Wind tunnel experiments are performed in both neutral and stable boundary layers to study the effect of thermal stability on the wake of a single turbine and on the wakes of two axially aligned turbines, thereby also showing the influence of the second turbine on the impinging wake. In the undisturbed stable boundary layers, the turbulence length scales are significantly smaller in the vertical and longitudinal directions (up to 50 % and $\approx$40 %, respectively), compared with the neutral flow, while the lateral length scale is unaffected. The reductions are larger with the imposed inversion of a second stable case, except in the near-wall region. In the neutral case, the length scales in the wake flow of the single turbine are reduced both vertically and laterally (up to 50 % and nearly 40 %, respectively). While there is significant upstream influence of a second turbine (on mean and turbulence quantities), there is virtually no upstream effect on vertical length scales. However, curiously, the presence of the second turbine aids length-scale recovery in both directions. Longitudinally, each turbine contributes to successive reduction in coherence. The effect of stability on the turbulence length scales in the wake flows is non-trivial: at the top of the boundary layer, the reduction in the wall-normal length scale is dominated by the thermal effect, while closer to the wall, the wake processes strongly modulate this reduction. Laterally, the turbines’ rotation promotes asymmetry, while stability opposes this tendency. The longitudinal coherence, significantly reduced by the wake flows, is less affected by the boundary layer's thermal stability.

Thermoacoustic devices represent a significant future opportunity in the fields of energy generation and refrigeration. A key component of this type of device is the regenerator, where the conversion between acoustic energy and thermal energy takes place. This conversion occurs due to an externally imposed temperature gradient on the walls of the regenerator channels. Hence, this paper concerns the physics of sound waves in the proximity of such walls. It establishes a new analytical framework which clarifies the disturbance energy conservation in thermoacoustic devices. In this framework, a thermoacoustic production term is proposed to quantify the generation or consumption of disturbance energy originating from the temperature gradient. An extended disturbance energy flux term is identified to account for wave growth or decay through the regenerator. The disturbance energy balance relation states that the disturbance energy flux equals the thermoacoustic production less the viscous and thermal dissipation resulting from gradients of fluctuating velocity and temperature. The analytical framework is implemented in an axisymmetric cylindrical domain; the two-dimensional nature of this work helps to uncover that the wave always decays in the region close to the wall. A dimensional analysis is conducted to identify the controlling parameters, namely the Womersley, Helmholtz and Prandtl numbers. A parametric study of the Womersley and Helmholtz numbers is conducted to showcase the new analytical methodology; the results make it possible to optimize the geometry, wave properties and working conditions of a thermoacoustic device according to the preference of its efficiency, loss and output.

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

We study the stability of steady convection rolls in two-dimensional Rayleigh–Bénard convection with free-slip boundaries and horizontal periodicity over 12 orders of magnitude in the Prandtl number $(10^{-6} \leq Pr \leq 10^6)$ and 6 orders of magnitude in the Rayleigh number $(8{\rm \pi} ^4 < Ra \leq 10^8)$. The analysis is facilitated by partitioning our modal expansion into so-called even and odd modes. With aspect ratio $\varGamma = 2$, we observe that zonal modes (with horizontal wavenumber equal to zero) can emerge only once the steady convection roll state consisting of even modes only becomes unstable to odd perturbations. We determine the stability boundary in the $(Pr,Ra)$ plane and observe remarkably intricate features corresponding to qualitative changes in the solution, as well as three regions where the steady convection rolls lose and subsequently regain stability as the Rayleigh number is increased. We study the asymptotic limit $Pr \to 0$ and find that the steady convection rolls become unstable almost instantaneously, eventually leading to nonlinear relaxation osculations and bursts, which we can explain with a weakly nonlinear analysis. In the complementary large-$Pr$ limit, we observe that the zonal modes at the instability switch off abruptly at a large, but finite, Prandtl number.

The growth of perturbations subject to the Crow instability along two vortex rings of equal and opposite circulation undergoing a head-on collision is examined. Unlike the planar case for semi-infinite line vortices, the zero-order geometry of the flow (i.e. the ring radius, core thickness and separation distance) and by extension the growth rates of perturbations vary in time. The governing equations are therefore temporally integrated to characterize the perturbation spectrum. The analysis, which considers the effects of ring curvature and the distribution of vorticity within the vortex cores, explains several key flow features observed in experiments. First, the zero-order motion of the rings is accurately reproduced. Next, the predicted emergent wavenumber, which sets the number of secondary vortex structures emerging after the cores come into contact, agrees with experiments, including the observed increase in the number of secondary structures with increasing Reynolds number. Finally, the analysis predicts an abrupt transition at a critical Reynolds number to a regime dominated by a higher-frequency, faster-growing instability mode that may be consistent with the experimentally observed rapid generation of a turbulent puff following the collision of rings at high Reynolds numbers.

The interaction of supercritical turbulent flows with granular sediment beds is challenging to study both experimentally and numerically. This challenging task has hampered advances in understanding antidunes, the most characteristic bedform of supercritical flows. This article presents the first numerical attempt to simulate upstream-migrating antidunes with geometrically resolved particles and a liquid–gas interface. Our simulations provide data at a resolution higher than laboratory experiments, and they can therefore provide new insights into the mechanisms of antidune migration and contribute to a deeper understanding of the underlying physics. To manage the simulations’ computational costs and physical complexity, we employ the cumulant lattice Boltzmann method in conjunction with a discrete element method for particle interactions, as well as a volume-of-fluid scheme to track the deformable free surface of the fluid. By reproducing two flow configurations of previous experiments (Pascal et al., Earth Surf. Process. Landf., vol. 46, issue 9, 2021, pp. 1750–1765), we demonstrate that our approach is robust and accurately predicts the antidunes’ amplitude, wavelength and celerity. Furthermore, the simulated wall shear stress, a key parameter governing sediment transport, is in excellent agreement with the experimental measurements. The highly resolved data of fluid and particle motion from our simulation approach open new perspectives for detailed studies of morphodynamics in shallow supercritical flows.

We present the analytical solution for the two-dimensional velocity and density fields within an approximation for laminar stratified inclined duct (SID) flows where diffusion dominates over inertia in the along-channel momentum equation but is negligible in the density transport equation. We refer to this approximation as the hydrostatic/gravitational/viscous in momentum and advective in density (HGV-A) approximation due to the leading balances in the governing equations. The analytical solution is valid for laminar flows in a two-layer configuration in the limit of long ducts. The non-dimensional volume flux within the HGV-A approximation is given by $Fr^* ={{Re}}_g/(AK)$, which is a control parameter with ${{Re}}_g$ the gravitational Reynolds number, $A$ the aspect ratio of the duct and $K$ a geometrical parameter that depends on the tilt of the duct and is obtained from the analytical solution. This analytical solution was validated against results from laboratory experiments, and allows us to gain new insight into the dynamics and properties of SID flows. Most importantly, constant values of $Fr^*$ describe, in both horizontal and inclined ducts, the transitions between increasingly turbulent flow regimes: from laminar flow, to interfacial waves, to intermittent turbulence and sustained turbulence.

Understanding particle motion in narrow channels can guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of fluid-filled channel walls can slow down or increase the dispersion of tracer particles via entropic trapping in the wall bulges or hydrodynamic flows induced by wall fluctuations, respectively. Previous studies concentrated primarily on the case of a single Brownian tracer. Here, we address what happens when there is a large ensemble of interacting Brownian tracers – a common situation in applications. Introducing repulsive interactions between tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon reminiscent of that seen for single tracers in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of tracers numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Interactions between the fluctuating wall and the now-nearby particles then drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, our perturbation theory quantifies dispersion in generic advection–diffusion systems.

We investigate the dynamics and energy production capability of a flexible piezoelectric plate submerged close to the free surface and exposed to incident head gravity waves and current. A theoretical model is derived in which the flag and its wake are represented with a vortex line while the body of the fluid is considered to be inviscid. The model is employed to describe the hydrodynamic interactions between a flexible plate, its wake, gravity incident waves and the current. The model reveals two distinct vibration states of a piezoelectric device corresponding to almost similar optimal energy production levels. The first is associated with the cantilever fluttering mode of the plate, with limited dependency on the plate's flexibility across different Froude numbers and incoming wave frequencies. The other resembles the flow-induced flapping mode in more flexible plates, with the energy output showing a higher dependency on plate flexibility. The concurrent existence of these two energetic modes allows adjustment of the plate length to consistently achieve the maximum energy production level across different flow conditions. The role of the Froude number of the system's responses is explored and correlated to the appearance of gravity wave groups on the surface, each propagating with a different wavenumber. It is shown that a submergence depth of less than half of the body length is required to reach a high energetic condition in subcritical and critical flows. Finally, the optimal inductive and resistive values are related to proper matching between flow, mechanical and electrical time scales.

The present study is focused on obtaining the inviscid flow solution for a circular cylinder traversing steadily across an unbounded uniform-shear flow. The work is motivated by understanding the aerodynamics of bodies traversing across a shear flow, as well as by developing an understanding of fundamental concepts that are well understood for uniform free stream but not in the presence of shear. The results show that, in general, the presence of shear makes it impossible to define a unique approach-stream incidence angle $\unicode[STIX]{x1D6FC}$ relative to the cylinder. However, in the limit of, what we have termed ‘quasi-uniform’ flow, such an angle can be defined. We show that in this limit, the flow is also quasi-steady, and the static-cylinder solution can be used to solve for the moving-cylinder problem with good accuracy. This ‘quasi-uniform and quasi-steady’ (QUS) condition is attained when a single unsteadiness parameter $\dot{U}_{o}^{+}$ approaches zero. For small values of the cylinder-to-free-stream velocity ratio $V_{r}$, $\dot{U}_{o}^{+}\approx K_{eff}V_{r}$, where $K_{eff}$ is the effective non-dimensional shear rate. Away from the QUS flow limit, the flow field and the surface pressure distribution are significantly different between the moving and the static cylinders. However, a surprising result is that regardless of whether QUS conditions hold, the force acting on the moving cylinder in a Galilean frame of reference is always the same as that on a static cylinder in uniform-shear free stream but with non-dimensional shear rate and incidence angle equal to the moving cylinder’s instantaneous $K_{eff}$ and $\tan ^{-1}(V_{r})$, respectively.

The dynamics of turbulent flows past lateral cavities is relevant for multiple environmental applications. In rivers and coastal environments, these lateral recirculating regions constitute surface storage zones, where large-scale turbulent coherent structures control the transport and fate of contaminants. Mass transport in these flows is typically represented by one-dimensional first-order equations that predict the evolution of the spatially integrated concentration between the cavity and the main channel. These models, however, cannot represent the long-term evolution of the concentration or incorporate memory effects induced by turbulence. In this investigation, we carry out large-eddy simulations (LES) of the open-channel flow with a lateral square cavity of Mignot et al. (Phys. Fluids, vol. 28, issue 4, 2016, 045104). The model is coupled with an advection–diffusion equation and a Lagrangian particle model to investigate the transport mechanisms in the cavity and across the interface. From the simulations we provide quantitative comparisons of the physical processes from both perspectives, and investigate the effects of turbulent coherent structures on residence times and trajectories from finite-time Lyapunov exponents. From the Lagrangian results, we identify general spatial distributions of time scales in the cavity associated with the dynamics of coherent structures, providing new insights into the mechanisms that drive the global transport. We also show that an upscaled model informed by LES and based on a fractional derivative captures the evolution of concentration, and the exchange between the cavity and the main channel, providing accurate predictions of mass transport and reproducing the temporal dependence observed at larger scales.

Motile bacteria play essential roles in biology that rely on their dynamic behaviours, including their ability to navigate, interact and self-organize. However, bacteria dynamics on fluid interfaces are not well understood. Swimmers adsorbed on fluid interfaces remain highly motile, and fluid interfaces are highly non-ideal domains that alter swimming behaviour. To understand these effects, we study flow fields generated by Pseudomonas aeruginosa PA01 in the pusher mode. Analysis of correlated displacements of tracers and bacteria reveals dipolar flow fields with unexpected asymmetries that differ significantly from their counterparts in bulk fluids. We decompose the flow field into fundamental hydrodynamic modes for swimmers in incompressible fluid interfaces. We find an expected force-doublet mode corresponding to propulsion and drag at the interface plane, and a second dipolar mode, associated with forces exerted by the flagellum on the cell body in the aqueous phase that are countered by Marangoni stresses in the interface. The balance of these modes depends on the bacteria's trapped interfacial configurations. Understanding these flows is broadly important in nature and in the design of biomimetic swimmers.

In this paper the three-dimensional finite-time Lyapunov exponent (FTLE) field of a direct numerical simulation of a flat-plate turbulent boundary layer is analysed in several wall-parallel sections. The data consider a case at a low subsonic Mach number with a moderate positive pressure gradient in the streamwise direction. In contrast to other studies mainly focusing on the maxima of the FTLE field, particular emphasis is placed on the regions of minimal stretching between the vortices and shear layers of the three-dimensional turbulent flow field. These visually appear as contiguous islands or ‘valleys’ between the ‘ridges’ of the FTLE maxima, both at forward and backward integration of the flow field in time. To clearly distinguish the structures investigated from their more common counterparts (e.g. Lagrangian coherent structures, LCS), the acronym LAMS (Lagrangian areas of minimal stretching) is proposed to denote the associated cohesive fluid regions. Consistent with intuition, the largest LAMS occur near the boundary-layer edge, where large regions of homogeneous laminar external flow coexist with upwelling turbulent structures. Compensating for turbulent regions pushing upward, they sink from there down toward the wall, becoming smaller and longer. This process is associated with an increased relative velocity of the LAMS compared with the mean flow, which is observed over the whole boundary layer in the range $y^+ \gtrsim 10$. Furthermore, it is observed that the Q4 (sweep) events contained in the LAMS clearly dominate over Q2 (ejection) events above $y^+ \approx 10$. Thereby, local maxima occur at $y^+ \approx 20$ and near the boundary-layer edge. Below $y^+ \approx 10$, the relationship reverses. Sweeping LAMS from above $y^+ \approx 10$ and ejecting LAMS from below meet in the layer where the maximal vortical activity occurs. The latter is caused by mostly streamwise oriented vortices with maximal vortex stretching in the streamwise direction. Overall, LAMS are associated with cohesive fluid regions between the surrounding vortices and shear layers that both drop down from the boundary-layer edge toward the wall in the outer region of the boundary layer and lift from the wall in the near-wall region.

The present study investigates the linear spatio-temporal and weakly nonlinear stability of a pressure-driven two-layer channel flow subjected to a wall-normal temperature gradient commonly encountered in industrial applications. The liquid–liquid interface tension is assumed to be a linearly decreasing function of temperature. The study employs both numerical (pseudo-spectral method) and long-wave approaches. The general linear stability analysis (GLSA) predicts shear-flow and thermocapillary modes that arise due to the imposed pressure and temperature gradients, respectively. The previous stability analyses of the same problem predicted a negligible effect of the pressure-driven flow on the linear stability of the system. However, the GLSA reveals stabilising and destabilising effects of the pressure-driven flow depending on the viscosity ratio ($\mu _r$), thermal conductivity ratio ($\kappa _r$), interface position ($H$) and the sign of the imposed temperature gradient ($\beta _1$). The analysis predicts a range of $H$ for given $\mu _r$ and $\kappa _r$, which can not be stabilised by the thermocapillarity. The numerically predicted long-wave instability is then captured using the long-wave asymptotic approach. The arguments based on the physical mechanism further successfully explain the role of $\mu _r$, $\kappa _r$, $H$, the sign of $\beta _1$ and the interaction between the velocity and temperature perturbations in stabilising/destabilising the flow. The spatio-temporal analysis reveals the dominance of the spanwise mode in causing the absolutely unstable flow. The weakly nonlinear analysis reveals a subcritical pitchfork bifurcation without shear flow. However, with the shear flow, the streamwise mode undergoes a supercritical Hopf bifurcation.

The starting vortex generated at the trailing edge of a flat plate, that is impulsively translated at fixed angle of attack, is a widely studied canonical problem. Recent work that examined the effect of plate rotation on this starting vortex found that two new and distinct vortex sheet types can arise. We generalise this work to study the starting vortex generated at any sharp and straight edge of an arbitrary body under a general time-dependent two-dimensional motion. The dimensionless velocity field of the attached flow near any sharp edge is assumed to take the form, $\hat {z}^{-1/2} f(T) + g(T) + o (1)$, where $\hat {z}$ is the dimensionless position referenced to the edge, $f(T)$ and $g(T)$ are functions of dimensionless time, $T$, associated with the local flow perpendicular and parallel to the edge, respectively. This enables starting vortices to be generally calculated and their types related by simply inspecting the forms of $f(T)$ and $g(T)$. We elucidate the physics underlying all three vortex types and show that these vortices are generated by pure translation of the sharp edge. Several case studies are explored, including the leading/trailing edge vortices of a flat plate which can simultaneously be of different type (relevant to low-speed aircraft), the vortex formed by translation of a semi-infinite flat plate and the trailing-edge vortex of Joukowski aerofoils. With the ability to calculate the vortices at all edges, the theory is used to develop a general formula for the lift force of a flat plate which can find application in practice.