The vortex-induced vibration of a flexible filament attached behind a stationary cylinder is studied in the two-dimensional, laminar flow regime. We explore the response of the filament for a wide range of flexibility and inertia. Lock-in with a large number of normal modes of the filament, each in a different regime of reduced speed, is observed. Reduced speed is the free-stream speed of the incoming flow non-dimensionalized with the first natural frequency of the structure and the diameter of the cylinder. Several branches, based on response of the filament, are identified and the contributions of various structural modes along these branches are quantified. Contribution from a particular structural mode increases significantly during lock-in, accompanied by a large amplitude of vibration. The transition between different branches is found to be hysteretic and intermittent. The flow exhibits a variety of vortex-shedding patterns, including the $\mathsf {2P+2S}$ mode. The modes of shedding show a systematic variation with amplitude and frequency. The map of vortex-shedding patterns in the amplitude–frequency plane resembles the corresponding map for forced vibration of a rigid cylinder. The transformation of wake from one mode of shedding to another is explained phenomenologically. Variation of rate of energy transfer between the fluid and filament with space and time is analysed to determine optimal placement of transducers for harvesting energy.

This study performs global stability/receptivity analyses of hypersonic flows over a swept blunt body with infinite span. For the first time, we obtain the characteristics of the leading attachment-line mode to the variation of sweep angles from $20^{\circ }$ to $70^{\circ }$. The global eigenfunctions exhibit the characteristics of the attachment-line instability at the leading edge. At the same time, cross-flow (at small sweep angles) or second Mack mode (at larger sweep angles) dominates further downstream. We establish an adjoint-based bi-orthogonal eigenfunction system to address the receptivity problem of such flows to any external forces and boundary perturbations. The receptivity analyses indicate that the global modes are the most responsive to external forces and surface perturbations applied in the vicinity of the attachment line, regardless of the sweep angles. It is also proven that the present global extension of the bi-orthogonal eigenfunction system can be successfully applied to complex hypersonic flows.

Oscillatory flow features are common in the unstart of hypersonic mixed-compression intakes and can be classified as low-amplitude or high-amplitude oscillatory unstarted flows. The low-amplitude oscillatory unstarted flow is driven by the shear layer from shock interactions ahead of the cowl, while the high-amplitude oscillatory unstarted flow is driven by the separation caused by shock–boundary-layer interaction on the ramp. While previous studies have observed these flow features and reported their associated frequency, there is no simple criterion available for predicting which mode will occur, and there is a lack of consensus on the appropriate frequency scaling parameter. We study a mixed-compression hypersonic intake in a hypersonic wind tunnel by varying the internal contraction ratio and the throttling ratio to observe various kinds of unstart regimes. Two significant conclusions emerge from considering the results for high-throttling-ratio conditions $(TR > 0.55)$ from the current as well as previous studies. Firstly, the actual shock-on-lip condition at the cowl corresponding to the unthrottled condition, as observed from schlieren images, demarcates the boundary between the two modes of oscillatory unstart flows upon throttling. Secondly, a suitable length scale $(l^*)$, defined as the extent of the subsonic region in the unstarted flow (as observed from the experimental schlieren images), gives the appropriate frequency scaling parameter ($f^* = a_0/4l^*$ where $a_0$ is the stagnation acoustic speed).

In a sheared suspension, the chaotic motion of the particles disperses the suspending liquid and drives an exponential and broadly distributed growth of the elongation of its material lines. This paper addresses experimentally and theoretically the consequences of this complex advection on the mixing of an initially segregated blob of diffusive dye, at large Péclet number and down to the finest scales of mixing. As the suspension is sheared, the combined action of the mean and fluctuating components of the flow stretches and folds the blob into a multi-scale lamellar structure. At short time, overlaps between the lamellae are scarce and the probability distribution concentration can be understood from the local stretching statistics only. At intermediate times, dispersion limits the volume within which lamellae deploy; overlaps become abundant and their statistics determine the concentration distribution. At longer times, the dye becomes homogeneous at the particle scale and the concentration distribution is set by dispersion only. Predictions for both the concentration distribution and the transitions between these successive stages of mixing are provided and compared to the experimental results.

A recent statistical analysis, proposed by Shnapp (J. Fluid Mech., vol. 913, 2021, R2), of Lagrangian velocity measurements in a wind tunnel in the presence of a canopy (a forest or urban morphology), using three-dimensional particle tracking velocimetry (Shnapp et al., Sci. Rep., vol. 9, issue 1, 2019, pp. 1–13), is a great read. In this strongly anisotropic situation, despite the additional roughness induced by the canopy, it is shown that fluctuations of Lagrangian velocity increments over small time scales display very similar behaviour as those observed in homogeneous and isotropic turbulent flows. This is all the more true when focussing on the non-Gaussian and intermittent nature of these fluctuations. At much larger time scales, of the order and greater than the characteristic turnover time scale of the flow, anisotropies implied by the presence of the canopy are quantified using averages of the fluctuating kinetic energy conditioned upon the direction of Lagrangian velocity with respect to the mean Eulerian flow. Shnapp (2021) evidences that, indeed, the canopy modifies the velocity along the trajectories at large scales, in particular its variance, but leaves unchanged its local regularity, as it is pinpointed by the power-law exponents of the structure functions.

An experimental investigation was carried out in a low-turbulence wind tunnel to study the early development of artificially initiated turbulent spots in a laminar boundary layer over a flat plate. The reproducibility of the experiments allowed us to observe fine structural details that have not been observed previously. Initial velocity disturbances quickly developed into hairpin-like structures that multiplied downstream, which increased the width, length and height of the incipient turbulent spots. Only those disturbances that were greater than a threshold value developed into turbulent spots while the others decayed. The rate of development was also affected by the duration of the initial disturbances. We found that the behaviour of turbulence generation within a turbulent spot is similar to the burst events in the turbulent boundary layer, where ejection events are followed by sweep events.

Coherent structures in turbulent round jets are evaluated for a jet Reynolds number up to $Re_d=50\,000$ with the aid of two-point measurements and an existing direct numerical simulation (DNS) dataset at $Re_d=7290$. The experimental data comprise simultaneous velocity time series acquired with both radial and azimuthal separations between the sensors. A spectral correlation analysis is applied to these data that reveals that the coherent structures in the jet flow consist of two principal configurations, which correspond to two main spectral domains. One spectral domain, which is signified by small to medium wavelengths, is associated with hierarchical eddy structures (ESs) for which a physical aspect ratio of $1.2:1:1$ in the axial, radial and azimuthal directions is observed. The other spectral domain, indicated by large wavelengths, is associated with very-large-scale motions (VLSMs). The wavelength marking the boundary between these spectral domains is used to decompose the velocity fluctuations into ES and VLSM components, and the corresponding ES and VLSM components of two-point correlations are obtained from the experimental data. The VLSM component of two-point correlations denotes helical structures as the dominant VLSMs in the jet turbulent region. Instantaneous axial velocity fluctuation fields from DNS support the prevalence of helical VLSMs in the jet. Moreover, the ES signatures are evident in the unwrapped axial–azimuthal planes of the DNS, indicating that the VLSMs are formed by the concatenation of ESs. Consistent with the experimental two-point correlations and DNS flow fields, a conceptual model is proposed for the ESs and VLSMs, which illustrates their arrangements.

In this work, we investigate the dynamics of long non-axisymmetric fibres in turbulent channel flow. The experimental facility is the TU Wien Turbulent Water Channel, consisting of a closed water channel (aspect ratio of 10), and the experiments are performed at a shear Reynolds number of 360. Fibres are neutrally buoyant rods that are curved and characterised by a length-to-diameter ratio of 120. Illumination is provided by a laser sheet and the motion of fibres is recorded by four high-speed cameras in a fully developed flow section. We apply multiplicative algebraic reconstruction techniques to the recorded images from four high-speed cameras to identify the three-dimensional location, shape and orientation of the fibres. The fibres are also tracked in time to obtain their three-dimensional vectors of velocity and rotation rate. We investigate the behaviour of the fibres, from the near-wall region to the channel centre, and we produce original statistics on the effect of curvature of the fibres on their orientation and rotation rate. Specifically, we measured the orientation and rotation rate of the fibres, and we can confirm that in the centre, the most homogeneous part of the channel, statistics, although influenced by the curvature, bear similarities to those obtained in previous investigations in homogeneous isotropic turbulence. In addition, we have been able to compare the tumbling rate of our long non-axisymmetric fibres with previous solutions for curved ellipsoids in simple shear flow.

We study the decay of compressible magnetohydrodynamic (MHD) turbulence, emphasizing exchanges of energy between compressive and incompressive kinetic energies, magnetic energy, and thermal energy. A recently developed high order finite difference code is employed for compressible runs with a Mach number up to 2. Varying the nature of the initial conditions (magnitudes of velocity and magnetic fluctuations), and initial Mach numbers permits examination of various dynamical regimes characterized here by the changes between different energy reservoirs. Acoustic waves are responsible for the oscillatory exchange between compressive kinetic and thermal energy through the pressure dilatation term. The results indicate that exchange between kinetic and magnetic energy is dominated by interactions involving the solenoidal velocity. Several systematic rapid adjustments are found to be reproducible with simple scalings derived from the empirical data.

A computational parameter study of the viscous axisymmetric supersonic flow over a double cone is made with a view to determining the boundary of the region in which such flows are unsteady. The study is restricted to the case when the boundary layer is laminar. The features of both the steady and unsteady flows in different characteristic regions of the parameter space are described. In particular, the phenomenon of pulsating flow typical of spiked blunt bodies (small first-cone angle, $\theta _1$, and large second-cone angle, $\theta _2$), is shown to be inviscid in nature. In $\theta _1$–$\theta _2$ space, the region of unsteady flow is enclosed in a loop with a lower and an upper $\theta _2$ branch with a maximum $\theta _1$ between. The location of the lower $\theta _2$ branch is determined by the second-cone detachment angle $\theta _{2d}$. For this reason, the gas model in one of the conditions is chosen to be thermally perfect carbon dioxide (at Mach number 8) for which $\theta _{2d}$ is quite large. In the other cases, the gas model is perfect-gas nitrogen at Mach numbers 2, 4 and 7.7. In the hypersonic range, within the uncertainties, and in the parameter range covered, the unsteadiness boundary is shown to depend on only three dimensionless parameters.

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with geostrophically balanced turbulent flows. Advection and refraction by such flows lead to wave scattering, redistributing IGW energy in the position–wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, makes no assumption of spatial scale separation, and neglects wave–wave interactions. It extends previous work restricted to near-inertial waves, barotropic flows or waves much shorter than the flow scales. The kinetic equation describes energy transfers that are restricted to IGWs with the same frequency, as a result of the time scale separation between waves and flow. We formulate the kinetic equation on the constant-frequency surface – a double cone in wavenumber space – using polar spherical coordinates, and we examine the form of the two scattering cross-sections involved, which quantify energy transfers between IGWs with, respectively, the same and opposite directions of vertical propagation. The kinetic equation captures both the horizontal isotropisation and the cascade of energy across scales that result from scattering. We focus our attention on the latter to assess the predictions of the kinetic equation against direct simulations of the three-dimensional Boussinesq equations, finding good agreement.

A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics is separated into deterministic contributions representing the global mode and a stochastic contribution representing the intrinsic turbulent forcing. Stochastic models are developed that account for the interaction between the two and allow the determination of the dynamic properties of the flow from stationary data. The deterministic contributions are modelled by an amplitude equation, which describes the oscillatory dynamics of the instability, and in a second approach by a mean-field model, which additionally captures the interaction between the instability and the mean-flow corrections. The stochastic contributions are considered as coloured noise forcing, representing the spectral characteristics of the stochastic turbulent perturbations. The methodology is applied to a turbulent swirling jet with a dominant global mode. Particle image velocimetry measurements are conducted to ensure that the mode is the most dominant coherent structure, and further pressure measurements provide long time series for the model calibration. The supercritical Hopf bifurcation is identified from the linear growth rate of the global mode, and the excellent agreement between measured and estimated statistics suggest that the model captures the relevant dynamics. This work demonstrates that the sole observation of limit-cycle oscillations is not sufficient to determine the stability of turbulent flows, since the stochastic perturbations obscure the actual bifurcation point. However, the proposed separation of deterministic and stochastic contributions in the dynamical model allows the identification of the flow state from stationary measurements.

The adjustment of equatorial pressure anomalies is studied using high-resolution numerical simulations within one- and two-layer shallow-water systems on a rotating sphere, which include a simple self-consistent parameterization of the dynamical effects of condensation (the so-called moist-convective shallow-water equations). A systematic generation of localized, moving eastward along the equator cyclonic pairs, termed the equatorial modons, is observed in the one-layer model for sufficiently intense initial perturbations. The modons are strongly enhanced by the moist convection. In the two-layer model with a relatively small depth ratio, baroclinic equatorial modons are also observed. In both the one-layer model and the baroclinic mode of the two-layer model, the emergence of a transient Gill pattern preceding the generation of modons is demonstrated. It is found that the breaking of circumnavigating moist Kelvin waves, generated in the adjustment process, induces extensive easterly jets, which weaken the eastward nonlinear advection tendency of the modons. Finally, an inductive generation of the modons over oceanic warm-pools, modelled as local humidity maxima, is discovered, and explained on the basis of conservation of moist potential vorticity.

The universality of the statistics of small-scale motions within the turbulent/non-turbulent interface (TNTI) layer that exists at the edges of turbulent free shear flows (i.e. mixing layers) and in turbulent boundary layers is analysed using direct numerical simulations of turbulent jets, wakes and in turbulent fronts evolving without mean shear. The Taylor based Reynolds number of the simulations is $Re_{\lambda } \gtrsim 200$ while the resolution is comparable to the Kolmogorov micro-scale ${\rm \Delta} x \approx \eta$. It is shown that, when properly normalised by using the local Kolmogorov velocity and length scales, the statistics of the vorticity, strain and related quantities, such as the invariants of the velocity gradient tensor, are universal, i.e. virtually equal for the same position within the TNTI layer, which implies the universality of the small-scale ‘nibbling’ associated with the turbulent entrainment mechanism. The results show that the small scales of motion near the TNTI layer are statistically very close to homogeneous, except for a distance of about 10 Kolmogorov micro-scales from the outer surface of the TNTI layer. The proposed normalisation allows for a much more clear identification of the viscous superlayer and the turbulent sublayer within the TNTI layer.

We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertically entering into initially calm water at constant speed. Surface tension, viscosity and the compressibility of the liquid are neglected. The flow is potential. The region of contact of the water with the body surface starts from a single point and grows monotonically in time. The effects of gravity on the size of the contact region, the hydrodynamic force on the body, the hydrodynamic pressure distribution on the wetted part of the body surface, and the free-surface elevation are analysed for the initial stage of impact, using asymptotic methods with a small-valued gravity-related parameter. It has been well accepted that the effects of gravity on water impact characteristics are small. The analysis reveals that the effects of gravity are relatively small even for impact conditions, where formally these effects should be included in the model. It is found that gravity: slows down the contact points, reduces the hydrodynamic pressure at the periphery of the contact region, but increases the pressure in the central part of the wetted region, and hence increases the total fluid force on the body. The asymptotic contributions are sensitive to the gravity correction to the size of the contact region, even though it is relatively small. The effects of gravity become more important with time for the later stages.

The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a region in the frequency space in which there are three real roots of the dispersion equation and hence three propagating modes. This multiplicity leads to mode conversion when scattering occurs. In one of these modes, the energy propagation direction is opposite to the wavenumber, making enforcement of the Sommerfeld radiation condition challenging. The focus here is on a canonical problem in flexural-gravity wave scattering, the scattering of waves by a crack. Formulae are developed that apply uniformly at all frequencies, including through the blocking frequencies. This solution is developed by tracking the movement of the dispersion relation roots carefully in the complex plane. The mode conversion is verified by the scattering matrix of the process and through an energy identity. This energy identity for the case of more than one progressive modes is established using Green's theorem and later applied in the scattering matrix to identify the incident and transmitted waves in the scattering process and derive the radiation condition. Appropriate scaling of the reflection and transmission coefficients are provided with the energy identity. The solution method is illustrated with numerical examples.

Flow of a semidilute neutrally buoyant and non-colloidal suspension is numerically studied in the Taylor–Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction ${\phi _b} = 0.1$, the radius ratio $(\eta = {r_i}/{r_o} = 0.877)$ and two particle size ratios $\mathrm{\epsilon }\,( = \; d\textrm{/}a) = 60,\;200$, where d is the gap width ($= {r_o} - {r_i}$) between cylinders, a is the suspended particles’ radius and $r_i$ and $r_o$ are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counter-rotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of $\mathrm{\epsilon } = 200$, the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of non-axisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of $\mathrm{\epsilon } = 60$; thus, the transitions occur following the sequence of CCF → SVF → WSVF → WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow.

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. This is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow–sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour–deposition patterns associated with the deployment of energy converters or other flow obstructions.

Miscible viscous fingering (VF) of the annulus of a more viscous fluid radially displaced by a less viscous fluid is investigated through both numerical computations and experimental study. We aim to understand how VF with finiteness in a radial displacement different from the classical radial VF and the instability of a slice displaced rectilinearly with a uniform velocity. It is observed that the VF of a miscible annular ring is a persistent phenomenon in contrast to the transient nature of VF of a miscible slice. Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time when diffusion is the ultimate dominating force. A statistical analysis is performed for the numerical data and it is found that the second moment of the averaged profile, variance, is a non-monotonic function of time, contrary to variance in classical radial VF and rectilinear VF with one fluid sandwiched between layers of another. The minimum in the variance indicates the interaction of two fronts which is visible in terms of pressure fingers, but not the concentration fingers indicating a faster growth of pressure than the concentration growth. In addition, for existence of critical parameters for instability in terms of viscosity contrast and amount of sample, the variation of the finger length with flow rate is found to be dependent on the amount of the more viscous fluid confined in the annulus.

We consider the active Brownian particle model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer obeys a Fokker–Planck equation defined on the configuration space, whose structure depends on the swimmer's shape, centre of rotation and domain of swimming. We enforce zero probability flux at the boundaries of configuration space. At first neglecting hydrodynamic interactions, we derive a reduced equation for a swimmer in an infinite channel, in the limit of small rotational diffusivity, and find that the invariant density depends strongly on the swimmer's precise shape and centre of rotation. We also give a formula for the mean reversal time: the expected time taken for a swimmer to completely reverse direction in the channel. Using homogenization theory, we find an expression for the effective longitudinal diffusivity of a swimmer in the channel, and show that it is bounded by the mean reversal time. Finally, we include hydrodynamic interactions with walls, and examine the role of shape.