Internal phoretic flows due to the interactions of solid boundaries with local chemical gradients may be created using chemical patterning. Alternatively, we demonstrate here that internal flows might also be induced by geometric asymmetries of chemically homogeneous surfaces. We characterise the circulatory flow created in a cavity enclosed between two eccentric cylindrical walls of uniform chemical activity. Local gradients of the diffusing solute induce a slip flow along the surface of the cylinders, leading to a circulatory bulk flow pattern which can be solved analytically in the diffusive limit. The flow strength can be controlled by adjusting the relative positions of the cylinders, and an optimal configuration is identified. These results provide a model system for tunable phoretic pumps.

The generation of indirect combustion noise by compositional inhomogeneities is examined theoretically. For this, the compact-nozzle theory of Marble & Candel (J. Sound Vib., vol. 55 (2), 1977, pp. 225–243) is extended to a multi-component gas mixture, and the chemical potential function is introduced as an additional acoustic source mechanism. Transfer functions for subcritical and supercritical nozzle flows are derived, and the contribution of compositional noise is compared to entropy noise and direct noise by considering an idealized nozzle downstream of the combustor exit. It is shown that compositional noise is dependent on the local mixture composition and can exceed entropy noise for fuel-lean conditions and supercritical nozzle flows. This suggests that the compositional indirect noise requires potential consideration with the implementation of low-emission combustors.

Impulsively started, low-aspect-ratio elliptical flat plates have been investigated experimentally to understand the vortex pinch-off dynamics at transitional and fully turbulent Reynolds numbers. The range of Reynolds numbers investigated is representative of those observed in animals that employ rowing and paddling modes of drag-based propulsion and manoeuvring. Elliptical flat plates with five aspect ratios ranging from one to two have been considered, as abstractions of propulsor planforms found in nature. It has been shown that Reynolds-number scaling is primarily determined by plate aspect ratio in terms of both drag forces and vortex pinch-off. Due to vortex-ring growth time scales that are longer than those associated with the development of flow instabilities, the scaling of drag is Reynolds-number-dependent for the aspect-ratio-one flat plate. With increasing aspect ratio, the Reynolds-number dependency decreases as a result of the shorter growth time scales associated with high-aspect-ratio elliptical vortex rings. Large drag peaks are observed during early-stage vortex growth for the higher-aspect-ratio flat plates. The collapse of these peaks with Reynolds number provides insight into the evolutionary convergence process of propulsor planforms used in drag-based swimming modes over diverse scales towards aspect ratios greater than one.

TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions $L$ : $D$ : $W$$=$ 6 : 1 : 2 to unsteadiness. The steady laminar three-dimensional flow loses stability at $\mathit{Re}_{D,cr}\approx 1080$ as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.

A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\times 10^{4}$, $Re_{o}=1.1\times 10^{5}$ and $Re_{o}=2.2\times 10^{5}$. The ratio of radii ${\it\eta}=r_{i}/r_{o}$ was fixed to ${\it\eta}=0.909$ to mitigate the effects of curvature. Axially periodic boundary conditions were used, with the aspect ratio of vertical periodicity ${\it\Gamma}$ fixed to ${\it\Gamma}=2.09$. Being linearly stable, TC flow with outer cylinder rotation is known to have very different behaviour than TC flow with pure inner cylinder rotation. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

A submerged body subject to a sudden shape change experiences large forces due to the variation of added-mass energy. While this phenomenon has been studied for single actuation events, application to sustained propulsion requires the study of periodic shape change. We do so in this work by investigating a spring–mass oscillator submerged in quiescent fluid subject to periodic changes in its volume. We develop an analytical model to investigate the relationship between added-mass variation and viscous damping, and demonstrate its range of application with fully coupled fluid–solid Navier–Stokes simulations at large Stokes number. Our results demonstrate that the recovery of added-mass kinetic energy can be used to completely cancel the viscous damping of the fluid, driving the onset of sustained oscillations with amplitudes as large as four times the average body radius $r_{0}$. A quasi-linear relationship is found to link the terminal amplitude of the oscillations $X$ to the extent of size change $a$, with $X/a$ peaking at values from 4 to 4.75 depending on the details of the shape-change kinematics. In addition, it is found that pumping in the frequency range of $1-a/2r_{0}<{\it\omega}^{2}/{\it\omega}_{n}^{2}<1+a/2r_{0}$, with ${\it\omega}/{\it\omega}_{n}$ being the ratio between frequency of actuation and natural frequency, is required for sustained oscillations. The results of this analysis shed light on the role of added-mass recovery in the context of shape-changing bodies and biologically inspired underwater vehicles.

The flux Richardson number $R_{f}$ (often referred to as the mixing efficiency) is a widely used parameter in stably stratified turbulence which is intended to provide a measure of the amount of turbulent kinetic energy $k$ that is irreversibly converted to background potential energy (which is by definition the minimum potential energy that a stratified fluid can attain that is not available for conversion back to kinetic energy) due to turbulent mixing. The flux Richardson number is traditionally defined as the ratio of the buoyancy flux $B$ to the production rate of turbulent kinetic energy $P$. An alternative generalized definition for $R_{f}$ was proposed by Ivey & Imberger (J. Phys. Oceanogr., vol. 21, 1991, pp. 650–658), where the non-local transport terms as well as unsteady contributions were included as additional sources to the production rate of $k$. While this definition precludes the need to assume that turbulence is statistically stationary, it does not properly account for countergradient fluxes that are typically present in more strongly stratified flows. Hence, a third definition that more rigorously accounts for only the irreversible conversions of energy has been defined, where only the irreversible fluxes of buoyancy and production (i.e. the dissipation rates of $k$ and turbulent potential energy ($E_{PE}^{\prime }$)) are used. For stationary homogeneous shear flows, all of the three definitions produce identical results. However, because stationary and/or homogeneous flows are typically not found in realistic geophysical situations, clarification of the differences/similarities between these various definitions of $R_{f}$ is imperative. This is especially true given the critical role $R_{f}$ plays in inferring turbulent momentum and heat fluxes using indirect methods, as is commonly done in oceanography, and for turbulence closure parameterizations. To this end, a careful analysis of two existing direct numerical simulation (DNS) datasets of stably stratified homogeneous shear and channel flows was undertaken in the present study to compare and contrast these various definitions. We find that all three definitions are approximately equivalent when the gradient Richardson number $Ri_{g}\leqslant 1/4$. Here, $Ri_{g}=N^{2}/S^{2}$, where $N$ is the buoyancy frequency and $S$ is the mean shear rate, provides a measure of the stability of the flow. However, when $Ri_{g}>1/4$, significant differences are noticeable between the various definitions. In addition, the irreversible formulation of $R_{f}$ based on the dissipation rates of $k$ and $E_{PE}^{\prime }$ is the only definition that is free from oscillations at higher gradient Richardson numbers. Both the traditional definition and the generalized definition of $R_{f}$ exhibit significant oscillations due to the persistence of linear internal wave motions and countergradient fluxes that result in reversible exchanges between $k$ and $E_{PE}^{\prime }$. Finally, we present a simple parameterization for the irreversible flux Richardson number $R_{f}^{\ast }$ based on $Ri_{g}$ that produces excellent agreement with the DNS results for $R_{f}^{\ast }$.

A novel reduced-order model for time-varying nonlinear flows arising from a resolvent decomposition based on the time-mean flow is proposed. The inputs required for the model are the mean-flow field and a small set of velocity time-series data obtained at isolated measurement points, which are used to fix relevant frequencies, amplitudes and phases of a limited number of resolvent modes that, together with the mean flow, constitute the reduced-order model. The technique is applied to derive a model for the unsteady three-dimensional flow in a lid-driven cavity at a Reynolds number of 1200 that is based on the two-dimensional mean flow, three resolvent modes selected at the most active spanwise wavenumber, and either one or two velocity probe signals. The least-squares full-field error of the reconstructed velocity obtained using the model and two point velocity probes is of the order of 5 % of the lid velocity, and the dynamical behaviour of the reconstructed flow is qualitatively similar to that of the complete flow.

An analytical model is proposed for flow around a plane bubble rising steadily in a channel. The fluid surrounding the bubble is assumed to be inviscid, and the flow is assumed to be irrotational. The resulting potential flow is sought as the sum of a uniform stream and a source in the unit strip. Explicit expressions for the bubble shape and rise velocity, and for the streamlines, are given as functions of the dimensionless surface tension. The predictions are in good agreement with existing experimental and numerical results.

The mean velocity profile (MVP) in thermally stratified atmospheric surface layers (ASLs) deviates from the classic logarithmic form. A theoretical framework was recently proposed (Katul et al.Phys. Rev. Lett., vol. 107, 2011, 268502) to link the MVP to the spectrum of turbulence and was found to successfully predict the MVP for unstable stratification. However, the theory failed to reproduce the MVP in stable conditions (Salesky et al.Phys. Fluids, vol. 25, 2013, 105101), especially when ${\it\zeta}>0.2$ (where ${\it\zeta}$ is the atmospheric stability parameter). In the present study, it is demonstrated that this shortcoming is due to the failure to identify the appropriate length scale that characterizes the size of momentum transporting eddies in the stable ASL. Beyond ${\it\zeta}\approx 0.2$ (near where the original theory fails), the Ozmidov length scale becomes smaller than the distance from the wall $z$ and hence is a more stringent constraint for characterizing the size of turbulent eddies. An expression is derived to connect the Ozmidov length scale to the normalized MVP (${\it\phi}_{m}$), allowing ${\it\phi}_{m}$ to be solved numerically. It is found that the revised theory produces a prediction of ${\it\phi}_{m}$ in good agreement with the widely used empirical Businger–Dyer relation and two experimental datasets in the stable ASL. The results here demonstrate that the behaviour of ${\it\phi}_{m}$ in the stable ASL is closely linked to the size of momentum transporting eddies, which can be characterized by the Ozmidov scale under mildly to moderately stable conditions ($0.2<{\it\zeta}<1-2$).

The focus of this study is to analyse the tip region of a hydraulic fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a fracture through the concept of a hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a hydraulic fracture is analysed by focusing on steady propagation of a semi-infinite hydraulic fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite hydraulic fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.

We report on a study, employing direct numerical simulations, of the turbulent/non-turbulent interface of a wake in a stably stratified fluid. It is found that thresholds for both enstrophy and potential enstrophy are needed to identify the interface. Using conditional averaging relative to the location of the interface, various quantities of interest are examined. The thickness of the interface is found to scale with the Kolmogorov scale. From an examination of the Ozmidov and Kolmogorov length scales as well as the buoyancy Reynolds number, it is found that the buoyancy Reynolds number decreases and becomes of order 1 near the interface, indicating the suppression of the turbulence there by the stable stratification. Finally the overall rate of loss of energy due to internal wave radiation is found to be comparable to the overall rate of loss due to turbulent kinetic energy dissipation.

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.

We present two spanwise-localized travelling-wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.

Parallel shear flows cannot be kinematic dynamos on their own (Zel’dovich, Sov. Phys. JETP, vol. 4, 1957, pp. 460–462), but the addition of small flow perturbations can trigger dynamo action. Using an optimization algorithm inspired by Willis (Phys. Rev. Lett., vol. 109 (25), 2012, 251101) and Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we identify the smallest perturbation that when added to Kolmogorov flow can trigger dynamo action at some fixed value of the magnetic Reynolds number. In this way we numerically measure the fragility of the Zel’dovich anti-dynamo theorem. The minimal perturbations have surprisingly simple spatial structures. Their magnitudes vary inversely proportional to the magnetic Reynolds number and are always much larger than theoretical lower bounds calculated here using the methods of Proctor (Geophys. Astrophys. Fluid Dyn., vol. 98 (3), 2004, pp. 235–240; J. Fluid Mech., vol. 697, 2012, pp. 504–510).

The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and find that the vortical-interaction network can be characterized by a weighted scale-free network. It is found that the turbulent flow network retains its scale-free behaviour until the characteristic value of circulation reaches a critical value. Furthermore, we show that the two-dimensional turbulence network is resilient against random perturbations, but can be greatly influenced when forcing is focused towards the vortical structures, which are categorized as network hubs. These findings can serve as a network-analytic foundation to examine complex geophysical and thin-film flows and take advantage of the rapidly growing field of network theory, which complements ongoing turbulence research based on vortex dynamics, hydrodynamic stability, and statistics. While additional work is essential to extend the mathematical tools from network analysis to extract deeper physical insights of turbulence, an understanding of turbulence based on the interaction-based network-theoretic framework presents a promising alternative in turbulence modelling and control efforts.

What is the turbulent drag force experienced by an object moving in a rotating fluid? This open and fundamental question can be addressed by measuring the torque needed to drive an impeller at a constant angular velocity ${\it\omega}$ in a water tank mounted on a platform rotating at a rate ${\it\Omega}$. We report a dramatic reduction in drag as ${\it\Omega}$ increases, down to values as low as 12 % of the non-rotating drag. At small Rossby number $Ro={\it\omega}/{\it\Omega}$, the decrease in the drag coefficient $K$ follows the approximate scaling law $K\sim Ro$, which is predicted in the framework of nonlinear inertial-wave interactions and weak-turbulence theory. However, stereoscopic particle image velocimetry measurements indicate that this drag reduction instead originates from a weakening of the turbulence intensity in line with the two-dimensionalization of the large-scale flow.

We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number $Fr={\it\epsilon}_{k}/(Nu^{2})$, where ${\it\epsilon}_{k}$ is the kinetic energy dissipation, $u$ is a turbulent horizontal velocity scale and $N$ is the Brunt–Väisälä frequency. For $Fr\gg 1$, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as ${\it\Gamma}\propto Fr^{-2}$, where ${\it\Gamma}={\it\epsilon}_{p}/{\it\epsilon}_{k}$ and ${\it\epsilon}_{p}$ is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with $Fr\ll 1$, we argue that ${\it\Gamma}$ should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of $Fr$ and confirm that at high $Fr$, ${\it\Gamma}\propto Fr^{-2}$, while at low $Fr$ it approaches a constant value close to ${\it\Gamma}=0.33$. The parametrization of ${\it\Gamma}$ based on $Re_{b}$ due to Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of ${\it\Gamma}$ in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value $Fr=0.3$ found in our simulations.

An experiment on a flat rectangular plate facing a uniform flow at $Re=264\,000$ shows the importance of the base pressure loading on the asymmetric static modes of the turbulent wake. The plate is free to rotate around its short symmetry axis. For plates with aspect ratio ${\it\kappa}<6$, the angular position exhibits strong random discontinuities between steady states of non-zero angles. The steady states have long time durations, more than one order of magnitude greater than the convective time scale. The discontinuities, comparable to rare and violent events, are due to strong fluid forces associated with a drastic global change of the three-dimensional wake – mainly the switching between the static asymmetric modes. A clear transition occurs at ${\it\kappa}=6$, for which the angular fluctuations are minimum, leading for ${\it\kappa}>6$ to a classical fluid structure interaction with periodic fluctuations. The transition is supported by a recent global stability analysis of rectangular fixed plates in the laminar regime.

Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.