Helical rotating turbulence is a chiral and anisotropic flow. The energy and helicity transfers of helical rotating turbulence are studied in this paper. First, we discuss the antisymmetry and conservation of energy and helicity transfers. There are three expressions for helicity transfers due to the commutability of differential operators. The first expression is derived here. The second expression violates antisymmetry, and the third one introduces non-physical effects. The relations of these expressions are discussed in detail, including those about the sum of all triads and partial triads, as well as those about helical wave decomposition. Through direct numerical simulations, we find that helicity can reduce inverse energy cascades. The inhibition is mainly associated with transhelical energy fluxes and the interactions of two-dimensional modes. The inverse cascades of decomposed energy fluxes are related to the two-dimensionalization. For helicity, rotation does not affect the total helicity flux but generally suppresses the decomposed helicity fluxes. Positive homochiral and negative heterochiral helicity fluxes are associated with corresponding positive anisotropic transfers. Notably, the transhelical helicity fluxes increase the amplitudes of both positive and negative helicity, which is related to the chirality polarization.

Laminar natural convection is investigated in an infinite vertical slot which has one wall with a corrugated profile, and which is subject to either a uniform or periodic heating profile. This configuration has the attractive feature that it enables a study of the effects that may be produced via the interaction of heating and topography patterns. It is found that the addition of the grooves to an isothermal plate leads to a reduction in the vertical fluid flow and an increase of the transverse heat flow. In contrast, imposing sinusoidal heating on a flat surface generates convection that appears as counter-rotating rolls but there is no net vertical flow. The combination of the two effects of corrugation together with periodic heating leads to a plethora of flow patterns involving a combination of rolls and stream tubes that carry the fluid along the slot. The details of this vertical flow are governed by a pattern interaction effect dictated by the relative positions of the heating and corrugation patterns; when hot spots of the imposed heating overlap the peaks in the grooves the net flow is upward; in contrast, when they lie over the troughs the resultant flow is downward. The interplay between the thermal and geometrical effects weakens as the wavelength of the structure is reduced. The inclusion of a sufficiently strong uniform heating also seems to wash away the pattern interaction effect.

When a charge neutral drop impacts on a flat solid substrate, a small air bubble is always trapped underneath due to the lubrication pressure coming from the viscous stress in the squeezed air film. Herein we find experimentally and numerically that the process of the air entrapment and the initial contact state of the drop with the substrate can be profoundly altered via an external electric field. In an electric field, the induced electric stresses at the bottom of the drop increase drastically right before the drop contacts the substrate, which acts against the lubrication pressure, resulting in reduced initial contact radius and air bubble size. When the external electric field reaches a critical value, the electrical stress accelerates the flow near the bottom of the drop and generates a conical tip quickly instead of a dimple, resulting in a centre contact and eliminating the air bubble entrapment. Based on the dipole mirror charge model, we find the dimensionless strength of critical electric field scales with the square root of capillary number based on the air viscosity. This scaling law of the critical electric field for eliminating the air bubble entrapment is verified experimentally and numerically. This work may offer a new way to mitigate defects caused by air bubble entrapment for inkjet printing and droplet-based additive manufacturing.

The cell cytoskeleton is a dynamic assembly of semi-flexible filaments and motor proteins. The cytoskeleton mechanics is a determining factor in many cellular processes, including cell division, cell motility and migration, mechanotransduction and intracellular transport. Mechanical properties of the cell, which are determined partly by its cytoskeleton, are also used as biomarkers for disease diagnosis and cell sorting. Experimental studies suggest that in whole cell scale, the cell cytoskeleton and its permeating cytosol may be modelled as a two-phase poro-viscoelastic (PVE) material composed of a viscoelastic (VE) network permeated by a viscous cytosol. We present the first general solution to this two-phase system in spherical coordinates, where we assume that both the fluid and network phases are in their linear response regime. Specifically, we use generalized linear incompressible and compressible VE constitutive equations to describe the stress in the fluid and network phases, respectively. We assume a constant permeability that couples the fluid and network displacements. We use these general solutions to study the motion of a rigid sphere moving under a constant force inside a two-phase system, composed of a linear elastic network and a Newtonian fluid. It is shown that the network compressibility introduces a slow relaxation of the sphere and non-monotonic network displacements with time along the direction of the applied force. Our results can be applied to particle-tracking microrheology to differentiate between PVE and VE materials, and to measure the fluid permeability as well as VE properties of the fluid and the network phases.

The structural design of the rudder, traditionally based on quasisteady loads generated during worst manoeuvres, should account for load fluctuations associated with the interaction with the wake of the propeller in order to comply with the more stringent requirements on ship vibration and noise pollution. In this context, the present work analyses the dynamic response of a marine rudder located in the wake of the INSEAN E779A propeller by the one-way fluid–structure interaction approach. The time-dependent pressure distribution on the rudder, obtained through detached eddy simulation, is used to evaluate the pressure field that is the input for a structural solver to determine the resulting deformations and stresses. The computations consider the propeller at moderate loading, and rudder deflection angles at neutral and $4^{\circ }$. The analysis discusses the different contribution of the tip and hub vortex of the propeller on the static and vibratory response of the rudder in the two configurations.

In this study, we perform boundary-integral simulations to investigate the role of interfacial viscosity in the deformation and breakup of a single droplet suspended in an axisymmetric extensional flow under the Stokes flow regime. We model the insoluble surfactant monolayer using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. We compare the deformation and breakup results from our boundary-element simulations with results from small deformation perturbation theories. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared with a clean droplet. We present the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values reported in experimental studies on surfactants, lipid bilayers and proteins. In the second half of the paper, we incorporate the effect of surfactant transport by solving the time-dependent convection–diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration. We explore the coupled influence of pressure-dependent surface viscosity and Marangoni stresses on droplet deformation and breakup. In the case of a droplet with pressure-dependent surface shear viscosity, we find that a droplet with pressure-thinning/thickening surfactant is less/more deformed than a droplet with pressure-independent surfactant. We conclude by discussing the combined impact of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.

Bragg scattering of nonlinear surface waves over a wavy bottom is studied using two-dimensional fully nonlinear numerical wave tanks (NWTs). In particular, we consider cases of high nonlinearity which lead to complex wave generation and transformations, hence possible multiple Bragg resonances. The performance of the NWTs is well verified by benchmarking experiments. Classic Bragg resonances associated with second-order triad interactions among two surface (linear incident and reflected waves) and one bottom wave components (class I), and third-order quartet interactions among three surface (linear incident and reflected waves, and second-order reflected/transmitted waves) and one bottom wave components (class III) are observed. In addition, class I Bragg resonance occurring for the second-order (rather than linear) transmitted waves, and Bragg resonance arising from quintet interactions among three surface and two bottom wave components, are newly captured. The latter is denoted class IV Bragg resonance which magnifies bottom nonlinearity. It is also found that wave reflection and transmission at class III Bragg resonance have a quadratic rather than a linear relation with the bottom slope if the bottom size increases to a certain level. The surface wave and bottom nonlinearities are found to play opposite roles in shifting the Bragg resonance conditions. Finally, the results indicate that Bragg resonances are responsible for the phenomena of beating and parasitic beating, leading to a significantly large local free surface motion in front of the depth transition.

Direct numerical simulations employing the finitely extensible nonlinear elastic constitutive model closed with Peterlin's approximation (FENE-P) are used to investigate the far-field region of turbulent planar wakes of viscoelastic fluids and to develop the theory describing these flows. The theoretical results display excellent agreement with the simulations and provide new scaling laws for the evolution of the shear layer thickness $\delta (x) \sim x^{1/2}$, mean velocity deficit ${\rm \Delta} U(x) \sim x^{-1/2}$ and, for very high Deborah numbers, of the maximum polymer shear stresses $\sigma ^{[p]}_c(x) \sim x^{-2}$ and averaged polymer chain extension $\textrm {tr}(\bar {C}(x) - \boldsymbol{\mathsf{I}}) \sim x^{-2}$, where $x$ is the streamwise distance from the solid body generating the wake. The theory is able to show the existence of self-similarity for the profiles of mean velocity, mean polymer shear stress, averaged polymer chain extension and the conditions for similarity of the turbulent shear stress, and is very well supported by the numerical simulations. Similarly to the case of viscoelastic turbulent planar jets (Guimarães et al., J. Fluid Mech., vol. 899, 2020, p. A11), when the inlet Weissenberg and Deborah numbers are sufficiently large, turbulent viscoelastic wakes exhibit a considerable reduction of the spreading rate and of the normalised Reynolds stresses. However, for very large downstream locations the turbulent viscoelastic wake recovers the classical evolution laws observed for Newtonian turbulent planar wakes.

Recent experiments have reported a novel transition to elasto-inertial turbulence in the Taylor–Couette flow of a dilute polymer solution. Unlike previously reported transitions, this newly discovered scenario, dubbed vortex merging and splitting (VMS) transition, occurs in the centrifugally unstable regime and the mechanisms underlying it are two-dimensional: the flow becomes chaotic due to the proliferation of events where axisymmetric vortex pairs may be either created (vortex splitting) or annihilated (vortex merging). In this paper, we present direct numerical simulations, using the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive equation to model the polymer dynamics, which reproduce the experimental observations with great accuracy and elucidate the reasons for the onset of this surprising dynamics. Starting from the Newtonian limit and increasing progressively the fluid's elasticity, we demonstrate that the VMS dynamics is not associated with the well-known Taylor vortices, but with a steady pattern of elastically induced axisymmetric vortex pairs known as diwhirls. The amount of angular momentum carried by these elastic vortices becomes increasingly small as the fluid's elasticity increases and it eventually reaches a marginal level. When this occurs, the diwhirls become dynamically disconnected from the rest of the system and move independently from each other in the axial direction. It is shown that vortex merging and splitting events, along with local transient chaotic dynamics, result from the interactions among diwhirls, and that this complex spatio-temporal dynamics persists even at elasticity levels twice as large as those investigated experimentally.

Large-eddy simulation was used to model turbulent atmospheric surface layer (ASL) flow over canopies composed of streamwise-aligned rows of synthetic trees of height, $h$, and systematically arranged to quantify the response to variable streamwise spacing, $\delta _1$, and spanwise spacing, $\delta _2$, between adjacent trees. The response to spanwise and streamwise heterogeneity has, indeed, been the topic of a sustained research effort: the former resulting in formation of Reynolds-averaged counter-rotating secondary cells, the latter associated with the $k$- and $d$-type response. No study has addressed the confluence of both, and results herein show secondary flow polarity reversal across ‘critical’ values of $\delta _1$ and $\delta _2$. For $\delta _2/\delta \lesssim 1$ and $\gtrsim 2$, where $\delta$ is the flow depth, the counter-rotating secondary cells are aligned such that upwelling and downwelling, respectively, occurs above the elements. The streamwise spacing $\delta _1$ regulates this transition, with secondary cell reversal occurring first for the largest $k$-type cases, as elevated turbulence production within the canopy necessitates entrainment of fluid from aloft. The results are interpreted through the lens of a benchmark prognostic closure for effective aerodynamic roughness, $z_{0,{Eff.}} = \alpha \sigma _h$, where $\alpha$ is a proportionality constant and $\sigma _h$ is height root mean square. We report $\alpha \approx 10^{-1}$, the value reported over many decades for a broad range of rough surfaces, for $k$-type cases at small $\delta _2$, whereas the transition to $d$-type arrangements necessitates larger $\delta _2$. Though preliminary, results highlight the non-trivial response to variation of streamwise and spanwise spacing.

The decay of stably stratified turbulence generated by a towed rake of vertical plates is investigated by direct numerical simulations (DNS) of temporally evolving grid turbulence in a linearly stratified fluid. The Reynolds number $Re_M=U_0M/\nu$ is 5000 or 10 000 while the Froude number $Fr_M=U_0/MN$ is between 0.1 and 6 ($U_0$: towing speed; $M$: mesh size; $\nu$: kinematic viscosity; $N$: Brunt–Väisälä frequency). The DNS results are compared with the theory of stably stratified axisymmetric Saffman turbulence. Here, the theory is extended to a viscosity-affected stratified flow regime with low buoyancy Reynolds number $Re_b$, and power laws are derived for the temporal variations of the horizontal velocity scale ($U_H$) and the horizontal and vertical integral length scales ($L_H$ and $L_V$). Temporal grid turbulence initialized with the mean velocity deficit of wakes exhibits a $k^{2}$ energy spectrum at a low-wavenumber range and invariance of $U_H^2L_H^2L_V$, which are the signatures of axisymmetric Saffman turbulence. The decay of various quantities follows the power laws predicted for low-$Re_b$ Saffman turbulence when $Fr_M$ is sufficiently small. However, the decay of $U_H^2$ at $Fr_M=6$ is no longer expressed by a power law with a constant exponent. This behaviour is related to the scaling of kinetic energy dissipation rate $\varepsilon$, for which $\alpha =\varepsilon /(U_H^3/L_H)$ is constant during the decay for $Fr_M\leq 1$ while it varies with time for $Fr_M=6$. We also examine the experimental data of towed-grid experiments by Praud et al. (J. Fluid Mech., vol. 522, 2005, pp. 1–33), which is shown to agree with the theory of low-$Re_b$ Saffman turbulence.

Microorganisms can efficiently navigate in anisotropic complex fluids, but the precise swimming mechanisms remain largely unexplored. Their dynamics is determined by the interplay between multiple effects, including the fluid's orientation order, swimmer's undulatory gait and the finite length. Here, we extend the numerical study of the two-dimensional undulatory motions of a flexible swimmer in lyotropic liquid-crystalline polymers (LCPs) by Lin et al. (J. Fluid Mech., vol. 921, 2021, p. A25) to the scenario of arbitrary swimming directions with respect to the nematic director. The swimmer is modelled as a nearly inextensible yet flexible fibre with imposed travelling-wave-like actuation. We investigate the orientation-dependent swimming behaviours in nematic LCPs for an infinitely long sheet (i.e. Taylor's swimming sheet model) and finite-length swimmers. We demonstrate that the swimmer must be sufficiently stiff to produce undulatory deformations to gain net motions. Moreover, a motile finite-length swimmer can reorient itself to swim parallel with the nematic director, due to a net body torque arising from the asymmetric distribution of the polymer force along the body.

When a droplet impacts a solid with a heterogeneous wettability surface, the generated asymmetric forces can manipulate the droplet, and its counterforces can also actuate the solid in theory. In this study, a water droplet impacting a movable hydrophobic substrate, which is decorated with a hydrophilic stripe and restrained by two linear dampers, is studied numerically. After preliminarily checking the effects of the solid mass and damping coefficient of linear dampers, the dynamic mechanisms of solid motion are explored by analysing the variations in the lateral force and instantaneous displacement distance of the solid. After that, the effects of the impact parameters on the solid lateral motion are mainly investigated, including the initial droplet diameter, impact velocity and offset distance between the impact point and hydrophilic stripe. On this basis, the reciprocating solid motion under successive droplet impacts is studied, and periodic motion with different amplitudes can be realized under appropriate impact conditions. The obtained results can shed some fresh insight into the potential applications of droplet–solid interactions, which are valuable for the collection and utilization of energy from natural environments.

Recent progress in the direct measurement of turbulent dissipation in the Arctic Ocean has highlighted the need for an improved parametrization of the turbulent diapycnal diffusivities of heat and salt that is suitable for application in the turbulent environment characteristic of this polar region. In support of this goal we describe herein a series of direct numerical simulations of the turbulence generated in the process of growth and breaking of Kelvin–Helmholtz billows. These simulations provide the data sets needed to serve as basis for a study of the stratified turbulent mixing processes that are expected to exist in the Arctic Ocean environment. The mixing properties of the turbulence are studied using a previously formulated procedure in which the temperature and salinity fields are sorted separately in order to enable the separation of irreversible Arctic mixing from reversible stirring processes and thus the definition of turbulent diffusivities for both heat and salt that depend solely upon irreversible mixing. These analyses allow us to demonstrate that the irreversible diapycnal diffusivities for heat and salt are both solely dependent on the buoyancy Reynolds number in the Arctic Ocean environment. These are found to be in close agreement with the functional forms inferred for these turbulent diffusivities in the previous work of Bouffard & Boegman (Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). Based on a detailed comparison of our simulation data with this previous empirical work, we propose an algorithm that can be used for inferring the diapycnal diffusivities from turbulent dissipation measurements in the Arctic Ocean.

Understanding flow and transport of bacteria in porous media is crucial to technologies such as bioremediation, biomineralization and enhanced oil recovery. While physicochemical bacteria filtration is well documented, recent studies showed that bacterial motility plays a key role in the transport process. Flow and transport experiments performed in microfluidic chips containing randomly placed obstacles confirmed that the distributions of non-motile bacteria stays compact, whereas for the motile strains, the distributions are characterized by both significant retention as well as fast downstream motion. For motile bacteria, the detailed microscopic study of individual bacteria trajectories reveals two salient features: (i) the emergence of an active retention process triggered by motility, (ii) enhancement of dispersion due to the exchange between fast flow channels and low flow regions in the vicinity of the solid grains. We propose a physical model based on a continuous time random walk approach. This approach accounts for bacteria dispersion via variable pore-scale flow velocities through a Markov model for equidistant particle speeds. Motility of bacteria is modelled by a two-rate trapping process that accounts for the motion towards and active trapping at the obstacles. This approach captures the forward tails observed for the distribution of bacteria displacements, and quantifies an enhanced hydrodynamic dispersion effect that originates in the combined effect of pore-scale flow variability and bacterial motility. The model reproduces the experimental observations, and predicts bacteria dispersion and transport at the macroscale.

The present work investigates the mechanical behaviour of finite-size, elastic and inertial fibres freely moving in a homogeneous and isotropic turbulent flow at moderate Reynolds number. Four-way coupled, direct numerical simulations, based on a finite difference discretisation and the immersed boundary method, are performed to mutually couple the dynamics of fibres and fluid turbulence, allowing us to account for the backreaction of the dispersed phase to the carrier flow. An extensive parametric study is carried out in zero-gravity condition over the characteristic properties of the suspension, i.e. fibre's linear density (from iso-dense to denser-than-the-fluid fibres), length (from short fibres comparable with the dissipative scale to long fibres comparable with the integral scale) and bending stiffness (from highly flexible to almost rigid fibres), as well as the concentration (from dilute to non-dilute suspensions). Results reveal the existence of a robust turbulence modulation mechanism that is primarily controlled by the mass fraction of the suspension (with only a minor influence of the fibre's bending stiffness), which is characterised in detail by means of a scale-by-scale analysis in Fourier space. Despite such alteration with respect to the single-phase case due to the non-negligible backreaction, fibres experience only two possible flapping states (previously identified in the very dilute condition) while being transported and deformed by the flow. In addition, we show that the maximum curvature obeys different scaling laws that can be derived from the fibre dynamical equation. Finally, we explore the clustering and preferential alignment of fibres within the flow, highlighting the peculiar role of inertia and elasticity.

The separating and reattaching turbulent flow past a rectangular cylinder is studied to describe how small and large scales contribute to the sustaining mechanism of the velocity fluctuations. The work is based on the anisotropic generalised Kolmogorov equations, exact budget equations for the second-order structure function tensor in the space of scales and in the physical space. Scale-space energy fluxes show that forward and reverse energy transfers occur simultaneously in the flow, with interesting modelling implications. Over the longitudinal cylinder side, the Kelvin–Helmholtz instability of the leading edge shear layer generates large spanwise rolls, which get stretched into hairpin-like vortices and eventually break down into smaller streamwise vortices. Independent sources of velocity fluctuations act at different scales. The flow dynamics is dominated by pressure–strain: the flow impingement on the cylinder surface in the reattachment zone produces spanwise velocity fluctuations very close to the wall, and at larger wall distances reorients them to feed streamwise-aligned vortices. In the near wake, large von Kármán-like vortices are shed from the trailing edge and coexist with smaller turbulent structures, each with its own independent production mechanism. At the trailing edge, the sudden disappearance of the wall changes the structure of turbulence: streamwise vortices vanish progressively, while spanwise structures close to the wall are suddenly turned into vertical fluctuations by the pressure–strain.

Global instabilities in swirling flows can significantly alter the flame and flow dynamics of swirl-stabilized flames, such as those in modern gas turbine engines. In this study, we characterize the interaction between the precessing vortex core (PVC), which is the consequence of a global hydrodynamic instability, and thermoacoustic instabilities, which are the result of a coupling between combustor acoustics and the unsteady heat release rate. This study is performed using experimental data obtained from a model gas turbine combustor employing two concentric swirling nozzles of air, separated by a ring of fuel injectors, operating at five bar pressure. The flow split between the two streams is systematically varied to observe the impact of flow structure variation on the system dynamics at both non-reacting and reacting conditions. High-speed stereoscopic particle image velocimetry, OH planar laser-induced fluorescence and acetone planar laser-induced fluorescence are used to obtain information about the velocity fields, flame and fuel flow behaviour, respectively. Spectral proper orthogonal decomposition and a complex network analysis are used to identify and characterize the dominant oscillation mechanisms driving the system. In the non-reacting data, a PVC is present in most cases and the amplitude of the oscillation increases with increasing flow through the centre nozzle. In the reacting data, three dominant modes are seen: two thermoacoustic modes and the PVC. Our results show that in the cases where the frequency of the PVC overlaps with either of the thermoacoustic modes, the thermoacoustic modes are suppressed. The complex network analysis coupled with a weakly nonlinear theoretical analysis suggests the mechanisms by which this coupling and suppression of the thermoacoustic mode occur.

Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physicochemical hydrodynamics. Recently, Li et al. (Phys. Rev. Lett., vol. 120, 2018, 224501) and Kim & Stone (J. Fluid Mech., vol. 850, 2018, pp. 769–783) reported a segregative behaviour (i.e. demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, we investigate the flow dynamics after the occurrence of the phase segregation. As example, we take the 1,2-hexanediol–water binary droplet system. First, we reveal experimentally the overall physicochemical hydrodynamics of the evaporation process, including the segregative behaviour and the resulting flow structure close to the substrate. By quantifying the evolution of the radial flow, we identify three successive life stages of the evaporation process. At Stage I, a radially outward flow is observed, driven by the Marangoni effect. At the transition to Stage II, the radial flow reverses partially, starting from the contact line. This flow breaks the axial symmetry and remarkably is driven by the segregation itself. Finally at Stage III, the flow decays as the evaporation ceases gradually. At this stage, the segregation has grown to the entire droplet, and the flow is again controlled by the Marangoni effect. The resulting Marangoni flow homogenizes the distribution of the entrapped volatile water over the whole droplet.

We study the effect of gas rarefaction and wall confinement on the propagation of vibroacoustic disturbances in a microchannel, generated by non-uniform (localized) time-harmonic oscillations of one of the channel walls. The problem is studied in the entire range of gas rarefaction rates, combining continuum and free-molecular limit analyses with direct simulation Monte Carlo calculations. Gas rarefaction is found to strongly increase the signal decay rate, varying between a slowly decaying propagating wave parallel to the channel walls at continuum conditions, to a near-source confined acoustic perturbation in the free-molecular regime. The impact of the stationary scattering wall is examined in detail, and the effect of replacing between fully diffuse and specular boundary reflections is found to slightly reduce the decay rate of the signal. The frequency dependence of the force generated by the gas film on the channel walls is calculated. Here, gas rarefaction smooths the transition between resonance and antiresonance behaviours observed in the continuum regime. A model set-up of a fully specular channel with a point delta source is examined, for which closed-form expressions are found for the effect of the stationary wall on the hydrodynamic perturbations and the acoustic force. These expressions assist in rationalizing the fundamental effect of the scattering wall on the system response.