Rotating Rayleigh–Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness $S$ is produced by the interaction between the $n=0,1$ and $n=1,2$ vertical eigenmodes. The $n=0$ (barotropic) mode contributes positively to $S$ mainly by stretching the vertical relative vorticity, an ageostrophic effect. The $n=2$ mode makes a minor negative contribution to $S$ by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts $S$ to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, ${Ro_g}$. The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then the system enters the equilibrium stage. The stretching of vertical vorticity still contributes to $S$ dominantly. At ${Ro_g}\gtrsim 0.5$, the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength, and weakens its influence on $S$.

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

The diffusiophoresis of charged hydrophobic nanoparticles (NPs) governed by an imposed ionic concentration gradient is analysed. The main objective is to elucidate the impact of the laterally mobile adsorbed surface ions at the interface on the propulsion of the hydrophobic NPs in diffusiophoresis. In addition, the dielectric polarization due to the difference in dielectric constant between the NPs and the suspension medium is also considered. The mobile surface ions create a friction as well as an electric force at the hydrophobic surface, which leads to a modification of the slip velocity condition and the slip length. We obtain an exact numerical solution of the governing electrokinetic equations in their full form by adopting a control volume formulation. The numerical model is supplemented by analytical solutions derived based on the Debye–Hückel linearization. We find that the lateral mobility of the surface ions obstruct the coions to diffuse from the higher concentration side to the lower concentration side, which results in a repulsive force to the particle leading to the occurrence of a negative mobility. Based on the numerical results and analytical solutions, we have shown that for a fully mobile surface charge, the diffusiophoresis of a hydrophobic NP is identical to the diffusiophoresis of a liquid droplet whose viscosity is related to the slip length of the hydrophobic particle. We establish that the dielectric polarization enhances the velocity of a hydrophobic particle, which has potential applications in the practical context.

We conducted an axisymmetric numerical study of drop impact on a thin film of the same liquid in order to generate maps identifying the fluid elements in the drop and film that are transferred to the corolla during impact. We find that mass contribution from the drop comes from a surprisingly thin surface layer on the drop, and furthermore, that the shape of this layer in the drop and the film scales with film thickness, not the Weber number and Reynolds number as one might expect. The maps could be used to tailor drop composition for applications such as coatings or encapsulations.

Standing acoustic waves have been known to generate Eulerian time-mean ‘streaming’ flows at least since the seminal investigation of Lord Rayleigh in the 1880s. Nevertheless, a recent body of numerical and experimental evidence has shown that inhomogeneities in the ambient density distribution lead to much faster flows than arise in classical Rayleigh streaming. The emergence of these unusually strong flows creates new opportunities to enhance heat transfer in systems in which convective cooling cannot otherwise be easily achieved. To assess this possibility, a theoretical study of acoustic streaming in an ideal gas confined in a rectangular channel with top and bottom walls maintained at fixed but differing temperatures is performed. A two time scale system of equations is utilized to efficiently capture the coupling between the fast acoustic waves and the slowly evolving streaming flow, enabling strongly nonlinear regimes to be accessed. A large suite of numerical simulations is carried out to probe the streaming dynamics, to highlight the critical role played by baroclinically generated wave vorticity and to quantify the additional heat flux induced by the standing acoustic wave. Proper treatment of the two-way coupling between the waves and mean flow is found to be essential for convergence to a self-consistent steady state, and the variation of the resulting acoustically enhanced steady-state heat flux with both the amplitude of the acoustic wave and the $O(1)$ aspect ratio of the channel is documented. For certain parameters, heat fluxes almost two orders of magnitude larger than those realizable by conduction alone can be attained.

Flow resistance reduction, quantified as a change in flow rate with respect to a reference isothermal flow driven by the same pressure gradient, is realizable in a channel flow using a thermal wave applied on the bounding wall. Countercurrent waves provide a resistance-reducing effect at any wave velocity, Reynolds number and wavenumber considered. Cocurrent waves can reduce resistance only if the wave velocity is lower than a certain threshold, and the Reynolds number is larger than a certain threshold, otherwise, such waves increase resistance. The increase of the wave amplitude increases resistance reduction and resistance increase up to a specific limit. It is possible to reduce resistance up to 20 times compared with the isothermal channel using proper waves. It is shown that the same effect is achieved regardless of the waves applied at the upper and lower walls. The wave-modified flows are shown to be stable for the conditions used in this study.

The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.

This work examines the control of cross-flow instabilities (CFIs) and laminar–turbulent transition on a swept wing, through the plasma-based base flow modification (BFM) technique. The effect of experimentally derived plasma body forces on the steady boundary layer base flow is explored through numerical simulations. Linear stability theory is subsequently used to predict the net BFM effect on CFIs. Based on these preliminary predictions, experiments are conducted in a low-turbulence wind tunnel where a spanwise-invariant plasma actuator is installed near the wing leading edge and operated at constant input voltage and frequency. Various flow parameters governing the plasma-based BFM technique are investigated, namely the Reynolds number, angle of attack and wavelength of excited stationary CFI modes. Stationary and travelling CFIs are quantified by planar particle image velocimetry while the transition topology and location are recorded by infrared thermography. The results confirm the stabilising effect of BFM on the swept-wing boundary layer. However, the plasma-based BFM is found to render the boundary layer more susceptible to travelling CFIs. In the presence of both net BFM effect and intrinsic plasma unsteady perturbations, the plasma-based BFM technique achieves transition delay with specific combinations of Reynolds number, angle of attack and wavelength of excited stationary CFI modes. The present findings provide insights into the fundamental principles of operating plasma actuators within the context of BFM control.

Scale dependence of local shearing motion is investigated experimentally in decaying homogeneous isotropic turbulence generated through multiple-jet interaction. The turbulent Reynolds number, based on the Taylor microscale, is between approximately 900 and 400. Velocity fields, measured using particle image velocimetry, are analysed through the triple decomposition of a low-pass filtered velocity gradient tensor, which quantifies the intensities of shear and rigid-body rotation at a given scale. These motions manifest predominantly as layer and tubular vortical structures, respectively. The scale dependence of the moments of velocity increments, associated with shear and rigid-body rotation, exhibits power-law behaviours. The scaling exponents for shear are in quantitative alignment with the anomalous scaling of the velocity structure functions, suggesting that velocity increments are influenced predominantly by shearing motion. In contrast, the exponents for rigid-body rotation are markedly smaller than those predicted by Kolmogorov scaling, reflecting the high intermittency of rigid-body rotation. The mean flow structure associated with shear at intermediate scales is investigated with conditional averages around locally intense shear regions in the filtered velocity field. The averaged flow field exhibits a shear layer structure with aspect ratio approximately 4.5, surrounded by rotating motion. The analysis at different scales reveals the existence of self-similar structures of shearing motion across various scales. The mean velocity jump across the shear layer increases with the layer thickness. This relationship is well predicted by Kolmogorov's second similarity hypothesis, which is useful in predicting the mean characteristics of shear layers across a wide range of scales.

High angle of attack flows over swept three-dimensional wings based on the NACA 0015 profile are studied numerically at low Reynolds numbers. Linear stability analysis is used to compute instability and receptivity of the flow via the respective three-dimensional (triglobal) direct and adjoint eigenmodes. The magnitude of the adjoint eigenvectors is used to identify regions of maximum flow receptivity to momentum forcing. It is found that such regions are located above the primary three-dimensional separation line, their spanwise position varying with wing sweep. The wavemaker region corresponding to the leading global eigenmode is computed and found to lie inside the laminar separation bubble (LSB) at the spanwise location of peak recirculation. Increasing the Reynolds number leads to the wavemaker becoming more compact in the spanwise direction, and concentrated in the top and bottom shear layers of the LSB. As sweep is introduced, the wavemaker moves towards the wing tip, following the spanwise displacement of maximum recirculation. Flow modifications resulting from application of different types of forcing are studied by direct numerical simulation initialised with insights gained from stability analysis. Periodic forcing at the regions of maximum receptivity to momentum forcing results in greater departure from the baseline case compared to same (low, linear) amplitude forcing applied elsewhere, underlining the potential of linear stability analysis to identify optimal regions for actuator positioning.

The present study investigates streamwise ($\overline {u^2}$) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the $\overline {u^2}$ production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number ($Re_{\tau }$). These properties are analysed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of $Re_{\tau }$, revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of $\overline {u^2}$ are always associated with local maxima in the $\overline {u^2}$ production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of $\overline {u^2}$, thereby classifying the $\overline {u^2}$ profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the ‘inner’ and ‘outer’ regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in $\overline {u^2}$ profiles. Conditional averaging suggests existence of similar phenomena even in low $Re_{\tau }$ canonical and/or weak APG TBLs, albeit with the outer-region mechanisms weaker than those in the inner region. This explains the absence of their $\overline {u^2}$ outer peak and the dominance of $\overline {u^2}$ wall-normal transport away from the wall, which potentially originates from the inner region. Given that the wall-ward/away-from-wall transport of $\overline {u^2}$ is governed by the $Q_4$(sweeps)/$Q_2$(ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the $\overline {u^2}$ outer peak corresponds with the statistical dominance of $Q_4$ events in the outer region. Besides unravelling the dynamical significance of $Q_2$ and $Q_4$ events in the outer region of TBLs, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high $Re_{\tau }$.

We use multiphase direct numerical simulations to identify, analyse and quantify components of wall-normal heat flux distributions in evaporative vertical falling films with surface modifications at industrially relevant conditions. Previous experiments showed a potential increase of the heat transfer rate through the film by up to 100 % using various types of modifications. We show that the modifications induce significant advective heat transport and hypothesise that four synergistic mixing mechanisms are behind the heat transfer rate improvement. Additionally, we examine how the important surface topology parameters, pitch $\hat {p}$ (distance between modifications), height $\hat {h}$ and the liquid Prandtl number $\mathit {Pr}_l$, influence the mode of heat transport and the Nusselt number $\mathit {Nu}$. We show that $\hat {p}/\hat {h} \approx 10$ maximises $\mathit {Nu}$ and that the optimal pitch is related to the recirculation zone length $L_r$ behind the modification. We find that $L_r/\hat {h} \approx 3.5$ and that $\mathit {Nu} \propto \mathit {Pr}_l^{0.42}$ in the investigated parameter ranges. We also show that all our cases on both smooth and modified surfaces have $\mathit {Pe}_l \gg 1$ and collapse well on a line $\mathit {Nu} \propto (\mathit {Pe}_l/\mathit {Re})^{0.35}$. This relation suggests that $\mathit {Nu}$ is governed by the balance of film mixing, thermal resistance and diffusivity, and that the ratio $\mathit {Pe}_l/\mathit {Re}$ can be used to estimate $\mathit {Nu}$. Our methodology and findings extend the knowledge concerning the mechanisms behind the heat transfer improvement due to surface modifications and facilitate guidelines for designing more efficient modified surfaces in industrial evaporators.

In this paper it is shown that a modal detuned instability of periodic near-wall streaks originates a large-scale structure in the bulk of the turbulent channel flow. The effect of incoherent turbulent fluctuations is included in the linear operator by means of an eddy viscosity. The base flow is an array of periodic two-dimensional streaks, extracted from numerical simulations in small domains, superposed to the turbulent mean profile. The stability problem for a large number of periodic units is efficiently solved using the block-circulant matrix method proposed by Schmid et al. (Phys. Rev. Fluids, vol. 2, 2017, 113902). For friction Reynolds numbers equal or higher than $590$, it is shown that an unstable branch is present in the eigenspectra. The most unstable eigenmodes display large-scale modulations whose characteristic wavelengths are compatible with the large-scale end of the premultiplied velocity fluctuation spectra reported in previous computational studies. The wall-normal location of the large-wavelength near-wall peak in the spanwise spectrum of the eigenmode exhibits a power-law dependence on the friction Reynolds number, similarly to that found in experiments of pipes and boundary layers. Lastly, the shape of the eigenmode in the streamwise-wall-normal plane is reminiscent of the superstructures reported in the recent experiments of Deshpande et al. (J. Fluid Mech., vol. 969, 2023, A10). Therefore, there is evidence that such large-wavelength instabilities generate large-scale motions in wall-bounded turbulent flows.

Many natural and industrial processes involve the flow of fluids made of solid particles suspended in non-Newtonian liquid matrices, which are challenging to control due to the fluid's nonlinear rheology. In the present work, a Taylor–Couette canonical system is used to investigate the flow of dilute to semi-dilute suspensions of neutrally buoyant spherical particles in highly elastic base polymer solutions. Friction measurement synchronized with direct flow visualization are combined to characterize the critical conditions for the onset of elasto-inertial instabilities, expected here as a direct transition to elasto-inertial turbulence (EIT). Adding a low particle volume fraction (${\leq }2\,\%$, dilute regime) does not affect the nature of the primary transition and reduces the critical Weissenberg number for the onset of EIT, despite a significant decrease in the apparent fluid elasticity. However, for particle volume fractions ${\geq }6\,\%$ (semi-dilute regime), EIT is no longer observed in the explored Reynolds range, suggesting an apparent relaminarization with yet not further decrease in fluid elasticity. Instead, a new regime, termed here elasto-inertial dissipative (EID), was uncovered. It originates from particle–particle interactions altering particle–polymer interactions and occurring under elasto-inertial conditions comparable to those of EIT. Increasing particle volume fraction in the semi-dilute regime and, in so, the particle contribution to the overall viscosity, delays the onset of EID similarly to what was observed previously for EIT in lower elasticity fluids. After this onset, a decrease in the pseudo-Nusselt number observed with increasing inertia and particle-to-polymer concentration ratio confirms a particle-induced alteration of energy transfer in the flow.

Solving the three-dimensional boundary layer equations carries theoretical significance and practical applications, which also poses substantial challenges due to its inherent complexity. In this paper, the laminar boundary layer equations for the symmetry plane of three-dimensional bodies are derived in an orthogonal curvilinear coordinate system associated with the principal curvatures. The derivation of the boundary layer equations is based not only on the common symmetric properties of the flow, as given by Hirschel et al. (Three-Dimensional Attached Viscous Flow, 2014, Academic Press, pp. 183–187), but also incorporates the geometric symmetry properties of the body. The derived equations are more representative and simplified. Notably, these equations can degenerate to a form consistent with or equivalent to the commonly used boundary layer equations for special bodies such as flat plates, cones and spheres. Furthermore, for hypersonic flows, the crossflow velocity gradient at the boundary layer edge on the symmetry plane is derived based on Newtonian theory. Subsequently, this parameter can provide the necessary boundary condition needed for solving the boundary layer equations using existing methods. Finally, as examples, the equations developed in this paper are solved using the difference-differential method for several typical three-dimensional blunt shapes that appeared on hypersonic vehicles. They prove to be useful in the analysis and interpretation of boundary layer flow characteristics in the symmetry plane of blunt bodies.

Free transverse oscillations of an elastically mounted circular cylinder with low mass-damping are studied with a focus on the effects of the cylinder end condition on structural oscillations and vortex shedding. While the top end of the cylinder pierces the free surface of a water channel, the lower end is changed to have three end conditions: an attached endplate, an endplate unattached from the cylinder at varying gaps and no endplate. All three response branches are examined, with the reduced velocity sweeping $2 \le {U^\ast } \le 15$ (corresponding to a Reynolds number range of $2000 \le Re \le 14\;700$). Although the cylinder oscillations are unaffected by the end condition in the initial and upper branches, they show significant dependency on the end condition in the lower branch. When the endplate is attached or unattached with a small gap, the upper-to-lower branch transition occurs with a sudden decrease in oscillation amplitude, after which the lower branch maintains a near-constant amplitude. For larger gaps or no endplate, with increasing reduced velocity, the oscillation amplitude decreases gradually from its peak without any discernible sign of transition between the upper and lower branches. The three-dimensional effects of the gap are the basis for these differences in oscillation. Atop the strong tip vortex, a low-magnitude streamwise velocity region develops downstream of the cylinder, which delays upper-to-lower branch transition over the cylinder span that sees this low-velocity region. With increasing gap, this low-velocity region and the delay in transition spread over larger spanwise extents, forcing the overall body to oscillate at larger amplitudes.

We numerically study the influence of a soluble surfactant on the microjetting mode of the liquid–liquid flow focusing configuration. The surfactant adsorbs on the interface next to the feeding capillary and accumulates in front of the emitted jet, significantly lowering the surface tension there. The resulting Marangoni stress substantially alters the balance of the tangential stresses at the interface but does not modify the interface velocity. The global stability analysis at the minimum flow rate stability limit shows that the Marangoni stress collaborates with soluto-capillarity to stabilize the microjetting mode. Our analysis unveils the noticeable effect of the Marangoni stress associated with the surface tension perturbation. Surfactant diffusion and desorption hardly affect the stability limit. Transient numerical simulations show how subcritical and supercritical base flows respond to a spatially localized initial perturbation. Our parametric study indicates that the minimum flow rate ratio depends on the adsorption constant and the surfactant concentration through the product of these two variables. The surfactant stabilizing effect increases with the outer stream flow rate. We show that surfactants not only stabilize the microemulsion resulting from the jet breakup in hydrodynamic focusing, but also allow for the reduction of droplet size. Our findings advance the fundamental understanding of the complex role of surfactants in tip streaming via hydrodynamic focusing. In particular, our results contradict the common assumption that adding surfactant favours tip streaming simply because it reduces the meniscus tip surface tension.

Nonlinear steady solutions of the barotropic quasi-geostrophic equation in basins, gulfs and channels on a $\beta$-plane are presented. The domains are rectangular with arbitrary aspect ratios. The two-dimensional solutions assume a linear relationship between the potential vorticity $q$ and the stream function $\psi$. The sign of the slope in the linear $q\unicode{x2013}\psi$ relationship defines two broad sets of solutions. For a positive slope, the solutions in a closed basin correspond to the inertial gyres derived by Fofonoff in 1954. The negative slope solutions consist of normal modes that can be resonant. For gulfs and channels, the conditions at the open boundaries are almost arbitrary flows entering or leaving the domain. Such conditions allow a great variety of solutions in the interior, characterised mainly by arrays of vortices with alternate signs. Several examples are presented and discussed.

We propose a simple method to identify unstable parameter regions in general inviscid unidirectional shear flow stability problems. The theory is applicable to a wide range of basic flows, including those that are non-monotonic. We illustrate the method using a model of Jupiter's alternating jet streams based on the quasi-geostrophic equation. The main result is that the flow is unstable if there is an interval in the flow domain for which the reciprocal Rossby Mach number (a quantity defined in terms of the zonal flow and potential vorticity distribution), surpasses a certain threshold or ‘hurdle’. The hurdle height approaches unity when we can take the hurdle width to greatly exceed the atmosphere's intrinsic deformation length, as holds on gas giants. In this case, the Kelvin–Arnol’d sufficient condition of stability accurately detects instability. These results improve the theoretical framework for explaining the stable maintenance of Jupiter and Saturn's jets over decadal time scales.

This study explores the implementation of an online control strategy based on dynamic mode decomposition in the context of flow control. The investigation is conducted mainly with a fixed Reynolds number of $Re = 100$, focusing on the flow past a circular cylinder constrained between two walls to mitigate vortex shedding. The control approach involves the activation of two synthetic jets on the cylinder through blowing and suction. Velocity fluctuations in the wake, specifically in the $x$-direction, are harnessed to ascertain the mass flow rate of the jets using the linear quadratic regulator and online dynamic mode decomposition. The study systematically assesses the control performance across various configurations, including different values of the input penalty factor ${\boldsymbol {R}}$, varying numbers of probes and distinct probe arrangement methods. The synthetic jets prove effective in stabilising the separation bubble, and their interaction with the unsteady wake leads to a notable reduction in drag force, its fluctuations and the amplitude of the lift force. Specifically, the mean and standard deviation of the drag coefficient witness reductions of $7.44\,\%$ and $96.67\,\%$, respectively, and the standard deviation of the lift coefficient experiences an impressive reduction of $85.18\,\%$. The robustness of the proposed control method has also been tested on two more complicated cases, involving unsteady incoming flows with multiple frequency components. Comparatively, the methodology employed in this paper yields results akin to those obtained through deep reinforcement learning in terms of control effectiveness. However, a noteworthy advantage lies in the substantial reduction of computational resource consumption, highlighting the efficiency of the proposed approach.