We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh–Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense, these states behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear state may provide an explanation for the strong zonal flows observed recently in experiments and simulations of rapidly rotating convection at high Rayleigh number.

In this work, we theoretically investigate the motion of a Taylor swimming sheet immersed in a viscosity-stratified fluid. The propulsion of the swimmer disturbs the surrounding fluid, which influences the transport of the stratifying agent described by the advection–diffusion equation. We employ a regular perturbation scheme to solve the coupled differential equations of motion up to the second order with the small parameter given by the ratio of the wave amplitude and the wavelength. The expression for the swimming velocity is linear in the magnitude of the viscosity gradient, while depending on the Péclet number in a non-monotonic way. Interestingly, we find that the Péclet number governs the propensity of the sheet to propel towards regions of favourable viscosities. In particular, for small Péclet numbers ($0<Pe<3$), the swimmer prefers regions of low viscosity, while for high Péclet numbers ($Pe>3$), the swimmer prefers regions of high viscosity. Our analysis shows that purely hydrodynamic effects might be responsible for the experimentally observed accumulation of swimmers near favourable viscosity regions. We find that viscosity gradients influence other motility characteristics of the swimmer, such as power expenditure and hydrodynamic efficiency, and provide analytical expressions for both.

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al., J. Fluid Mech., vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh–Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number $0.025$ and Rayleigh and Hartmann numbers up to $10^{9}$ and $1400$, respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh–Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.

Experiments on the receptivity of two-dimensional boundary layers to acoustic disturbances from two-dimensional roughness strips were performed in a low-turbulence wind tunnel on a flat plate model. The free stream was subjected to a plane acoustic wave so that a Stokes layer (SL) was created on the plate, thus generating a Tollmien–Schlichting (T–S) wave through the receptivity process. An improved technique to measure the T–S component is described based on a retracting two-dimensional roughness, which allowed for phase-locked measurements at the acoustic wave frequency to be made. This improved technique enables both protuberances and cavities to be explored in the range $30~\unicode[STIX]{x03BC}\text{m}<|h|<750~\unicode[STIX]{x03BC}\text{m}$ (equivalent to $0.025<|h|/\unicode[STIX]{x1D6FF}_{B}^{\ast }<0.630$ in relative roughness height to the local unperturbed Blasius boundary layer displacement thickness). These depths are designed to cover both the predicted linear and nonlinear response of the T–S excitation. Experimentally, cavities had not previously been explored. Results show that a linear regime is identifiable for both positive and negative roughness heights up to ${\approx}150~\unicode[STIX]{x03BC}\text{m}$ ($|h|/\unicode[STIX]{x1D6FF}_{B}^{\ast }\approx 0.126$). The departure from the linear behaviour is, however, dependent on the geometry of the surface imperfection. For cavities of significant depth, the nonlinear behaviour is found to be milder than in the case of protuberances – this is attributed to the flow physics in the near field of the surface features. Nonetheless, results for positive heights agree well with previous theoretical work which predicted a linear disturbance response for small-height perturbations.

Internal solitary and solitary-like waves (ISW) play an important role in mixing and sediment resuspension in naturally occurring stratified fluids, primarily through various instabilities and wave-breaking mechanisms. When shoaling into shallow waters, waves of depression may either fission into a packet of waves of elevation over mild slopes or break over steep slopes. The fissioning process is generally considered a less efficient transport and resuspension mechanism, compared to wave breaking, since very little turbulent mixing or energy dissipation occurs during this process. In the present work, however, we found that this is not always the case, at least in the particular context of ISW boundary-layer interaction. Using high-resolution numerical simulations performed in a domain representing a tilted laboratory tank, we found that boundary-layer instability in the form of a separation bubble consistently occurs during the fissioning process. The separation bubble is generated beneath the wave of elevation that emerges from the fissioning process, and is vitally influenced by currents induced by the leading wave of depression. As the waves shoal further, the growth and breakdown of the separation bubble leads to significant cross-boundary-layer transport. The results suggest that the fissioning process, which occurs over a considerable geographical region in the ocean, can be as efficient as wave breaking when it comes to cross-boundary-layer transport.

Surface waves called meniscus waves often appear in systems that are close to the capillary length scale. Since the meniscus shape determines the form of the meniscus waves, the resulting streaming circulation has features distinct from those caused by other capillary–gravity waves recently reported in the literature. In the present study, we produce symmetric and antisymmetric meniscus shapes by controlling boundary wettability and excite meniscus waves by oscillating the meniscus vertically. The symmetric and antisymmetric configurations produce different surface capillary–gravity wave modes and streaming flow structures. The root-mean-square speed of the streaming circulation increases with the second power of the forcing amplitude in both configurations. The flow symmetry of streaming circulation is retained under the symmetric meniscus, while it is lost under the antisymmetric meniscus. The streaming circulation pattern beneath the meniscus observed in our experiments is qualitatively explained using the method introduced by Nicolás & Vega (Fluid Dyn. Res., vol. 32 (4), 2003, pp. 119–139) and Gordillo & Mujica (J. Fluid Mech., vol. 754, 2014, pp. 590–604).

The link between jet-installation noise and the near-field flow features of the corresponding isolated jet is studied by means of lattice-Boltzmann numerical simulations. The computational set-up consists of a flat plate placed in proximity to a jet, replicating the interaction benchmark study carried out at NASA Glenn. Installation effects cause low-frequency noise increase with respect to the isolated case, mainly occurring in the direction normal to the plate and upstream of the jet’s exit plane. It is shown that the Helmholtz number, based on the wavelength of eddies in the mixing layer and their distance to the plate trailing edge, predicts the frequency range where installation noise occurs. Based on the isolated jet near field, scaling laws are also found for the far-field noise produced by different plate geometries. The linear hydrodynamic field of the isolated jet shows an exponential decay of pressure fluctuations in the radial direction; it is shown that the far-field spectrum follows the same trend when moving the plate in this direction. In the axial direction, spectral proper orthogonal decomposition is applied to filter out jet acoustic waves. The resultant hydrodynamic pressure fluctuations display a wavepacket behaviour, which can be fitted with a Gaussian envelope. It is found that installation noise for different plate lengths is proportional to the amplitude of the Gaussian curve at the position of the plate trailing edge. These analyses show that trends of jet-installation noise can be predicted by analysing the near field of the isolated case, reducing the need for extensive parametric investigations.

Rewetting is the establishment of water–surface contact that occurs during quenching of high temperature surfaces by water jet impingement. Rewetting is an unexpectedly complex phenomenon that has been reported to occur at surface temperatures significantly higher than the superheating limit of water. The presence of intermittently wet and dry episodes, and in particular the occurrence of so-called explosive boiling, is one of the theories to explain the contact of water with high temperature surfaces. However, there is a lack of experimental data in the literature to prove the presence of explosive boiling and intermittent wetting due to the small duration and scale of the rewetting phenomenon. In this study, recordings of the jet stagnation zone during rewetting are provided at a frame rate of 81 kfps. The high-speed recordings show a flashing regime consisting of intermittent (dry) bubble-rich and (wet) bubble-free periods at frequencies up to 40 kHz when the rewetted surface temperature exceeds the water superheat limit. As far as the authors know, these are the first direct observations of intermittent dry–wet periods occurring in the jet stagnation zone during quenching by water jet impingement. The dependency of the flashing frequency on initial surface temperature is quantified. A correlation between the size of the rewetting patch and the flashing frequency is found. Finally, a hypothesis to explain the role of water subcooling in maintaining the water–surface contact at surface temperatures well above the superheating limit of water is presented.

Drop deformation and disintegration regimes have been studied in many contexts ranging from an impact on a solid surface or a liquid layer of varying thickness to a liquid drop suspended in air and hit by a propagating aerodynamic shock wave. As a counterpart, deformation and disintegration of an initially static drop of controlled shape and size sitting on an impulsively driven stiff membrane are explored here experimentally. A significant amount of collected experimental data is used to map the possible drop morphological changes along with the transitions between them. In order to elucidate the effects of impulse intensity, viscosity, surface tension and wetting, we measured the crown height and radius in the drop deformation regimes, as well as the drop detachment and breakup times along with probability density functions of the secondary droplets in the drop disintegration regimes. With the goal to convey the physical mechanisms behind these transient responses, the observations are interpreted with phenomenological models, scalings and estimates highlighting the rich multiscale physics of the impulse-driven drop phenomena.

This study develops a comprehensive description of local streamline geometry and uses the resulting shape features to characterize velocity gradient ($\unicode[STIX]{x1D608}_{ij}=\unicode[STIX]{x2202}u_{i}/\unicode[STIX]{x2202}x_{j}$) dynamics. The local streamline geometric shape parameters and scale factor (size) are extracted from $\unicode[STIX]{x1D608}_{ij}$ by extending the linearized critical point analysis. In the present analysis, $\unicode[STIX]{x1D608}_{ij}$ is factorized into its magnitude ($A\equiv \sqrt{\unicode[STIX]{x1D608}_{ij}\unicode[STIX]{x1D608}_{ij}}$) and normalized tensor $\unicode[STIX]{x1D623}_{ij}\equiv \unicode[STIX]{x1D608}_{ij}/A$. The geometric shape is shown to be determined exclusively by four $\unicode[STIX]{x1D623}_{ij}$ parameters: second invariant, $q$ ($=Q/A^{2}$); third invariant, $r$ ($=R/A^{3}$); intermediate strain rate eigenvalue, $a_{2}$; and vorticity component along intermediate strain rate eigenvector, $\unicode[STIX]{x1D714}_{2}$. Velocity gradient magnitude, $A$, plays a role only in determining the scale of the local streamline structure. Direct numerical simulation data of forced isotropic turbulence ($Re_{\unicode[STIX]{x1D706}}\sim 200{-}600$) is used to establish streamline shape and scale distribution, and then to characterize velocity-gradient dynamics. Conditional mean trajectories (CMTs) in $q$–$r$ space reveal important non-local features of pressure and viscous dynamics which are not evident from the $\unicode[STIX]{x1D608}_{ij}$-invariants. Two distinct types of $q$–$r$ CMTs demarcated by a separatrix are identified. The inner trajectories are dominated by inertia–pressure interactions and the viscous effects play a significant role only in the outer trajectories. Dynamical system characterization of inertial, pressure and viscous effects in the $q$–$r$ phase space is developed. Additionally, it is shown that the residence time of $q$–$r$ CMTs through different topologies correlate well with the corresponding population fractions. These findings not only lead to improved understanding of non-local dynamics, but also provide an important foundation for developing Lagrangian velocity-gradient models.

Particle migration in viscoelastic suspensions is vital in many applications in the biomedical community and the chemical/oil industries. Previous studies have provided insight into the motion of spherical particles in simple viscoelastic flows, yet the combined effect of more complex flow profiles and particle shapes is under-explored. Here, we develop approximate analytical expressions for the polymeric force and torque on an arbitrarily shaped particle in a second-order fluid, subject to a general quadratic flow field. This model is exact for the case when the first and second normal stress coefficients satisfy $\unicode[STIX]{x1D713}_{1}=-2\unicode[STIX]{x1D713}_{2}$. Under this assumption, we examine how particle shape alters cross-stream particle migration (i.e. lift) and particle orientation in both shear- and pressure-driven flows. In shear-driven flows, we observe that spheroidal particles adjust their orientation to align their longer axis along the vorticity direction, although significant deviations from slender-body theories occur for finite aspect ratios. In a slit-like pressure-driven flow, we identify scaling theories to quantify how the particle lift depends on shape for a wide variety of shapes. We find that prolate particles slowly transition to a log-rolling state as they approach the flow centre, with the lift initially being larger than that of an equal-volume sphere, but then becoming smaller as log-rolling emerges. The net effect is a smaller average migration speed for particles with larger aspect ratio. Lastly, we discuss future directions for experimental studies on particle dynamics as well as directions to extend the current work towards more complicated systems.

We show that, in the case of turbulent Rayleigh–Bénard convection, shadowgraph can be used to gain quantitative results on the plume statistics and velocity. For this purpose, we compare the experimental shadowgraph of a Rayleigh–Bénard cell with the synthetic shadowgraph obtained by calculating the integrated two-dimensional Laplacian of the temperature field from a numerical simulation very similar to the experiment. We use image processing tools to enhance the quality of the shadowgraph image, and obtain quantitative statistics for the thermal plumes, such as plume density and plume velocity distribution. To highlight the efficiency of this new process of plume counting, we use, both in the experiment and in the numerical simulation, a turbulent Rayleigh–Bénard convection cell with a rough bottom surface and a smooth top surface, where the statistics of the plumes can be influenced (or not) by the roughness. In addition, the distribution of velocity obtained from processing the synthetic shadowgraph images of the direct numerical simulations (DNS) or the experimental shadowgraph images, are compared to the velocity fluid at mid-plane of the DNS or particle image velocimetry measurement in the experiment, respectively. It will be shown that the mean velocity profile measured using the advection of the plumes is different from the average Eulerian velocity profile.

The flow-induced flapping dynamics of a flexible two-dimensional heated flag in the mixed convection regime is studied here. A linear stability analysis is first used to predict the flutter stability using three dimensionless parameters of reduced flow velocity, mass ratio and Richardson number. This is followed by fully coupled computational simulations to investigate the role of flapping motion on the flag’s thermal performance. The results show that an increase of Richardson number has a non-monotonic stabilizing effect on the flag response over the range of reduced velocities. The distinct flapping response regimes previously reported in the literature are recovered here and expanded upon by finding new flapping modes within the limit-cycle regime. It is found that mode switching is associated not only with the frequency response of the system but is also highly coupled to the flag’s thermal performance. The average Nusselt number over the structure attains the highest value when the flag vibrates in its higher fluttering mode, wherein it shows a higher sensitivity to Richardson number. We also report the correlations for the Nusselt number for the different flapping modes and identify an unexpected dependency of the modes on the flag inertia in the presence of the thermal effects.

We perform direct numerical simulations of flows over unswept finite-aspect-ratio NACA 0015 wings at $Re=400$ over a range of angles of attack (from $0^{\circ }$ to $30^{\circ }$) and (semi) aspect ratios (from 1 to 6) to characterize the tip effects on separation and wake dynamics. This study focuses on the development of three-dimensional separated flow over the wing. We discuss the flow structures formed on the wing surface as well as in the far-field wake. Vorticity is introduced from the wing surface into the flow in a predominantly two-dimensional manner. The vortex sheet from the wing tip rolls up around the free end to form the tip vortex. At its inception, the tip vortex is weak and its effect is spatially confined. As the flow around the tip separates, the tip effects extend farther in the spanwise direction, generating noticeable three dimensionality in the wake. For low-aspect-ratio wings ($sAR\approx 1$), the wake remains stable due to the strong tip-vortex induced downwash over the entire span. Increasing the aspect ratio allows unsteady vortical flow to emerge away from the tip at sufficiently high angles of attack. These unsteady vortices shed and form closed vortical loops. For higher-aspect-ratio wings ($sAR\gtrsim 4$), the tip effects retard the near-tip shedding process, which desynchronizes from the two-dimensional shedding over the midspan region, yielding vortex dislocation. At high angles of attack, the tip vortex exhibits noticeable undulations due to the strong interaction with the unsteady shedding vortices. The spanwise distribution of force coefficients is found to be related to the three-dimensional wake dynamics and the tip effects. Vortical elements in the wake that are responsible for the generation of lift and drag forces are identified through the force element analysis. We note that at high angles of attack, a stationary vortical structure forms at the leading edge near the tip, giving rise to locally high lift and drag forces. The analysis performed in this paper reveals how the vortical flow around the tip influences the separation physics, the global wake dynamics, and the spanwise force distributions.

This study focuses on the process of the circulation deposition in the Richtmyer–Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11 % of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave–turbulence interactions.

A detailed assessment of the inter-scale energy budget of the turbulent flow in a von Kármán mixing tank has been performed based on two extensive experimental data sets. Measurements were performed at a Taylor microscale Reynolds number of $Re_{\unicode[STIX]{x1D706}}=199$ in the central region of the tank, using scanning particle image velocimetry (PIV) to fully resolve the velocity gradient tensor (VGT), and stereoscopic PIV for an expanded field of view. Following a basic flow characterisation, the Kármán–Howarth–Monin–Hill equation was used to investigate the inter-scale energy transfer. Access to the full VGT enabled the contribution of the different terms of the energy budget to be evaluated without any assumptions or approximations. The scale-space distribution of the dominant terms was also reported to assess the isotropy of the energy transfer. The results show a highly anisotropic distribution of energy transfer in scale space. Energy transfer was shown in a spherically averaged sense to be dominated at the small scales by the nonlinear inter-scale transfer term. However, in contrast to flows considered in previous studies, the local energy transfer is found to depend heavily on the linear contribution associated with the mean flow. Analysis of the scale-to-scale transfer of energy also allowed direct assessment of the classical picture of the energy cascade. It was found that while the inter-scale energy cascade driven by the turbulent fluctuations always proceeds in the forward direction, the total energy cascade driven by both the turbulent fluctuations and the mean flow exhibits significant inverse cascade regions, where energy is transferred from smaller to larger scales.

The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers up to 0.75 and large Reynolds numbers is studied by using high-resolution direct numerical simulations. To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behaviour of turbulent kinetic energy derivatives. The results show that each regime has a unique type of dependence on both Atwood and Reynolds numbers. It is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. It is also observed that, at higher Atwood numbers, different flow features reach their asymptotic Reynolds-number behaviour at different times. The energy spectrum defined based on the Favre fluctuations momentum has less large-scale contamination from viscous effects for variable-density flows with constant properties, compared to other forms used previously. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from $-7/3$ to $-1$, as a function of the production-to-dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed.

Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and a forward helicity cascade at scales smaller than the energy forcing scale. In contrast to previous studies using decimated triads, our simulations contain all possible triads. By computing the shell-to-shell energy fluxes, we show that the inverse energy cascade results from weakly non-local interactions among homochiral triads. Varying the helicity injection range of scales leads to necessary conditions to obtain an inverse energy cascade.

A theoretical analysis of the dynamic electrophoretic mobility of surfactant-stabilized nano-drops is undertaken. Whereas the theory for rigid spherical nanoparticles is well developed, its application to nano-drops is questionable due to fluid mobility of the interface and of the surfactant molecules adsorbed there. At zero frequency, small drops with surface impurities are well known to behave as rigid spheres due to concentration-gradient-induced Marangoni stresses. However, at the megahertz frequencies of electroacoustic (and other spectral-based) diagnostics, the interfacial concentration gradients are dynamic, coupling electromigration, advection and diffusion fluxes. This study addresses a parameter space that is relevant to anionic-surfactant-stabilized oil–water emulsions, using sodium-dodecylsulfate-stabilized hexadecane as a specific example. The drop size is several hundred nanometres, much larger than the diffuse-layer thickness, thus motivating thin-double-layer approximations. The theory demonstrates that fluid mobility and fluctuating Marangoni stresses can have a profound influence on the magnitude and phase of the dynamic mobility. We show that the drop interface transits from a rigid/immobile one at low frequency to a fluid one at high frequency. The model unifies electrokinetics and equilibrium interfacial thermodynamics. Therefore, with knowledge of how the interfacial tension varies with electrolyte composition (oil, surfactant and added salt concentrations), the particle radius might be adopted as the primary fitting parameter (rather than the customary $\unicode[STIX]{x1D701}$-potential) from an experimental measure of the dynamic mobility. This theory is general enough that it might be applied to aerosols and bubbly dispersions (at sufficiently high frequencies).