A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low-order Helmholtz solver. A large eddy simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on dynamic mode decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700–750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy–acoustic mode, where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows one to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The delayed entropy coupled boundary condition (DECBC) (Motheau, Selle & Nicoud, J. Sound Vib., vol. 333, 2014, pp. 246–262) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.

Collisions of counter-propagating solitary waves are investigated experimentally. Precision measurements of water-surface profiles are made with the use of the laser induced fluorescence (LIF) technique. During the collision, the maximum wave amplitude exceeds that calculated by the superposition of the incident solitary waves, and agrees well with both the asymptotic prediction of Su & Mirie (J. Fluid Mech., vol. 98, 1980, pp. 509–525) and the numerical simulation of Craig et al. (Phys. Fluids, vol. 18, 2006, 057106). The collision causes attenuation in wave amplitude: the larger the wave, the greater the relative reduction in amplitude. The collision also leaves imprints on the interacting waves with phase shifts and small dispersive trailing waves. Maxworthy’s (J. Fluid Mech., vol. 76, 1976, pp. 177–185) experimental results show that the phase shift is independent of incident wave amplitude. On the contrary, our laboratory results exhibit the dependence of wave amplitude that is in support of Su & Mirie’s theory. Though the dispersive trailing waves are very small and transient, the measured amplitude and wavelength are in good agreement with Su & Mirie’s theory. Furthermore, we investigate the symmetric head-on collision of the highest waves possible in our laboratory. Our laboratory results show that the runup and rundown of the collision are not simple reversible processes. The rundown motion causes penetration of the water surface below the still-water level. This penetration causes the post-collision waveform to be asymmetric, with each departing wave tilting slightly backward with respect to the direction of its propagation; the penetration is also the origin of the secondary dispersive trailing wavetrain. The present work extends the studies of head-on collisions to oblique collisions. The theory of Su & Mirie, which was developed only for head-on collisions, predicts well in oblique collision cases, which suggests that the obliqueness of the collision may not be important for this ‘weak’ interaction process.

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi, Moin & Kim, J. Fluid Mech., vol. 262, 1994, pp. 75–110) as an example. Under this formulation, the velocity field for turbulent pipe flow is decomposed into a series of highly amplified (rank-1) response modes, identified from a gain analysis of the Fourier-transformed Navier–Stokes equations. These rank-1 velocity responses represent propagating structures of given streamwise/spanwise wavelength and temporal frequency, whose wall-normal footprint depends on the phase speed of the mode. Opposition control, introduced via the boundary condition on wall-normal velocity, affects the amplification characteristics (and wall-normal structure) of these response modes; a decrease in gain indicates mode suppression, which leads to a decrease in the drag contribution from that mode. With basic assumptions, this rank-1 model reproduces trends observed in previous direct numerical simulation and large eddy simulation, without requiring high-performance computing facilities. Further, a wavenumber–frequency breakdown of control explains the deterioration of opposition control performance with increasing sensor elevation and Reynolds number. It is shown that slower-moving modes localized near the wall (i.e. attached modes) are suppressed by opposition control. Faster-moving detached modes, which are more energetic at higher Reynolds number and more likely to be detected by sensors far from the wall, are further amplified. These faster-moving modes require a phase lag between sensor and actuator velocity for suppression. Thus, the effectiveness of opposition control is determined by a trade-off between the modes detected by the sensor. However, it may be possible to develop control strategies optimized for individual modes. A brief exploration of such mode-optimized control suggests the potential for significant performance improvement.

The onset of two-dimensional instabilities in the flow past two side-by-side circular cylinders is numerically investigated in the ranges $0.1\leq g\leq 3$ and $\mathit{Re}<100$, with $g$ being the non-dimensional gap spacing between the surfaces of the two cylinders and $\mathit{Re}$ the Reynolds number. A comprehensive, global stability analysis of the symmetric base flow is carried out, indicating that three harmonic modes and one steady antisymmetric mode become unstable at different values of $g$ and $\mathit{Re}$. These modes are known to promote distinct flow regimes at increasing values of $g$: single bluff-body, asymmetric, in-phase and antiphase synchronized vortex shedding. For each mode, the inherent structural sensitivity is examined in order to identify the core region of the related instability mechanism. In addition, by exploiting the structural sensitivity analysis to base flow modifications, a passive control strategy is proposed for the simultaneous suppression of the two synchronized shedding modes using two small secondary cylinders. Its effectiveness is then validated a posteriori by means of direct numerical simulations.

Despite its fundamental and practical relevance, flow structure and evolution within volatile mixture drops remains largely unexplored. We study experimentally, using particle image velocimetry (PIV), the evolution of internal flow during the evaporation of ethanol–water mixture drops for different initial concentrations. The investigation revealed the existence of three stages in the evolving flow behaviour within these binary volatile drops. We propose an analysis of the nature of the flow and focus on understanding successive flow stages as well as transition from multiple vortices to a monotonic outward flow. We show that the existence of multiple vortices during the first stage is driven by local concentration gradients along the interface. When the more volatile component (in this case ethanol) is depleted, the intensity of this Marangoni flow abruptly declines. Towards the end of the first stage, ethanol is driven from the bulk of the drop to the interface to sustain weakening concentration gradients. Once these gradients are too weak, the solutal Marangoni number becomes sub-critical and the driving force for the flow switches off. The evolution of flow structure and transition between stages is found to be well correlated with the ratio of Marangoni and Reynolds numbers. Furthermore, we argue that whilst the observed vortices are driven by surface tension shear stress originating at the liquid/vapour interface, the transition in flow and its dynamics is entirely determined by viscous dissipation. The comparison between the analytical expression for vorticity decay based on viscous dissipation and the experimental data shows a very good agreement. The analysis also shows that regardless of the initial concentration, for same sized drops, the transition in flow follows exactly the same trend. This further supports the hypothesis of a viscous dissipation transition of the flow. The last stage is satisfactorily explained based on non-uniform evaporation and continuity-driven flow.

We propose a point-particle model for two-way coupling of water droplets dispersed in the turbulent flow of a carrier gas consisting of air and water vapour. We adopt an Euler–Lagrangian formulation based on conservation laws for the mass, momentum and energy of the continuous phase and on empirical correlations describing momentum, heat and mass transfer between the droplet phase and the carrier gas phase. An incompressible flow formulation is applied for direct numerical simulation of differentially heated turbulent channel flow. The two-way coupling is investigated in terms of its effects on mass and heat transfer characteristics and the resulting droplet size distribution. Compared to simulations without droplets or those with solid particles with the same size and specific heat as the water droplets, a significant increase in Nusselt number is found, arising from the additional phase changes. The Nusselt number increases with increasing ambient temperature and is almost independent of the heat flux applied to the walls of the channel. The time-averaged droplet size distribution displays a characteristic dependence on position expressing the combined effect of turbophoresis and phase changes in turbulent wall-bounded flow. In the statistically steady state that is reached after a long time, the resulting flow exhibits a mean motion of water vapour from the warm wall to the cold wall, where it condenses on average, followed by a net mean mass transfer of droplets from the cold wall to the warm wall.

Precipitation of sodium chloride driven by evaporation at the surface of a porous medium is studied from a combination of experiments, continuum simulations, pore network simulations and a simple efflorescence growth model on a lattice. The distribution of ions concentration maxima at the porous medium surface, which are seen as the incipient precipitation spots, is shown to be strongly dependent on the factors affecting the velocity field within the porous medium owing to the significance of advection on ion transport. These factors include the evaporation flux distribution at the surface at Darcy’s scale as well as the scale of surface menisci and the internal disorder of the porous medium, which induce spatial fluctuations in the velocity field. The randomness of the velocity field within the porous medium and at its surface explains the discrete nature of incipient precipitation spots at the surface of a porous medium. Experiments varying the mean size of the beads forming the porous medium lead to the identification of two main types of efflorescence, referred to as crusty and patchy, and the impact of these two types on evaporation is completely different. The crusty efflorescence severely reduces the evaporation rate whereas the patchy efflorescence can enhance the evaporation rate compared with pure water. The crusty–patchy transition is analysed from a simple growth model on a lattice taking into account the porous nature of efflorescence structures.

Hydrodynamic focusing of cells along the region of the most rapid flow is a robust feature in downflowing suspensions of swimming gyrotactic microorganisms. Experiments performed in a downward pipe flow have reported that the focused beam-like structure of the cells is often unstable and results in the formation of regular-spaced axisymmetric blips, but the mechanism by which they are formed is not well understood. To elucidate this mechanism, in this study, we perform a linear stability analysis of a downflowing suspension of randomly swimming gyrotactic cells in a two-dimensional vertical channel. On increasing the flow rate, the basic state exhibits a focused beam-like structure. It is found that this focused beam is unstable with the varicose mode, the spatial structure, wavelength, phase speed and behaviour with the flow rate of which are remarkably similar to those of the blip instability in the pipe flow experiment. To understand the physical mechanism of the varicose mode, we perform an analysis which calculates the term-by-term contribution to the instability. It is shown that the leading physical mechanism in generating the varicose instability originates from the horizontal gradient in the cell-swimming-vector field formed by the non-uniform shear in the base flow. This mechanism is found to be supplemented by cooperation with the gyrotactic instability mechanism observed in uniform suspensions.

The existence of an infinite class of buoyant flows in a vertical porous channel with adiabatic and impermeable boundary walls, called adiabatic eigenflows, is discussed. A uniform heat source within the saturated medium is assumed, so that a stationary state is possible with a net vertical through-flow convecting away the excess heat. The simple isothermal flow with uniform velocity profile is a special adiabatic eigenflow if the power supplied by the heat source is zero. The linear stability analysis of the adiabatic eigenflows is carried out analytically. It is shown that these basic flows are unstable. The only exception, when the power supplied by the heat source is zero, is the uniform isothermal flow, which is stable. The existence of adiabatic eigenflows and their stability analysis is extended to the case of spanwise lateral confinement, viz. in the case of a vertical rectangular channel. A generalisation of this study to a vertical channel with an arbitrary cross-sectional shape is also presented.

A new framework for spatio-temporally adaptive turbulence simulations is proposed. The method is based on a variable-fidelity representation that tightly integrates numerics and modelling of subgrid-scale turbulence and aims to capture the flow physics on a near-optimal adaptive mesh. The integration is achieved by combining hierarchical wavelet-based computational modelling with spatially and temporally varying wavelet threshold filtering. The proposed approach provides automatic smooth transition from directly resolving all flow physics to capturing only the energetic/coherent structures, which leads to a dynamically adaptive variable-fidelity approach. The self-regulating continuous switch between different fidelity regimes is accomplished through a two-way feedback mechanism between the modelled dissipation and the local grid resolution, which is based on spatio-temporal variation of the wavelet filtering threshold. The proposed methodology systematically accounts for and exploits the spatial and temporal intermittency of turbulence. Thus, it overcomes the major limitation of all existing wavelet-based multi-resolution techniques, namely, the use of a global thresholding criterion. The procedure consists of tracking the wavelet thresholding factor within a Lagrangian frame by exploiting a Lagrangian path-line diffusive averaging approach, based on either interpolation along characteristics or direct solution of the corresponding evolution equation. This new methodology is tested for linearly forced homogeneous turbulence at different Reynolds numbers and provides very promising results on a benchmark with time-varying prescribed level of turbulence resolution.

Direct numerical simulations were carried out to investigate the spatial features of large- and very-large-scale motions (LSMs and VLSMs) in a turbulent channel flow ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }=930$). A streak detection method based on the streamwise velocity fluctuations was used to individually trace the cores of LSMs and VLSMs. We found that both the LSM and VLSM populations were large. Several of the wall-attached LSMs stretched toward the outer regions of the channel. The VLSMs consisted of inclined outer LSMs and near-wall streaks. The number of outer LSMs increased linearly with the streamwise length of the VLSMs. The temporal features of the low-speed streaks in the outer region revealed that growing and merging events dominated the large-scale (1–$3\delta $) structures. The VLSMs $({>}3\delta )$ were primarily created by merging events, and the statistical analysis of these events supported that the merging of large-scale upstream structures contributed to the formation of VLSMs. Because the local convection velocity is proportional to the streamwise velocity fluctuations, the streamwise-aligned structures of the positive- and negative-$u$ patches suggested a primary mechanism underlying the merging events. The alignment of the positive- and negative-$u$ structures may be an essential prerequisite for the formation of VLSMs.

Turbulence facilitates collisions between particles suspended in a turbulent flow. Two effects have been proposed that can enhance the collision rate at high turbulence intensities: ‘preferential concentration’ (a clustering phenomenon) and the ‘sling effect’ (arising from the formation of caustic folds in the phase space of the suspended particles). We have determined numerically the collision rate of small heavy particles as a function of their size and densities. The dependence on particle densities allows us to quantify the contribution of the sling effect to the collision rate. Our results demonstrate that the sling effect provides the dominant mechanism to the enhancement of the collision rate of particles, when inertia becomes significant.