Numerical modelling of deformation in hydromechanical systems can be time-consuming using fully coupled classical numerical methods for large representative porous media samples. In this paper, we present a new two-way coupled partitioned fluid–solid system. The coupled system is applied for simulating geomechanical processes at the pore-scale. We track the deformation of the solid resulting from the drainage of resident fluids in the pores, as well as the evolution of fluid properties from dynamic loading. The finite element method is responsible for capturing the structural deformation in the coupled system while the dynamic pore network is used for modelling multiphase flow in the fluid subsystem. A fictitious fluid–solid interface is created at each pore network-finite element node junction via convex hulling, followed by data exchange using linear interpolation. The results show good agreement with a pre-existing coupled finite volume model and the computations are completed in much less time.

The flow over a superhydrophobic and a smooth circular cylinder is investigated using particle image velocimetry-based experiments. The objective is to understand the effect of surface modification on the ensuing flow. The experiments are conducted over a wide range of Reynolds numbers, $Re=45{-}15\,500$, thereby uncovering the effect of superhydrophobicity in various flow regimes of a cylinder wake. Superhydrophobicity is found to substantially affect the flow. An increased recirculation length is observed for the superhydrophobic cylinder in the steady regime. The onset of vortex shedding is delayed for the superhydrophobic cylinder. The superhydrophobic cylinder helps in an early rolling-up of vortices; therefore, the recirculation length reduces in unsteady regimes. The velocity deficit experienced by the superhydrophobic cylinder wake is comparatively less and the effect is more profound in the $Re$ range 300–860. A maximum drag reduction of 15 % is observed at $Re=860$. The Reynolds shear stress and turbulent kinetic energy values are higher for the superhydrophobic cylinder in the unsteady regime. Also, the peaks of the turbulent wake parameters lie closer to the superhydrophobic cylinder compared to the smooth cylinder. The effect of superhydrophobicity on coherent structures is examined using proper orthogonal decomposition, and a considerable difference in the wake structure is noticed at $Re=860$. A larger number of coherent structures and change in vortex shedding pattern to $\text{P}+\text{S}$ are observed in the near wake of the superhydrophobic cylinder. The results of this study show that surface modification can reduce the drag coefficient and have a profound effect on the near wake.

We perform direct numerical simulations of wall sheared Rayleigh–Bénard convection for Rayleigh numbers up to $Ra=10^{8}$, Prandtl number unity and wall shear Reynolds numbers up to $Re_{w}=10\,000$. Using the Monin–Obukhov length $L_{MO}$ we observe the presence of three different flow states, a buoyancy dominated regime ($L_{MO}\lesssim \unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$; with $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$ the thermal boundary layer thickness), a transitional regime ($0.5H\gtrsim L_{MO}\gtrsim \unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$; with $H$ the height of the domain) and a shear dominated regime ($L_{MO}\gtrsim 0.5H$). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed $Ra$ and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number $Nu$ effectively scales as $Nu\sim Ra^{\unicode[STIX]{x1D6FC}}$ with $\unicode[STIX]{x1D6FC}\ll 1/3$, while we find $\unicode[STIX]{x1D6FC}\simeq 0.30$ in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is $\unicode[STIX]{x1D6FC}>1/3$, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.

Enhancing solute dispersion in electrically actuated flows has always been a challenging proposition, as attributed to the inherent uniformity of the flow field in the absence of surface patterns. Over the years, researchers have focused their attention towards circumventing this limitation, by employing several fluidic and geometric modulations. However, the corresponding improvements in solute dispersion often turn out to be inconsequential. Here we reveal that by exploiting the interplay between an externally imposed temperature gradient, subsequent electrical charge redistribution and ionic motion, coupled with the rheological complexities of the fluid, one can achieve enhancement of up to one order of magnitude of solute dispersion in a pressure-driven flow of an electrolyte solution. Our results demonstrate that the complex coupling between thermal, electrical, hydrodynamic and rheological parameters over small scales, responsible for such exclusive phenomenon, can be utilized in designing novel thermally actuated microfluidic and bio-microfluidic devices with favourable solute separation and dispersion characteristics.

We study the formation, longevity and breakdown of convective rings during impulsive spin up in square and cylindrical containers using direct numerical simulations. The rings, which are axisymmetric alternating regions of up- and downwelling flow that can last for $O(100)$ rotation times, were first demonstrated experimentally and arise due to a balance between Coriolis and viscous effects. We study the formation of these rings in the context of the Greenspan–Howard spin-up process, the disruption of which modifies ring formation and evolution. We show that, unless imprinted by boundary geometry, convective rings can only form when the surface providing buoyancy forcing is a free-slip surface, thereby explaining an apparent disagreement between experimental results in the literature. For Prandtl numbers from 1–5 we find that the longest-lived rings occur for intermediate Prandtl numbers, with a Rossby number dependence. Finally, we find that the constant evaporative heat-flux conditions imposed in the experiments are essential in sustaining the rings and in maintaining the vortices that form in consequence of the ring breakdown.

In this work ice breaking caused by a pair of interacting collapsing bubbles was studied by an experimental approach. The bubbles were generated by an underwater electric discharge simultaneously, positioned either horizontally or vertically below a floating ice plate and observed via high-speed photography. The bubble-induced shock waves, which turn out to be crucial to the fracturing of the ice, were visualized using a shadowgraph method and also measured using pressure transduces. Unique bubble behaviour was observed, including bubble coalescence, bubble splitting, inclined counter-jets and asymmetric toroidal bubble collapse. Bubble dynamic properties, such as jet speed, jet energy and bubble centre displacement, were measured. Shock wave emission and ice breaking capability of the two bubbles were investigated over a range of inter-bubble and bubble–boundary distances. Regions where the damaging potential of the bubble pair are strengthened or weakened were summarized and possible reasons for the variation in the ice breaking capability were analysed based on bubble morphology, jet characteristics and shock wave pressure. The findings may contribute to more efficient ice breaking and also inspire new ways to manipulate cavitation bubble damage.

An investigation of optimal feedback controllers’ performance and robustness is carried out for vortex shedding behind a two-dimensional cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier–Stokes equations into an input–output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to high-dimensional flow systems is overcome by using low-order models identified from frequency responses. These low-order models are used to design optimal controllers using ${\mathcal{H}}_{\infty }$ loop shaping. Two distinct single-input single-output control arrangements are considered. In the first arrangement, a velocity sensor located in the wake drives a pair of body forces near the cylinder. Complete suppression of shedding is observed up to $Re=110$. Due to the convective nature of vortex shedding and the corresponding time delays, we observe a fundamental trade-off: the sensor should be close enough to the cylinder to avoid excessive time lag, but it should be kept sufficiently far from the cylinder to measure unstable modes developing downstream. These two conflicting requirements become more difficult to satisfy for larger Reynolds numbers. In the second arrangement, we consider a practical set-up with an actuator that oscillates the cylinder according to the lift measurement. The system is stabilised up to $Re=100$, and we demonstrate why the performance of the resulting feedback controllers deteriorates more rapidly with increasing Reynolds number. The challenges of designing robust controllers for each control set-up are also analysed and discussed.

An artificial intelligence (AI) control system is developed to maximize the mixing rate of a turbulent jet. This system comprises of six independently operated unsteady minijet actuators, two hot-wire sensors placed in the jet and genetic programming for the unsupervised learning of a near-optimal control law. The ansatz of this law includes multi-frequency open-loop forcing, sensor feedback and nonlinear combinations thereof. Mixing performance is quantified by the decay rate of the centreline mean velocity of the jet. Intriguingly, the learning process of AI control discovers the classical forcings, i.e. axisymmetric, helical and flapping achievable from conventional control techniques, one by one in the order of increased performance, and finally converges to a hitherto unexplored forcing. Careful examination of the control landscape unveils typical control laws, generated in the learning process, and their evolutions. The best AI forcing produces a complex turbulent flow structure that is characterized by periodically generated mushroom structures, helical motion and an oscillating jet column, all enhancing the mixing rate and vastly outperforming others. Being never reported before, this flow structure is examined in various aspects, including the velocity spectra, mean and fluctuating velocity fields and their downstream evolution, and flow visualization images in three orthogonal planes, all compared with other classical flow structures. Along with the knowledge of the minijet-produced flow and its effect on the initial condition of the main jet, these aspects cast valuable insight into the physics behind the highly effective mixing of this newly found flow structure. The results point to the great potential of AI in conquering the vast opportunity space of control laws for many actuators and sensors and in optimizing turbulence.

The influence of fluid–structure interaction on cloud cavitation about a hydrofoil is investigated by comparing results from a relatively stiff reference hydrofoil, presented in Part 1, with those obtained on a geometrically identical flexible hydrofoil. Measurements were conducted with a chord-based Reynolds number $Re=0.8\times 10^{6}$ for cavitation numbers, $\unicode[STIX]{x1D70E}$, ranging from 0.2 to 1.2 while the hydrofoil was mounted at an incidence, $\unicode[STIX]{x1D6FC}$, of $6^{\circ }$ to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras. The flexible composite hydrofoil was manufactured as a carbon/glass-epoxy hybrid structure with a lay-up sequence selected principally to consider spanwise bending deformations with no material-induced bend–twist coupling. Hydrodynamic bend–twist coupling is seen to result in nose-up twist deformations causing frequency modulation from the increase in cavity length. The lock-in phenomenon driven by re-entrant jet shedding observed on the stiff hydrofoil is also evident on the flexible hydrofoil at $0.70\leqslant \unicode[STIX]{x1D70E}\leqslant 0.75$, but occurs between different modes. Flexibility is observed to accelerate cavitation regime transition with reducing $\unicode[STIX]{x1D70E}$. This is seen with the rapid growth and influence the shockwave instability has on the forces, deflections and cavitation behaviour on the flexible hydrofoil, suggesting structural behaviour plays a significant role in modifying cavity physics. The reduced stiffness causes secondary lock-in of the flexible hydrofoil’s one-quarter sub-harmonic, $f_{n}/4$, at $\unicode[STIX]{x1D70E}$ = 0.4. This leads to the most severe deflections observed in the conditions tested along with a shift in phase between normal force and tip deflection.

The discrete velocity Boltzmann equations (DVBE) underlie the attainable properties of all numerical lattice Boltzmann methods (LBM). To that regard, a thorough understanding of their intrinsic hydrodynamic limits and stability properties is mandatory. To achieve this, we propose an analytical study of the eigenvalues obtained by a von Neumann perturbative analysis. It is shown that the Knudsen number, naturally defined as a particular dimensionless wavenumber in the athermal case, is sufficient to expand rigorously the eigenvalues of the DVBE and other fluidic systems such as Euler, Navier–Stokes and all Burnett equations. These expansions are therefore compared directly to one another. With this methodology, the influences of the lattice closure and equilibrium on the hydrodynamic limits and Galilean invariance are pointed out for the D1Q3 and D1Q4 lattices, without any ansatz. An analytical study of multi-relaxation time (MRT) models warns us of the errors and instabilities associated with the choice of arbitrarily large ratios of relaxation frequencies. Importantly, the notion of the Knudsen–Shannon number is introduced to understand which physics can be solved by a given LBM numerical scheme. This number is also shown to drive the practical stability of MRT schemes. In the light of the proposed methodology, the meaning of the Chapman–Enskog expansion applied to the DVBE in the linear case is clarified.

An analysis of the direct initiation of gaseous detonations in a spherical geometry is presented. The full set of constitutive equations is analysed by an asymptotic analysis in the double limit of Mach number close to unity (small heat release) and large thermal sensitivity. The quasi-steady curvature-induced quenching phenomenon is first revisited in this limit. Considering a realistic decrease rate of the rarefaction wave, the unsteady problem is reduced to a single nonlinear hyperbolic equation. The time-dependent velocity of the lead shock is an eigenfunction of the problem when two boundary conditions are imposed to the flow at the lead shock and at the burnt gas side. Following (Liñan et al., C. R. Méc., vol. 340, 2012, pp. 829–844), the boundary condition in the quasi-transonic flow of burnt gas is expressed in terms of the curvature. Focusing our attention on successful initiation, the time-dependent velocity of the lead shock of a detonation approaching the Chapman–Jouguet regime is the solution of a nonlinear integral equation investigated for stable and marginally unstable detonations. By comparison with the quasi-steady trajectories in the phase space ‘propagation velocity versus radius’, the solution exhibits the unsteady effect produced upon the detonation decay by the long time delay of the upstream-running mode for transferring the rarefaction-wave-induced deceleration across the inner detonation structure from the burnt gas to the lead shock. In addition, a new and intriguing phenomenon concerning pulsating detonations is described. Even if the results are not quantitatively accurate, they are qualitatively relevant for real detonations.

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the streamwise and cross-flow directions, and forced to rotate about its axis, are investigated via two- and three-dimensional simulations. The Reynolds number based on the body diameter and inflow velocity is equal to $100$. The impact of the imposed rotation on the flow–structure system behaviour is explored over wide ranges of values of the rotation rate (ratio between the cylinder surface and inflow velocities, $\unicode[STIX]{x1D6FC}\in [0,5.5]$) and of the reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by the inflow velocity and body diameter, $U^{\star }\in [1,25]$). Flow-induced vibrations are found to develop over the entire range of $\unicode[STIX]{x1D6FC}$, including in the intervals where the imposed rotation cancels flow unsteadiness when the body is rigidly mounted (i.e. not allowed to translate). The responses of the two-degree-of-freedom oscillator substantially depart from their one-degree-of-freedom counterparts. Up to a rotation rate close to $2$, the body exhibits oscillations comparable to the vortex-induced vibrations usually reported for a non-rotating circular cylinder: they develop under flow–body synchronization and their amplitudes present bell-shaped evolutions as functions of $U^{\star }$. They are, however, enhanced by the rotation as they can reach $1$ body diameter in each direction, which represents twice the peak amplitude of cross-flow response for $\unicode[STIX]{x1D6FC}=0$. The symmetry breaking due to the rotation results in deviations from the typical figure-eight orbits. The flow remains close to that observed in the rigidly mounted body case, i.e. two-dimensional with two spanwise vortices shed per cycle. Beyond $\unicode[STIX]{x1D6FC}=2$, the structural responses resemble the galloping oscillations generally encountered for non-axisymmetric bodies, with amplitudes growing unboundedly with $U^{\star }$. The response growth rate increases with $\unicode[STIX]{x1D6FC}$ and amplitudes larger than $20$ diameters are observed. The cylinder describes, at low frequencies, elliptical orbits oriented in the opposite sense compared to the imposed rotation. The emergence of subharmonic components of body displacements, leading to period doubling or quadrupling, induces slight variations about this canonical shape. These responses are not predicted by a quasi-steady modelling of fluid forcing, i.e. based on the evolution of the mean flow at each step of body motion; this suggests that the interaction with flow unsteadiness cannot be neglected. It is shown that flow–body synchronization persists, which is not expected for galloping oscillations. Within this region of the parameter space, the flow undergoes a major reconfiguration. A myriad of novel spatio-temporal structures arise with up to $20$ vortices formed per cycle. The flow three-dimensional transition occurs down to $\unicode[STIX]{x1D6FC}\approx 2$, versus $3.7$ for the rigidly mounted body. It is, however, shown that it has only a limited influence on the system behaviour.

The mechanism of turbulence amplification in shock-wave/boundary layer interactions is reviewed, and a new turbulence amplification mechanism is proposed based on the analysis of data from direct numerical simulation of an oblique shock-wave/flat-plate boundary layer interaction at Mach 2.25. In the upstream part of the interaction zone, the amplification of turbulence is not essentially shear driven, but induced by the interaction of the deceleration of mean flow with streamwise velocity fluctuations, which causes a rapid increase of turbulence intensity in the near-wall region. In the downstream part of the interaction zone, the high turbulence intensity is mainly due to the free shear layer generated in the interaction zone. During the initial stage of turbulence amplification, the characteristics of wall turbulence, including compact velocity streaks, streamwise vortices and an anisotropic Reynolds stress, are well preserved. The mechanism proposed explains the high level of turbulence in the near-wall region observed in some experiments and numerical simulations.

A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number ($Ca_{e}$) and study the effect of $Ca_{e}$, viscosity ratio ($\unicode[STIX]{x1D706}$) and surfactant coverage on the droplet behaviour. Results show that at low $Ca_{e}$ the droplet eventually reaches steady deformation and a constant moving velocity $u_{d}$. The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each $\unicode[STIX]{x1D706}$, a linear relationship is found between contact-line capillary number and $Ca_{e}$, but not between wall stress and $u_{d}$ due to Marangoni effects. As $\unicode[STIX]{x1D706}$ increases, $u_{d}$ decreases monotonically, but the deformation first increases and then decreases for each $Ca_{e}$. Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase $Ca_{e}$ and study droplet breakup for varying $\unicode[STIX]{x1D706}$, where the role of surfactants on the critical $Ca_{e}$ ($Ca_{e,c}$) of droplet breakup is identified by comparing with the clean case. As in the clean case, $Ca_{e,c}$ first decreases and then increases with increasing $\unicode[STIX]{x1D706}$, but its minima occurs at $\unicode[STIX]{x1D706}=0.5$ instead of $\unicode[STIX]{x1D706}=1$ in the clean case. The presence of surfactants always decreases $Ca_{e,c}$, and its effect is more pronounced at low $\unicode[STIX]{x1D706}$. Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest $\unicode[STIX]{x1D706}$ in the surfactant-covered case.

We study the nonlinear evolution of the axisymmetric centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semilinear approach. The model consists of two coupled equations: one for the linear evolution of the most unstable perturbation on the axially averaged mean flow and another for the evolution of the mean flow under the effect of the axially averaged Reynolds stresses due to the perturbation. Such a model is similar to the self-consistent model of Mantič-Lugo et al. (Phys. Rev. Lett, vol. 113, 2014, 084501) except that the time averaging is replaced by a spatial averaging. The nonlinear evolutions of the mean flow and the perturbations predicted by this semilinear model are in very good agreement with direct numerical simulations for the Rossby number $Ro=-4$ and both values of the Reynolds numbers investigated: $Re=800$ and $2000$ (based on the initial maximum angular velocity and radius of the vortex). An improved model, taking into account the second-harmonic perturbations, is also considered. The results show that the angular momentum of the mean flow is homogenized towards a centrifugally stable profile via the action of the Reynolds stresses of the fluctuations. The final velocity profile predicted by Kloosterziel et al. (J. Fluid Mech., vol. 583, 2007, pp. 379–412) in the inviscid limit is extended to finite high Reynolds numbers. It is in good agreement with the numerical simulations.

The sensitivity of turbulent dynamics in spatially evolving mixing layers to small skew angles $\unicode[STIX]{x1D703}$ is investigated via direct numerical simulation. Angle $\unicode[STIX]{x1D703}$ is a measure of the lack of parallelism between the two asymptotic flows, whose interaction creates the turbulent mixing region. The analysis is performed considering a large range of values of the shear intensity parameter $\unicode[STIX]{x1D6FC}$. This two-dimensional parameter space is explored using the results of a database of 18 direct numerical simulations. Instantaneous fields as well as time-averaged quantities are investigated, highlighting important mechanisms in the emergence of turbulence and its characteristics for this class of flows. In addition, a stochastic approach is used in which $\unicode[STIX]{x1D703}$ and $\unicode[STIX]{x1D6FC}$ are considered as random variables with a given probability distribution. The response surfaces of flow statistics in the parameter space are built through non-intrusive generalized polynomial chaos. It is found that variations of the parameter $\unicode[STIX]{x1D6FC}$ have a primary effect on the growth of the mixing region. A secondary effect associated with $\unicode[STIX]{x1D703}$ is observed as well. Higher values for the skew angle are responsible for a rapid increase in growth of the inlet structures, enhancing the development of the mixing region. The impact on the turbulence features and, in particular, on the Reynolds stress tensor is also significant. A modification of the normalized diagonal components of the Reynolds stress tensor due to $\unicode[STIX]{x1D703}$ is observed. In addition, the interaction between the parameters $\unicode[STIX]{x1D703}$ and $\unicode[STIX]{x1D6FC}$ is here the governing element.

Chaplygin’s hodograph method of classical fluid mechanics is applied to explicitly solve the Plateau problem of finding minimal surfaces. The minimal surfaces are formed between two mirror-symmetric polygonal frames having a common axis of symmetry. Two classes of minimal surfaces are found: the class of regular surfaces continuously connecting the supporting frames forming a tube with complex shape; and the class of singular surfaces which have a partitioning film closing the tube in between. As an illustration of the general solution, minimal surfaces supported by triangular frames are fully described. The theory is experimentally validated using soap films. The general solution is compared with the known particular solutions obtained by the Weierstrass inverse method.

In this paper we investigate the instability properties of Batchelor vortices with a large swirl number and a fixed axial velocity deficit. In particular, it elucidates the effect of the helicity profile on the instability of the vortices as swirling wakes. In a linear stability analysis, a negative helicity profile destabilised a vortex with a large swirl number; the name given to this instability is ‘helicity instability’. Note that helicity instability is qualified for the case of axial flow with wake. In contrast, a conventional Batchelor vortex was stable at swirl numbers above a value of circulation, which is determined by the axial velocity deficit. The instability was related to a parameter $D$ proportional to the square of the inverse azimuthal vorticity thickness. Decreasing this helicity-profile parameter increased the growth property of the vortex. Such unstable features (helicity effects) were also studied in direct numerical simulations of vortices subjected to small random disturbances at Mach numbers 2.5 and 5.0. The instability based on the vorticity thickness originally grew at the outer edge of the vortex, whereas the instability waves in a conventional Batchelor vortex originate inside the vortex core. The simulation results support the results of the linear stability analysis on the helicity profile when the parameter $D$ is small. Because of the helicity instability, the nonlinear developments yielded a large fluctuation field with many small scales and high radial spreading rates. Even at the Mach number of 5.0, negative helicity exerted a much greater destabilisation effect than a zero entropy gradient. Therefore, the investigated novel effect established a reasonably powerful instability in compressible fluids, which is favourable for supersonic mixing.