The study concerns a slender, heavy body moving with streamwise velocity in a boundary layer. Modelling assumptions on body size reduce the governing equations for the body motion to a pair of nonlinear integro-differential equations (IDEs) which displays a wide range of distinguished behaviours, including eventual collision with the wall (‘crash’), escape to infinity (‘fly away’) and repeatedly travelling far from the wall and back again without ever colliding or escaping (‘bouncing’). The paper gives a survey of the variety of behaviour, as well as asymptotic analysis and insight into each category of fluid/body interaction and the conditions under which crash, fly away and bouncing occur.

Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.

Experiments are performed to investigate the effect of nose-tip bluntness on the instability mechanisms leading to boundary-layer transition on a $7^{\circ }$ half-angle cone in a Mach-6 free stream. The development of disturbances is characterized using a combination of high-speed calibrated schlieren images and pressure measurements, and the data are compared with results computed using the parabolized stability equations. The approximately 414 mm long cone model is equipped with an interchangeable nose tip ranging from sharp to 5.08 mm in radius. For nose tips with a radius $R_{N}<2.54\ {\rm mm}$, second-mode instability waves are the dominant mechanism leading to transition. Time-averaged frequency spectra computed from the calibrated schlieren visualizations and pressure measurements are used to compute the second-mode most-amplified frequencies and integrated amplification rates ($N$ factors). Good agreement is observed between the measurements and computations in the linear-growth regime for the sharp-nose configuration at each free-stream condition. Additionally, a bispectral analysis identifies quadratic phase locking of frequency content responsible for the growth of higher harmonics. For nose tips of $R_{N}\geqslant 2.54\ {\rm mm}$, the schlieren visualization region is upstream of the entropy-layer swallowing length, and second-mode waves are no longer visible within the boundary layer; instead, elongated, steeply inclined features believed to be associated with non-modal instability mechanisms develop between the entropy-layer and boundary-layer edges. Simultaneously acquired surface pressure measurements reveal high-frequency pressure oscillations similar to second-mode instability waves associated with the trailing edge of these non-modal features.

The flow of non-spherical grains is strongly affected by the orientation of the grains, as observed in experiments and simulations. An existing model that predicts the orientation of grains as a function of the flow field and shape of the grains, is limited to homogenous orientational fields where the interaction of the grains with their surroundings is negligible. To address this limitation, we generalized the model to account for inhomogeneous orientational fields in the form of spatial non-convective orientational flux. The orientational flux accounts for the interactions of grains with their surroundings and the boundaries. The proposed model is used to study the influence of orientational diffusion and boundary conditions on the flow of dense granular material down an incline. It is shown that the boundary conditions can play a significant role in the orientation of grains in such flows.

Bileaflet mechanical heart valves (BMHV) create unphysiological turbulent flow. Such turbulent flow involves multiple instability mechanisms interacting with one another in a confined geometry. For instance, an impinging leading-edge vortex (ILEV) instability creates disturbances at the leading edge of the valve leaflets, while potentially promoting turbulence downstream of the BMHV (Zolfaghari and Obrist, Phys. Rev. Fluids, vol. 4, 2019). In this article, we use adjoint-based methods to study the structural sensitivity of the ILEV instability in the BMHV, and to quantify the role of this instability in the maximum disturbance energy growth in the wake of the BMHV. We first present a direct numerical simulation to show the effect of the ILEV instability on the turbulent flow in the wake of the valve. Second, we perform a modal linear stability analysis on a two-dimensional subdomain attached to the leading edge of one leaflet. We investigate the sensitivity of the global modes associated with this flow using their adjoints, and then show a passive control scenario using a local feedback source. This results in a partial improvement in the flow oscillations downstream of the leaflets. We finally present a non-modal approach to identify the optimal initial conditions for achieving maximum energy growth at arbitrary locations. We show that, for sufficiently large times, the optimal initial condition for highest energy growth in the wake points at the leading edge, which includes the ILEV instability. Our study illustrates that an improved leading-edge shape can effectively reduce turbulence in the wake of the BMHV.

The properties of bubble-laden turbulent flows at different scales are investigated experimentally, focusing on the flow kinetic energy, energy transfer and extreme events. The experiments employed particle shadow velocimetry measurements to measure the flow in a column generated by a homogeneous bubble swarm rising in water, for two different bubble diameters ($2.7$ mm and $3.9$ mm) and moderate gas volume fractions ($0.26\,\%\sim 1.31\,\%$). The two velocity components were measured at high resolution, and used to construct structure functions up to twelfth order for separations spanning the small to large scales in the flow. Concerning the flow anisotropy, the velocity structure functions are found to differ for separations in the vertical and horizontal directions of the flow, and the cases with smaller bubbles are the most anisotropic, with a dependence on void fraction. The degree of anisotropy is shown to increase as the order of the structure functions is increased, showing that extreme events in the flow are the most anisotropic. Our results show that the average energy transfer with the horizontal velocity component is downscale, just as for the three-dimensional single-phase turbulence. However, the energy transfer associated with the vertical component of the fluid velocity is upscale. The probability density functions of the velocity increments reveal that extreme values become more probable with decreasing Reynolds number, the opposite of the behaviour in single-phase turbulence. We visualize those extreme events and find that regions of intense small-scale velocity increments occur near the turbulent/non-turbulent interface at the boundary of the bubble wake.

Using direct numerical simulations of rotating Rayleigh–Bénard convection, we explore the transitions between turbulent states from a three-dimensional (3-D) flow state towards a quasi-2-D condensate known as the large-scale vortex (LSV). We vary the Rayleigh number $Ra$ as control parameter and study the system response (strength of the LSV) in terms of order parameters, assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the region of existence of the LSV in parameter space, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as a memoryless abrupt growth dynamics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system.

This article presents a three-dimensional theory of vorticity creation on generalised interfaces, including both non-slip and free-slip boundaries, which generalises a previous two-dimensional formulation (Terrington et al., J. Fluid Mech., vol. 890, 2020, p. A5). Under this description, vorticity may be created on a boundary by the inviscid relative acceleration between fluid elements on each side of the boundary, driven by either tangential pressure gradients or body forces. Viscosity acts to transfer circulation between the vortex sheet representing the slip velocity on the interface, and the fluid interior, but is not responsible for the creation of vorticity on the interface. This formulation also describes a principle of vorticity conservation for interfacial and free-surface flows: in many flow configurations, the net generation of vorticity on the interface is zero, and the total circulation remains constant throughout flow evolution.

We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin–Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilise by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than ${\sim}(k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$, destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth of total interface length in time. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface.

The stability of periodic travelling waves on fluid of infinite depth is examined in the presence of a constant background shear field. The effects of gravity and surface tension are ignored. The base waves are described by an exact solution that was discovered recently by Hur and Wheeler (J. Fluid Mech., vol. 896, 2020). Linear growth rates are calculated using both an asymptotic approach valid for small-amplitude waves and a numerical approach based on a collocation method. Both superharmonic and subharmonic perturbations are considered. Instability is shown to occur for any non-zero amplitude wave.

We study the properties of energy flux in wave turbulence via the Majda–McLaughlin– Tabak (MMT) equation with a quadratic dispersion relation. One of our purposes is to resolve the inter-scale energy flux $P$ in the stationary state to elucidate its distribution and scaling with spectral level. More importantly, we perform a quartet-level decomposition of $P=\sum _\varOmega P_\varOmega$, with each component $P_\varOmega$ representing the contribution from quartet interactions with frequency mismatch $\varOmega$, in order to explain the properties of $P$ as well as to study the wave turbulence closure model. Our results show that the time series of $P$ closely follows a Gaussian distribution, with its standard deviation several times its mean value $\bar {P}$. This large standard deviation is shown to result mainly from the fluctuation of the quasi-resonances, i.e. $P_{\varOmega \neq 0}$. The scaling of spectral level with $\bar {P}$ exhibits $\bar {P}^{1/3}$ and $\bar {P}^{1/2}$ at high and low nonlinearity, consistent with the kinetic and dynamic scalings, respectively. The different scaling laws in the two regimes are explained through the dominance of quasi-resonances ($P_{\varOmega \neq 0}$) and exact-resonances ($P_{\varOmega =0}$) in the former and latter regimes. Finally, we investigate the wave turbulence closure model, which connects fourth-order correlators to products of pair correlators through a broadening function $f(\varOmega )$. Our numerical data show that consistent behaviour of $f(\varOmega )$ can be observed only upon averaging over a large number of quartets, but with such $f(\varOmega )$ showing a somewhat different form from the theory.