Dispersion of microswimmers is widespread in environmental and biomedical applications. In the category of continuum modelling, the present study investigates the dispersion of microswimmers in a confined unidirectional flow under a diffuse reflection boundary condition, instead of the specular reflection and the Robin boundary conditions prevailing in existing studies. By the moment analysis based on the Smoluchowski equation, the asymptotic and transient solutions are directly obtained, as validated against random walk simulations, to illustrate the effects of mean flow velocity, swimming velocity and gyrotaxis on the migration and distribution patterns of elongated microswimmers. Under the diffuse reflection boundary condition, microswimmers are found more likely to exhibit M-shaped low-shear trapping and even pronounced centreline aggregation, and elongated shape affects depletion at the centreline. Along the flow direction, they readily form unimodal distributions oriented downstream, resulting in prominent downstream migration. Near the centreline, the migration is almost entirely downstream, while upstream and vertical migrations are confined near the boundaries. When the mean flow velocity and swimming velocity are comparable, the system undergoes a temporal transition from M-shaped low-shear trapping to M-shaped high-shear trapping and ultimately to centreline aggregation. The downstream migration continuously strengthens over time, while the upstream first strengthens and then weakens. Moreover, the coupling between swimming-induced diffusion and convective dispersion leads to non-monotonic, fluctuating trends in both drift velocity and dispersivity over time. These results contribute to a deeper understanding of the underlying mechanisms governing the locomotion and control of natural and synthetic microswimmers.

A series of new laboratory experiments explore the transient flow in an enclosed space of depth $H$, which is subject to an upward displacement ventilation flux, $Q_V$, and which contains a localised heat source of buoyancy flux $F_s$, when the buoyancy of the ventilation air changes by $\Delta g'$. Initially, the plume, produced by the heat source, entrains the ventilation air, leading to a two-layer stratification which depends on the dimensionless strength of convection, $\mu \propto F_s^{1/3}H^{5/3}/Q_V$. When the buoyancy of the ventilation air decreases, $\Delta g' \lt 0$, a new layer of relatively dense fluid grows next to the floor. The fluid entrained by the plume from this new layer causes the plume to intrude between the original upper and lower layers. For a sufficiently large decrease in buoyancy, $|\Delta g' Q_V /F_s| \gt 1$, then as the new lower layer grows, the plume eventually becomes negatively buoyant relative to the original lower layer and intrudes between the new lowest layer and the original lower layer. When the buoyancy of the air supply increases, $\Delta g'\gt 0$, it mixes with the fluid in the original lower layer. If the increase in buoyancy is sufficient, $\Delta g' Q_V/F_s\gt 1$, then the new supply air eventually also mixes with the original upper layer. In each case, a new two-layer stratification becomes re-established. We propose new models for the evolution of the transient flow, assuming that the buoyancy profile can be approximated by a staircase of well-mixed layers. These layers are emptied or filled through the action of the plume and ventilation. We find that the model predictions are consistent with our new experiments in each of the four regimes. We conclude by discussing the implications of these transient flows for thermal comfort and the mixing of contaminants into the occupied lower region of the space.

This study investigates the effects of thermal buoyancy on the ascent or descent dynamics and path instabilities of a finite-size sphere through direct numerical simulations with the immersed boundary method. By parametrically varying the density ratio $(\rho _r)$, Richardson number $({\textit{Ri}})$ and Galileo number $(\textit{Ga})$, four distinct motion regimes are identified: stable vertical, zigzagging, spiralling and chaotic regimes. These regimes emerge from the competition between particle inertial, gravitational forces and fluid thermal-buoyant forces. Compared with isothermal cases, particles with positive Richardson numbers exhibit accelerated motion due to thermal buoyancy. The critical Reynolds numbers ${\textit{Re}}_{p,cr}$ for their path instability are significantly reduced by amplifying wake recirculation zones and triggering vortex shedding. This destabilization mechanism is markedly more pronounced for light particles $(\rho _r \lt 1)$ than heavy particles $(\rho _r \gt 1)$. The present results reveal that the dynamics of heated light particles $(\rho _r=0.5, {\textit{Ri}}\gt 0)$ are governed by the codependent interplay of thermal-buoyancy intensity (${\textit{Ri}}$) and gravitational force (${\textit{Ga}}$), which collectively dictate velocity modulation and path instability patterns. Notably, thermal buoyancy elevates particle Reynolds numbers $({\textit{Re}}_p)$ while could reduce Nusselt numbers, arising from competing mechanisms between intensified convective transport and impaired conductive heat transfer – particularly pronounced for low ${\textit{Ga}}$ particles. These findings bridge the gap between fundamental fluid mechanics and thermal engineering, offering insights to optimize thermal management in particle-laden flows systems, such as industrial heat exchangers and fluidized bed reactors, where thermohydrodynamic coupling effect plays a key role in the performance.

The evolution of the mixing layer in rotation-driven Rayleigh–Taylor (RT) turbulence is investigated theoretically and numerically. It is found that the evolution of the turbulent mixing layer in rotation-driven RT turbulence is self-similar, but the width of the mixing layer does not follow the classical quadratic growth observed in planar RT turbulence induced by constant external acceleration. Based on the approach used in cylindrical RT turbulence without rotation (Zhao et al. 2021, Phys. Rev. E, vol. 104, 055104), a theoretical model is established to predict the growth of mixing widths in rotation-driven RT turbulence, and the model’s excellent agreement with direct numerical simulations (DNS) serves to validate its reliability. The model proposes a rescaled time that allows for the unification of the evolutions of the mixing layers in rotation-driven RT turbulence with various Atwood numbers and rotation numbers. It is further identified that the growth law described by the model of rotation-driven RT turbulence can be recovered to quadratic growth when the effects of geometrical curvature, radial inhomogeneity of the centrifugal force, and Coriolis force become negligible. Moreover, based on the DNS results, we find that turbulent mixing layers in rotation-driven RT turbulence cover a wide range of length scales. The strong rotation at the same Atwood number enhances the generation of fine-scale structures but is not conducive to overall fluid mixing within the mixing layer.

Addition of polymers modifies a turbulent flow in a manner that depends non-trivially on the interplay of fluid inertia, quantified by the Reynolds number $\textit{Re}$, and the elasticity of the dissolved polymers, given by the Deborah number $\textit{De}$. We use direct numerical simulations to study polymeric flows at different $\textit{Re}$ and $\textit{De}$ numbers, and uncover various features of their dynamics. Polymeric flows exhibit a non-unique scaling of the energy spectrum that is a function of $\textit{Re}$ and $\textit{De}$, owing to different dominant contributions to the total energy flux across scales, with the weakening of fluid nonlinearity with decreasing $\textit{Re}$ also leading to the reduction of the polymeric scaling range. This behaviour is also manifested in the real space scaling of structure functions. We also shed light on how the addition of polymers results in slowing down the fluid nonlinear cascade resulting in a depleted flux, as velocity fluctuations with less energy persist for longer times in polymeric flows, especially at intermediate $\textit{Re}$ numbers. These velocity fluctuations exhibit intermittent, large deviations similar to that in a Newtonian flow at large $\textit{Re}$, but differ more and more as $\textit{Re}$ becomes smaller. This observation is further supported by the statistics of fluid energy dissipation in polymeric flows, whose distributions collapse on to the Newtonian at large $\textit{Re}$, but increasingly differ from it as $\textit{Re}$ decreases. We also show that polymer dissipation is significantly less intermittent compared with fluid dissipation, and even less so when elasticity becomes large. Polymers, on an average, dissipate more energy when they are stretched more, which happens in extensional regions of the flow. However, owing to vortex stretching, regions with large rotation rates also correlate with large polymer extensions, albeit to a relatively less degree than extensional regions.

Lubricant viscoelasticity arises due to a finite polymer relaxation time ($\lambda$) which can be exploited to enhance lubricant performance. In applications such as bearings, gears, biological joints, etc., where the height-to-length ratio ($H_0 / \ell _x$) is small and the shear due to the wall velocity ($U_0$) is high, a simplified two-dimensional computational analysis across the channel length and height reveals a finite increase in the load-carrying capacity of the film purely due to polymer elasticity. In channels with a finite length-to-width ratio, $a$, the spanwise effects can be significant, but the resulting mathematical model is computationally intensive. In this work, we propose simpler reduced-order models, namely via (i) a first-order perturbation in the Deborah number ($\lambda U_0 / \ell _x$) and (ii) the viscoelastic Reynolds approach extended from Ahmed & Biancofiore (J. Non-Newtonian Fluid Mech., vol. 292, 2021, 104524). We predict the variation in the net vertical force exerted on the channel walls (for a fixed film height) versus increasing viscoelasticity, modelled using the Oldroyd-B constitutive relation, and the channel aspect ratio. The models predict an increase in the net force, which is zero for the Newtonian case, versus both the Deborah number and the channel aspect ratio. Interestingly, for a fixed $\textit{De}$, this force varies strongly between the two limiting cases (i) $a \ll 1$, an infinitely wide channel, and (ii) $a \gg 1$, an infinitely short channel, implying a change in the polymer response. Furthermore, we observe a different trend (i) for a spanwise-varying channel, in which a peak is observed between the two limits, and (ii) for a spanwise-uniform channel, where the largest load value is for $a \ll 1$. When $a$ is O($1$), the viscoelastic response varies strongly and spanwise effects cannot be ignored.

Direct numerical simulations (DNS) are performed to investigate the dependence of the Prandtl number ($\textit{Pr}$) and radius ratio ($\eta =r_{i}/r_{o}$) on the asymmetry of the mean temperature radial profiles in turbulent Rayleigh–Bénard convection (RBC) within spherical shells. Unlike planar RBC, the temperature drop, and the thermal and viscous boundary layer thicknesses, at the inner and outer boundaries are not identical in spherical shells. These differences in the boundary layer properties in spherical RBC contribute to the observed asymmetry in the radial profiles of temperature and velocity. The asymmetry originates from the differences in curvature and gravity at the two boundaries, and in addition, is influenced by $\textit{Pr}$. To investigate the $\eta$ and $\textit{Pr}$ dependence of these asymmetries, we perform simulations of Oberbeck–Boussinesq convection for $\eta = 0.2,0.6$ and $0.1 \leqslant Pr \leqslant 50$, and for a range of Rayleigh numbers ($Ra$) varying between $5 \times 10^{6}$ and $5 \times 10^{7}$. The Prandtl numbers that we choose cover a broad range of geophysical relevance, from low-$\textit{Pr}$ regimes ($\textit{Pr}=0.1$) representative of gas giants such as Jupiter and Saturn, to high-$\textit{Pr}$ regimes characteristic of organic flows used in the convection experiments ($\textit{Pr}=50$). A centrally condensed mass, with the gravity profile $g \sim 1/r^{2}$, is employed in this study. Our results show that the asymmetry at smaller $\eta$ exhibits a stronger $\textit{Pr}$ dependence than at larger $\eta$. Various assumptions for quantifying this asymmetry are evaluated, revealing that different assumptions are valid in different $\textit{Pr}$ regimes. It is shown that the assumption of the equal characteristic plume separation at the inner and outer boundaries, as well as the assumption of the identical thermal fluctuation scales between the two boundary layers, is valid only for $0.2 \lesssim Pr \lesssim 1$. In contrast, assumptions based on the equivalency of the local thermal boundary layer Rayleigh numbers and laminar natural-convective boundary layers are validated at $\textit{Pr}=50$ for the explored parameter space. Furthermore, new assumptions based on the statistical analysis of the inter-plume islands are proposed for $\textit{Pr}=0.1$ and $50$, and these are validated against the DNS data. These findings provide insights into the $(Pr,\eta)$ dependence of asymmetry in spherical RBC, and offer a framework for studying similar systems in geophysical and astrophysical contexts.

Plumes generated from a point buoyant source are relevant to hydrothermal vents in lakes and oceans on and beyond Earth. They play a crucial role in determining heat and material transport and thereby local biospheres. In this study, we investigate the development of rotating point plumes in an unstratified environment using both theory and numerical simulations. We find that in a sufficiently large domain, point plumes cease to rise beyond a penetration height $h_{{f}}$, at which buoyancy flux from the heat source is leaked laterally to the ambient fluid. The height $h_{{f}}$ is found to scale with the rotational length scale $h_{ \!{ f}}\sim L_{ \!\textit{ rot}}^p\equiv ({F_0}/{f^3})^{{1}/{4}},$ where $F_0$ is the source buoyancy flux, and $f=2\varOmega$ is the Coriolis parameter ($\varOmega$ is the rotation rate). In a limited domain, the plume may reach the top boundary or merge with neighbouring plumes. Whether rotational effects dominate depends on how $L_{\textit{rot}}^{p}$ compares to the height of the domain $H$ and the distance between the plumes $L$. Four parameter regimes can therefore be identified, and are explored here through numerical simulation. Our study advances the understanding of hydrothermal plumes and heat/material transport, with applications ranging from subsurface lakes to oceans in icy worlds such as Snowball Earth, Europa and Enceladus.

We study aeolian saltation over an erodible bed at full transport capacity in a wind tunnel with a relatively thick boundary layer. Lagrangian tracking of size-selected spherical particles resolves their concentration, velocity and acceleration. The mean particle concentration follows an exponential profile, while the mean particle velocity exhibits a convex shape. In contrast to current assumptions, both quantities appear sensitive to the friction velocity. The distributions of horizontal accelerations are positively skewed, though they contain negative tails associated with particles travelling faster than the fluid. The mean wind velocity profiles, reconstructed down to millimetric distances from the bed using the particle equation of motion, have an approximately constant logarithmic slope and do not show a focal point. The aerodynamic drag force increases with distance from the wall and, for the upward moving particles, exceeds the gravity force already at a few particle diameters from the bed. The vertical drag component resists the motion of both upward and downward moving particles with a magnitude comparable to the lift force, which is much smaller than gravity but non-negligible. Coupling the assumption of ballistic vertical motion and the measured streamwise velocities, the mean trajectories are reconstructed and found to be strongly influenced by aerodynamic drag. This is also confirmed by the direct identification of trajectory apexes, and demonstrated over a wide range of friction velocities. Taken together, these results indicate that aerodynamic drag and lift may play a more significant role in the saltation process than presently recognized, being complementary rather than alternative to splash processes.

This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately $52^\circ$ between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. We further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.

This study experimentally investigates wake recovery mechanisms behind a floating wind turbine subjected to imposed fore-aft (surge) and side-to-side (sway) motions. Wind tunnel experiments with varying free-stream turbulence intensities ($\textit{TI}_{\infty } \in [1.1, 5.8]\,\%$) are presented. Rotor motion induces large-scale coherent structures – pulsating for surge and meandering for sway – whose development critically depends on the energy ratio between the incoming turbulence and the platform motion. The results provide direct evidence supporting the role of these structures in enhancing wake recovery, as previously speculated by Messmer, Peinke & Hölling (J. Fluid Mech., vol. 984, 2024, A66). These periodic structures significantly increase Reynolds shear stress gradients, particularly in the streamwise–lateral direction, which are key drivers of wake recovery. However, their influence diminishes with increasing $\textit{TI}_{\infty }$: higher background turbulence weakens the coherent flow patterns, reducing their contribution to recovery. Beyond a threshold turbulence level – determined by the energy, frequency and direction of motion – rotor-induced structures no longer contribute meaningfully to recovery, which becomes primarily driven by the free-stream turbulence. Finally, we show that the meandering structures generated by sway motion are more resilient in turbulent backgrounds than the pulsating modes from surge, making sway more effective for promoting enhanced wake recovery.

The crystallisation that occurs when a drop is in contact with a cold surface is a particularly challenging phenomenon to capture experimentally and describe theoretically. The situation of a liquid–liquid interface, where crystals appear on a mobile interface is scarcely studied although it provides a defect-free interface. In this paper, we quantify the dynamics of crystals appearing upon the impact of a drop on a cool liquid bath. We rationalise our observations with a model considering that crystals appear at a constant rate depending on the thermal shock on the expanding interface. This model provides dimensionless curves on the number and the surface area of crystals that we compare with our experimental measurements.