Solid particles trapped in an acoustic standing wave have been observed to undergo propulsion. This phenomenon has been attributed to the generation of a steady streaming flow, with a reversal in the propulsion direction at a distinct frequency. We explain the mechanism underlying this reversal by considering the canonical problem of a sphere executing oscillatory rotation in an unbounded fluid that undergoes rectilinear oscillation; these two oscillations occur at identical frequency but with an arbitrary phase difference. Two distinct bifurcations in the flow field occur: (1) a stagnation point first forms with increasing frequency, which (2) splits into a saddle node and a vortex centre. Reversal in the propulsion direction is driven by reversal in the flow far from the sphere, which coincides with the second bifurcation. This flow is identified with that of a Stokeslet whose strength is the net force exerted on the particle, which has implications for studying the flow field around particles of non-spherical geometries and for modelling suspensions of particles in acoustic fields.

The squirmer is a popular model to analyse the fluid mechanics of a self-propelled object, such as a micro-organism. We demonstrate that some fore–aft symmetric squirmers can spontaneously self-propel above a critical Reynolds number. Specifically, we numerically study the effects of inertia on spherical squirmers characterised by an axially and fore–aft symmetric ‘quadrupolar’ distribution of surface-slip velocity; under creeping-flow conditions, such squirmers generate a pure stresslet flow, the stresslet sign classifying the squirmer as either a ‘pusher’ or ‘puller’. Assuming axial symmetry, and over the examined range of the Reynolds number $Re$ (defined based upon the magnitude of the quadrupolar squirming), we find that spontaneous symmetry breaking occurs in the puller case above $Re \approx 14.3$, with steady swimming emerging from that threshold consistently with a supercritical pitchfork bifurcation and with the swimming speed growing monotonically with $Re$.

Amplification of velocity gradients, a key feature of turbulent flows, is affected by the non-local character of the incompressible fluid equations expressed by the second derivative (Hessian) of the pressure field. By analysing the structure of the flow in regions where the vorticity is the highest, we propose an approximate expression for the pressure Hessian in terms of the local vorticity, consistent with the existence of intense vortex tubes. Contrary to the often used simplification of an isotropic form for the pressure Hessian, which in effect inhibits vortex stretching, the proposed approximate form of the pressure Hessian enables much stronger vortex stretching. The prediction of the approximation proposed here is validated with results of direct numerical simulations of turbulent flows.

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ($U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$, where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ($Fr=0.5, 2$) and Prandtl ($Pr=1, 7$) numbers forced so that $Re_{b}=50$, with resolutions up to $30\,240 \times 30\,240 \times 3780$. We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$.

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data of stratified flows. A fully connected deep neural network is trained using time-resolved experimental data in a salt-stratified inclined duct experiment, consisting of three-component velocity fields and density fields measured simultaneously in three dimensions at Reynolds number $= O(10^3)$ and at Prandtl or Schmidt number $=700$. The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions at the duct walls. These physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices of Holmboe waves; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed asymmetric Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of stratified turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$, implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ($Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$. Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$, the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.

In magnetoconvection, the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number $Nu$) versus the strength of buoyancy (Rayleigh number $Ra$) and electromagnetic forces (Hartmann number $Ha$). Here, we propose a theoretical model for the transition between these two regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents $\gamma$ in the buoyancy-dominated regime, $Nu\sim Ra ^\gamma$, and $\xi$ in the Lorentz-force-dominated regime, $Nu\sim (Ha^{-2}Ra)^\xi$, are related as $\xi =\gamma /(1-2\gamma )$, and the onset of the transition scales with $Ha^{-1/\gamma }Ra$. These theoretical results are supported by our direct numerical simulations for $10\leq Ha\leq 2000$, Prandtl number $Pr=0.025$ and $Ra$ up to $10^9$ and data from the literature.

Simultaneous time-resolved measurements of wall deformation and the 3-D velocity field in boundary layers over a compliant surface are performed by integrating Mach Zehnder interferometry with tomographic particle tracking velocimetry. The pressure is calculated by spatially integrating the material acceleration. Combining data obtained from several references, trends of the deformation r.m.s. scaled by the compliant wall thickness collapse when plotted vs pressure fluctuations scaled by the material shear modulus. For the present data, at all Reynolds numbers, the deformation waves travel at 53% of the free-stream velocity and have a preferred wavelength of three times the thickness. The latter is consistent with theoretical models. Adopting insight derived from atmospheric wind–wave interactions, the pressure–deformation correlations peak at or slightly above the ‘critical layer’, where the mean flow speed is equal to the surface wave speed. This layer is located within the log layer, and when expressed using inner variables, increases in elevation with increasing Reynolds number. For the entire region below the critical layer, wavenumber–frequency spectra of pressure and vertical velocity fluctuations indicate that the turbulence is phase locked and travels with the deformation, even for deformation amplitudes much smaller than a wall unit. In contrast, above the critical layer, the turbulence is advected at the local mean streamwise velocity, and its correlation with the deformation decays rapidly. These findings indicate that the height of the zone dominated by flow-deformation interactions is determined by the surface wave speed, and its variations are caused by deformation-induced modifications to the mean velocity profile.

Iceberg melting is a critical factor for climate change. However, the shape of an iceberg is an often neglected aspect of its melting process. Our study investigates the influence of different ice shapes and ambient flow velocities on melt rates by conducting direct numerical simulations of a simplified system of bluff body flow. Our study focuses on the ellipsoidal shape, with the aspect ratio as the control parameter. We found the shape plays a crucial role in the melting process, resulting in significant variations in the melt rate between different shapes. Without flow, the optimal shape for a minimal melt rate is the disk (two-dimensional) or sphere (three-dimensional), due to the minimal surface area. However, as the ambient flow velocity increases, the optimal shape changes with the aspect ratio. We find that ice with an elliptical shape (when the long axis is aligned with the flow direction) can melt up to 10 % slower than a circular shape when exposed to flowing water. Following the approach considered by Huang et al. (J. Fluid Mech., vol. 765, 2015, R3) for dissolving bodies, we provide a quantitative theoretical explanation for this optimal shape, based on the combined contributions from both surface-area effects and convective-heat-transfer effects. Our findings provide insight into the interplay between phase transitions and ambient flows, contributing to our understanding of the iceberg melting process and highlighting the need to consider the aspect-ratio effect in estimates of iceberg melt rates.

A uniform representation of the mean turbulent velocity profile in the sum of a wall function and a wake function, already introduced for other parallel geometries, is applied to an open channel. The open channel with its wake function is thus found to coherently fit in to the same theoretical picture previously drawn for plane Couette, plane closed-channel and circular-pipe flow, and to share with them a universal law of the wall and a universal logarithmic law with a common value of von Kármán's constant.

A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The open-loop, feed-forward control approach, based on a dynamic mode decomposition reduced-order model (DMD-ROM), computes forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the dynamics forwards in time. Since it effectively determines a linear response around the unsteady flow in the time domain, the method differs materially from typical techniques that use steady basic states, such as stability or input–output approaches that employ linearized Navier–Stokes operators in the frequency domain. The method presented naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing–suction actuator. The second examines time-local behaviour within critical feedback events, where the phase of actuation becomes important. For this, a conditional space–time mode is used to identify the optimal forcing phase that minimizes convective instability growth within the resonance cycle.

Eukaryotic swimming cells such as spermatozoa, algae or protozoa use flagella or cilia to move in viscous fluids. The motion of their flexible appendages in the surrounding fluid induces propulsive forces that balance viscous drag on the cells and lead to a directed swimming motion. Here, we use our recently built database of cell motility (BOSO-Micro) to investigate the extent to which the shapes of eukaryotic swimming cells may be optimal from a hydrodynamic standpoint. We first examine the morphology of flexible flagella undergoing waving deformation and show that their amplitude-to-wavelength ratio is near that predicted theoretically to optimise the propulsive efficiency of active filaments. Next, we consider ciliates, for which locomotion is induced by the collective beating of short cilia covering their surface. We show that the aspect ratios of ciliates are close to that predicted to minimise the viscous drag of the cell body. Both results strongly suggest a key role played by hydrodynamic constraints, in particular viscous drag, in shaping eukaryotic swimming cells.

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent ‘rortex–shear decomposition’ in stratified shear layers (Jiang et al., J. Fluid Mech., vol. 947, 2022, A30), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rortex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.

The scaling and mechanism of the propagation speed of turbulent fronts in pipe flow with the Reynolds number has been a long-standing problem in the past decades. Here, we derive an explicit scaling law for the upstream front speed, which approaches a power-law scaling at high Reynolds numbers, and we explain the underlying mechanism. Our data show that the average wall distance of low-speed streaks at the tip of the upstream front, where transition occurs, appears to be constant in local wall units in the wide bulk-Reynolds-number range investigated, between 5000 and 60 000. By further assuming that the axial propagation of velocity fluctuations at the front tip, resulting from streak instabilities, is dominated by the advection of the local mean flow, the front speed can be derived as an explicit function of the Reynolds number. The derived formula agrees well with the speed measured by front tracking. Our finding reveals a relationship between the structure and speed of a front, which enables a close approximation to be obtained of the front speed based on a single velocity field without having to track the front over time.

The present paper concerns the linear fate of transverse perturbations in a gravity-driven, thin-film flow over a soluble substrate. We propose a reduced-order model, based on a boundary-layer treatment of the solute transport and a depth-integration of the Stokes equations, using two extended lubrication methodologies found in the literature. We obtain a closed-form dispersion relation, which we compare to a previous, fully resolved analytical investigation (Bertagni and Camporeale, J. Fluid Mech., vol. 913, 2021, A34). The results allow us to distil the essential physical mechanisms behind the instability.

How locally injected turbulence spreads in space is investigated with direct numerical simulations. We consider a turbulent flow in a long triply periodic box generated by a forcing that is localized in space. The forcing is such that it does not inject any mean momentum into the flow. We show that at long times a statistically stationary state is reached where the turbulent energy density in space fluctuates around a mean profile that peaks at the forcing location and decreases fast away from it. We measure this profile as a function of the distance from the forcing region for different values of the Reynolds number. It is shown that, as the Reynolds number is increased, it converges to a Reynolds-number-independent profile, implying that turbulence spreads due to self-advection and not due to molecular diffusion. In this limit, therefore, turbulence plays the simultaneous role of cascading the energy to smaller scales and transporting it to larger distances. The two effects are shown to be of the same order of magnitude. Thus a new turbulent state is reached where turbulent transport and turbulent cascade are equally important and control its properties.

We derive expressions relating the entrainment fluxes of momentum and kinetic energy, relative to the mass flux entrained into a turbulent wake exposed to a turbulent background. These expressions contain correlations between the entrainment velocity and the turbulent fluctuations within the background. We perform high-resolution, simultaneous particle image velocimetry and planar laser-induced fluorescence experiments, and observe these correlations to be negligible in the far wake, such that momentum and kinetic energy are entrained into the wake with the same relative efficiency to mass as from an idealised, non-turbulent background. This is a useful result in the context of modelling, since the entrainment hypothesis (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471) can still be used to model the entrainment of momentum and kinetic energy. Nevertheless, the entrainment rate of mass is shown to vary spatially, and with the specific nature of the background turbulence, so this in turn drives a spatial/background-turbulence-specific entrainment rate of momentum/kinetic energy. Contrastingly, in the near wake, whilst momentum is entrained from a turbulent background with the same relative efficiency to mass as for an idealised non-turbulent background, this is not the case for kinetic energy. Owing to the sum of multiple positive, small-valued correlations between the fluctuations in the background and the entrainment velocity, kinetic energy is entrained more efficiently than in the idealised case. This includes entrainment from a non-turbulent background, where small correlations are observed between the irrotational background fluctuations and the entrainment velocity. Evidence is also presented that the entrainment velocity scales with the Kolmogorov velocity scale when the background is turbulent.

This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.

Two-dimensional horizontally periodic Rayleigh–Bénard convection between stress-free boundaries displays two distinct types of states, depending on the initial conditions. Roll states are composed of pairs of counter-rotating convection rolls. Windy states are dominated by strong horizontal wind (also called zonal flow) that is vertically sheared, precludes convection rolls and suppresses heat transport. Windy states occur only when the Rayleigh number $Ra$ is sufficiently above the onset of convection. At intermediate $Ra$ values, windy states can be induced by suitable initial conditions, but they undergo a transition to roll states after finite lifetimes. At larger $Ra$ values, where windy states have been observed for the full duration of simulations, it is unknown whether they represent chaotic attractors or only metastable states that would eventually undergo a transition to roll states. We study this question using direct numerical simulations of a fluid with a Prandtl number of 10 in a layer whose horizontal period is eight times its height. At each of seven $Ra$ values between $9\times 10^6$ and $2.25\times 10^7$ we have carried out 200 or more simulations, all from initial conditions leading to windy convection with finite lifetimes. The lifetime statistics at each $Ra$ indicate a memoryless process with survival probability decreasing exponentially in time. The mean lifetimes grow with $Ra$ approximately as $Ra^4$. This analysis provides no $Ra$ value at which windy convection becomes stable; it might remain metastable at larger $Ra$ with extremely long lifetimes.

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency, whereas traditional sinusoidal actuation requires ${O}(10)$ shedding cycles. Further, we analyse the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid–structure interactions and unsteady flow control.