A pipe conveying fluid is a model problem in fluid–structure interactions and nonlinear dynamics. Several experimental and theoretical studies exist on this problem and very rich nonlinear dynamics have been observed including super- and subcritical instabilities as well as various routes to chaos. Despite all the existing studies, we had not yet seen the fluid inside an oscillating pipe as the pipe undergoes different types of flow-induced instabilities. But the wait is over.

We experimentally examine a laser-induced underwater shock wave paying special attention to the pressure impulse, the time integral of the pressure evolution. Plasma formation, shock-wave expansion and the pressure in water are observed simultaneously using a combined measurement system that obtains high-resolution nanosecond-order image sequences. These detailed measurements reveal a distribution of the pressure peak which is not spherically symmetric. In contrast, remarkably, the pressure impulse is found to be symmetrically distributed for a wide range of experimental parameters, even when the shock waves are emitted from an elongated region. The structure is determined to be a collection of multiple spherical shock waves originating from point-like plasmas in the elongated region.

We have carried out wall-resolved unstructured fully compressible Navier–Stokes simulations of a complete standing-wave thermoacoustic–piezoelectric engine model inspired by the experimental work of Smoker et al. (J. Appl. Phys., vol. 111 (10), 2012, 104901). The model is axisymmetric and comprises a 51 cm long resonator divided into two sections: a small-diameter section enclosing a thermoacoustic stack and a larger-diameter section capped by a piezoelectric diaphragm tuned to the thermoacoustically amplified mode (388 Hz). The diaphragm is modelled with multi-oscillator broadband time-domain impedance boundary conditions (TDIBCs), providing higher fidelity over single-oscillator approximations. Simulations are first carried out to the limit cycle without energy extraction. The observed growth rates are shown to be grid convergent and are verified against a numerical dynamical model based on Rott’s theory. The latter is based on a staggered grid approach and allows jump conditions in the derivatives of pressure and velocity in sections of abrupt area change and the inclusion of linearized minor losses. The stack geometry maximizing the growth rate is also found. At the limit cycle, thermoacoustic heat leakage and frequency shifts are observed, consistent with experiments. Upon activation of the piezoelectric diaphragm, steady acoustic energy extraction and a reduced pressure amplitude limit cycle are obtained. A heuristic closure of the limit cycle acoustic energy budget is presented, supported by the linear dynamical model and the nonlinear simulations. The developed high-fidelity simulation framework provides accurate predictions of thermal-to-acoustic and acoustic-to-mechanical energy conversion (via TDIBCs), enabling a new paradigm for the design and optimization of advanced thermoacoustic engines.

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\in [10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^{3}$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.

The generation of tones in a supersonic planar jet impinging on a flat plate normally has been investigated by performing compressible large-eddy simulations using low-dissipation and low-dispersion finite differences. At the exit of a straight nozzle of height $h$, the jet is ideally expanded, and has a Mach number of 1.28 and a Reynolds number of $5\times 10^{4}$. Four distances between the nozzle and the plate between $3.94h$ and $9.1h$ have been considered. Flow snapshots and mean velocity fields are first presented. The variations of turbulence intensities and of the convection velocity in the jet shear layers are then examined. The properties of the jet near fields are subsequently described, in particular by applying Fourier decomposition to the pressure fields. Several coexisting tones appear to be generated by aeroacoustic feedback loops establishing between the nozzle lip and the flat plate, which also lead to the presence of hydrodynamic–acoustic standing waves. The tone frequencies are consistent with those given by the aeroacoustic feedback model and with measurements for high-aspect-ratio rectangular jets. The jet oscillation modes at these frequencies are characterized, and found to agree with experimental data. Their symmetric or antisymmetric natures are shown to be well predicted by a wave analysis carried out using a vortex sheet model of the jet, providing the allowable frequency ranges for the upstream-propagating acoustic waves. Thus, it is possible, for an ideally expanded impinging planar jet to predict both the frequencies of the tones and the symmetric or antisymmetric nature of the corresponding oscillation modes by combining the aeroacoustic feedback model and the wave analysis.

The influence of compressibility on the shear layer over a rectangular cavity of variable width has been studied in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. This contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width.

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).

Gravity–capillary solitary waves are generated by a moving ‘air-suction’ forcing instead of a moving ‘air-blowing’ forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Three different states are observed according to forcing speeds below $c_{min}$. At relatively low speeds below $c_{min}$, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to $c_{min}$, however, nonlinear three-dimensional (3-D) gravity–capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to $c_{min}$, oblique shedding phenomena of 3-D gravity–capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity–capillary solitary waves are observed ‘ahead of’ the air-suction forcing whereas the same waves are observed ‘behind’ the air-blowing forcing.

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

The crossflow instability in a hypersonic, laminar boundary layer is investigated using point measurements inside the boundary layer for the first time. Experiments are performed on a 7° right, circular cone with an adiabatic wall condition at 5.6° angle of incidence in the low-disturbance Mach 6 Quiet Tunnel at Texas A&M University. Measurements are made with a constant-temperature hot-wire anemometer system with a frequency response up to 180 kHz. Stationary crossflow waves are observed to grow and saturate. A travelling wave coexists with the stationary wave and occurs in a frequency band centred around 35 kHz. A type-I secondary instability is also observed in a frequency band centred around 110 kHz. The behaviour of all three modes is largely consistent with their low-speed counterparts prior to saturation of the stationary wave. Afterward, the behaviour remains in partial agreement with the low-speed case. Neither type-II secondary instability nor transition to turbulence are observed in this study.

Thermoacoustic instabilities in gas turbines and aeroengine combustors fall within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds for output-only model-based system identification. It has been shown recently that one can extract the governing parameters of the instabilities, namely the linear growth rate and the nonlinear component of the thermoacoustic feedback, using dynamic pressure time series only. This is highly relevant for practical systems, which cannot be actively controlled due to a lack of cost-effective actuators. The thermoacoustic stability is given by the linear growth rate, which results from the combination of the acoustic damping and the coherent feedback from the flame. In this paper, it is shown that it is possible to quantify the acoustic damping of the system, and thus to separate its contribution to the linear growth rate from the one of the flame. This is achieved by postprocessing in a simple way simultaneously acquired chemiluminescence and acoustic pressure data. It provides an additional approach to further unravel from observed time series the key mechanisms governing the system dynamics. This straightforward method is illustrated here using experimental data from a combustion chamber operated at several linearly stable and unstable operating conditions.

The flow of a planar jet (sheet) impinging onto a solid flat plate with slip is examined theoretically. The jet is assumed to spread out in a thin layer bounded by a hydraulic jump, and draining at the edge of the plate. In contrast to an adhering jet, a slipping jet does not admit a similarity solution. Taking advantage of the different scaling in each region, series expansions are used in the developing and fully viscous layers, which are matched at the transition point. We show that a slipping film exhibits a singularity in the normal stress at the leading edge of the boundary layer, as opposed to the singularity in velocity and shear stress for an adhering film. The boundary-layer and film heights are both found to decrease with slip relative to a smooth substrate, roughly like $\sqrt{30x/Re}-2S$, whereas the slip velocity intensifies like $S\sqrt{Re/30x}$ with slip. Here, $x$ is the distance along the plate, $S$ is the slip length and $Re$ is the Reynolds number (in units of the jet width). The transition is delayed by slip. Guided by the measurements of Duchesne et al. (Europhys. Lett., vol. 107, 2014, p. 54002) for a circular adhering jet, the hydraulic-jump height and location are determined for a planar jet, and are found to increase with the Froude number (flow rate) like $Fr^{1/4}$ and $Fr^{5/8}$ respectively, essentially independently of slip length.

Dynamic wetting failure in curtain coating of Newtonian liquids is studied in this work. A hydrodynamic model accounting for air flow near the dynamic contact line (DCL) is developed to describe two-dimensional (2D) steady wetting and to predict the onset of wetting failure. A hybrid approach is used where air is described by a one-dimensional model and liquid by a 2D model, and the resulting hybrid formulation is solved with the Galerkin finite element method. The results reveal that the delay of wetting failure in curtain coating – often termed hydrodynamic assist – mainly arises from the hydrodynamic pressure generated by the inertia of the impinging curtain. This pressure leads to a strong capillary-stress gradient that pumps air away from the DCL and thus increases the critical substrate speed for wetting failure. Although the parameter values used in the model are different from those in experiments due to computational limitations, the model is able to capture the experimentally observed non-monotonic behaviour of the critical substrate speed as the feed flow rate increases (Blake et al., Phys. Fluids, vol. 11, 1999, p. 1995–2007). The influence of insoluble surfactants is also investigated, and the results show that Marangoni stresses tend to thin the air film and increase air-pressure gradients near the DCL, thereby promoting the onset of wetting failure. In addition, Marangoni stresses reduce the degree of hydrodynamic assist in curtain coating, suggesting a possible mechanism for experimental observations reported by Marston et al. (Exp. Fluids, vol. 46, 2009, pp. 549–558).

The caudal fin of swimming animals can be modelled as a thrust-producing flapping foil. When considered alone, such a foil produces on average a jet wake with a positive net momentum. It has been argued that the instability characteristics of these averaged wakes are linked to the propulsion efficiency of swimming animals. Here, we reconsider this question by taking into account both the thrust and the drag exerted on a self-propelled swimming body. To do so, we study the stability of a family of momentumless wakes, constructed as the Oseen approximation of a force doublet moving at constant velocity. By performing a local stability analysis, we first show that these wakes undergo a transition from absolute to convective instability. Then, using the time stepper approach by integrating the linearised Navier–Stokes system, we investigate the global stability and reveal the influence of a non-parallel base flow as well as the role of the locally absolutely unstable upstream region in the wake. Finally, to complete the global scenario, we address the nonlinear evolution of the wake disturbance. These results are then discussed in the context of aquatic locomotion. According to the present stability results, and assuming the Oseen approximation whose validity has been assessed only for moderate Reynolds number, the momentumless wake of aquatic animals is generally stable, whereas the corresponding thrust part is unstable. It is therefore essential to consider all forces exerted on a self-propelled animal when discussing its wake stability and its propulsion efficiency.

The deformation of a slender drop in a nonlinear axisymmetric extensional and creeping flow has been theoretically studied. This problem, which was first suggested by Sherwood (J. Fluid Mech., vol. 144, 1984, pp. 281–295), is being revisited, and new results are presented. The problem is governed by three dimensionless parameters: the capillary number ($\mathit{Ca}\gg 1$), the viscosity ratio ($\unicode[STIX]{x1D706}\ll 1$), and the nonlinear intensity of the flow ($E\ll 1$). Contrary to linear extensional flow ($E=0$), where the local radius of the drop decreases monotonically (in the positive $z$ direction), in a nonlinear extensional flow ($E\neq 0$), two possible steady shapes exist: steady shapes (stable or unstable) with the local radius decreasing monotonically, and steady shapes (unstable) where the local radius of the drop has a local maximum, besides the one at the centre of the drop. Similar to linear extensional flow, the addition of nonlinear extensional effects does not change the end shape of the steady drop, which has pointed ends. A stability analysis has been done to distinguish between stable and unstable steady shapes and to determine the breakup point. Time-dependent studies reveal three types of breakup mechanism: a centre pinching mode, indefinite elongation, and a mechanism that remind us of tip-streaming, where a cusp is developed at the end of the drop.

The manipulation of a turbulent axisymmetric jet is experimentally investigated based on two unsteady radial minijets. The Reynolds number is 8000. The mass flow rate ratio $C_{m}$ of the two minijets to that of the main jet and the ratio $f_{e}/f_{0}^{\prime }$ of the excitation frequency $f_{e}$ to the preferred-mode frequency $f_{0}^{\prime }$ in the natural jet are examined. The decay rate $K$ of the jet centreline mean velocity exhibits a strong dependence on $C_{m}$ and $f_{e}/f_{0}^{\prime }$ and is classified into three distinct categories in terms of required $C_{m}$, achievable enhancement in $K$ and flow physics involved. Great effort is made to understand the flow physics associated with the first category of the manipulated jet, under which $K$ can be immensely improved with a very small $C_{m}$. Detailed measurements are conducted upstream and downstream of the nozzle exit using hot-wire, flow visualization and particle imaging velocimetry techniques. Whilst strong entrainment is predominant in the injection plane of the minijets, rapid spread occurs in the orthogonal non-injection plane. Three types of coherent structures are identified, i.e. the contorted ring vortex, two pairs of streamwise vortices and mushroom-like counter-rotating structures sequentially ‘tossed’ out radially in the non-injection plane. Their interactions account for the large rise in $K$. The unsteady disturbance of the minijets is found to play a key role in the formation and interaction of these vortices, which are distinct from those formed under the manipulation of steady minijets and other techniques. A conceptual model of the flow structure under manipulation is proposed.

We advance a quantitative description of the critical shear rate $\dot{\unicode[STIX]{x1D6FE}_{c}}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane experimental apparatus which enables measurement of $\dot{\unicode[STIX]{x1D6FE}_{c}}$ over a wide range of particle Reynolds number $Re_{p}$ from $10^{-3}$ to $1.5\times 10^{3}$. The condition to dislodge the particle is found to be consistent with the torque balance condition after including the torque component due to drag about the particle centre. The data for $Re_{p}<0.5$ are in good agreement with analytical calculations of the drag and lift coefficients in the $Re_{p}\rightarrow 0$ limit. For higher $Re_{p}$, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for $Re_{p}>1000$. We show that a linear combination of the hydrodynamic coefficients found in the viscous and inertial limits can describe the observed $\dot{\unicode[STIX]{x1D6FE}_{c}}$ as a function of the particle and fluid properties.

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.

A two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre–Su–Gardner–Green–Naghdi equations (a second-order shallow water approximation with respect to the parameter $H/L$, where $H$ is a characteristic water depth and $L$ is a characteristic wavelength). A simple model for vertical turbulent mixing is proposed governing the interaction between these layers. Stationary supercritical solutions to this model are first constructed, containing, in particular, a local turbulent subcritical zone at the forward slope of the wave. The non-stationary model was then numerically solved and compared with experimental data for the following two problems. The first one is the study of surface waves resulting from the interaction of a uniform free-surface flow with an immobile wall (the water hammer problem with a free surface). These waves are sometimes called ‘Favre waves’ in homage to Henry Favre and his contribution to the study of this phenomenon. When the Froude number is between 1 and approximately 1.3, an undular bore appears. The characteristics of the leading wave in an undular bore are in good agreement with experimental data by Favre (Ondes de Translation dans les Canaux Découverts, 1935, Dunod) and Treske (J. Hydraul Res., vol. 32 (3), 1994, pp. 355–370). When the Froude number is between 1.3 and 1.4, the transition from an undular bore to a breaking (monotone) bore occurs. The shoaling and breaking of a solitary wave propagating in a long channel (300 m) of mild slope (1/60) was then studied. Good agreement with experimental data by Hsiao et al. (Coast. Engng, vol. 55, 2008, pp. 975–988) for the wave profile evolution was found.

An experimental dataset of high-resolution velocity and concentration measurements is obtained under intense sediment transport regimes to provide new insights into the modification of turbulence induced by the presence of a mobile sediment bed. The physical interpretation of the zero-plane level in the law of the wall is linked to the bed-level variability induced by large-scale turbulent flow structures. The comparison between intrinsic and superficial Reynolds shear stresses shows that the observed strong bed-level variability results in an increased covariance between wall-normal ($w^{\prime }$) and streamwise ($u^{\prime }$) velocity fluctuations. This appears as an additional Reynolds shear stress in the near-wall region. It is also observed that the mobile sediment bed induces an increase of turbulence kinetic energy (TKE) across the boundary layer. However, the increased contribution of interaction events ($u^{\prime }w^{\prime }>0$, i.e. quadrants I and III in the ($u^{\prime },w^{\prime }$) plane) induces a decrease of the turbulent momentum diffusion and an increase of the turbulent concentration diffusion in the suspension region. This result provides an explanation for the modification of the von Kármán parameter and the turbulent Schmidt number observed in the literature for intense sediment transport.