet is cancelled by the cross-flow boundary layer. Hairpin vortices are observed. At $r>4$, the starting jets penetrate through the boundary layer, and vortex rings are generated. They are asymmetric in shape as the windward vortex ring core is thinner due to the interaction with the cross-flow. As the limiting case of zero cross-flow ($r\rightarrow \infty$) is approached, the asymmetry decreases and the formation time corresponding to maximum vortex ring circulation converges to the characteristic value of $t^*\approx 12$ recently determined for this type of non-parallel planar starting jets when emitted into quiescent surroundings (Steinfurth & Weiss, J. Fluid Mech., vol. 903, 2020, A16). The findings presented in the current article can promote the sophisticated selection of actuation parameters in active mixing and separation control.

We carry out high-resolution particle image velocimetry experiments to characterize the flow field of fractal grids located at the exit section of a turbulent round jet. We comment on the mean flow organization and on the turbulence properties of such jets by comparing the results with those obtained with square grids, a regular grid (having the same effective mesh length) and a jet without turbulator. We find that, different from the case of decaying grid turbulence, a correction must be accounted for to properly scale the turbulence intensity profiles with a length scale based on grid parameters. We perform a low-order reconstruction of the velocity field based on the most energetic proper orthogonal decomposition modes and we compare the flow-field structure produced in the lee of fractal grids with a single square object and the jet without turbulator. The typical turbulence intensity profile detailed in Cafiero et al. (Phys. Fluids, vol. 27, 2015, 115103) for jets with fractal grids is produced by the interaction of small eddies shed by the central grid item. In the single square grid case, the turbulence is built upon the interaction between larger structures. Conversely, the interaction of the outward spreading wake with the external shear layer produces pairs of vortical structures, which we relate to the higher entrainment rate featured by jets with fractal turbulators. The secondary grid iterations have a disruptive effect on the turbulence transport, with a corresponding large correlation between the velocity fluctuations at the jet core with those at the jet shear layer.

The description of the feedback mechanism is one of the crucial points in the understanding of self-sustained flow oscillations, such as the edge tone or the cavity tone. In this paper a new model for the edge tone, using linear adjoint modes is proposed for low speeds, when acoustic effects are negligible. The two crucial points of the model are (i) a new relationship between the jet oscillation and the generated vortex at the edge tip and (ii) a new model for the effect of the generated vortex on the oscillation. The frequency corresponding to the optimum open-loop gain of the feedback mechanism was compared with experimental data and good agreement was found.

In this paper, we designed two different configurations with locally isothermal sidewalls, where the temperature is set to be the bulk temperature, to control the large-scale circulation in turbulent Rayleigh–Bénard convection, namely two-point control and four-point control. At fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=2$, a series of direct numerical simulations are performed on both two-dimensional (2-D) and quasi-two-dimensional (quasi-2-D) cavities with both types of control, where the width of the control area is fixed at $\delta _c=0.05$ and the vertical distance from the cavity centre $h_c$ varies from 0 to 0.45 with an interval of 0.05. Our results show that the control effect depends on $h_c$, the control configurations as well as the flow dimensions. For 2-D cavities, both two-point control and four-point control suppress the flow reversal when $h_c \geq 0.05$, accompanied by the enhancement of vertical heat transfer and the strength of the large-scale circulation. For quasi-2-D cavities, the suppression of the flow reversals is obvious with two-point control and $h_c\geq 0.05$, while the effect is rather limited with four-point control. Further experiments with $Pr=5.7$ and $Ra$ up to $7.36\times10^8$ show that two-point control with $h_c=0.15$ can effectively suppress the flow reversal, while two-point control with $h_c=0$ can suppress the reversals at low $Ra=1.93\times 10^8$ and activate them at higher $Ra=7.36\times 10^8$, which agrees well with our numerical simulations.