The problem of a uniform current interacting with bodies submerged beneath a homogeneous ice sheet is considered, based on linearised velocity potential theory for fluid and elastic thin plate theory for ice sheet. This problem is commonly solved by the boundary element method (BEM) with the Green function, which is highly effective except when the Green function becomes singular, and the direct solution of the BEM is no longer possible. However, flow behaviour, body force and ice sheet deflection near the critical Froude numbers are of major practical interest, such as in ice breaking. The present work successfully resolves this challenge. A modified boundary integral equation (BIE) is derived, which converts the singular Green function term to a far-field one and removes the singularity. The BIE is then imposed at infinity for additional unknowns in the far field. It is proved that the solution is finite and continuous at the critical Froude number $F = F_c$, where the body starts generating travelling waves, and finite but discontinuous at depth-based Froude number $F = 1^\pm$. Case studies are conducted for single and double circular cylinders and an elliptical cylinder with various angles of attack. A comprehensive analysis is made on the hydrodynamic forces and the generated flexural gravity wave profiles, and their physical implications are discussed. It is also concluded that the method developed in this paper is not confined to the present case but is also applicable to a variety of related problems when the BEM fails at the critical points.

The extensional rheology of dilute suspensions of spheres in viscoelastic/polymeric liquids is studied computationally. At low polymer concentration $c$ and Deborah number $\textit{De}$ (imposed extension rate times polymer relaxation time), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by $\Delta \textit{De}_{\textit{local}}\gt 0$. This increases the suspension’s extensional viscosity with time and $\textit{De}$ for $De \lt 0.5$. When $\textit{De}$ exceeds 0.5, the coil-stretch transition value, the fully stretched polymers from the far-field collapse in regions with $\Delta \textit{De}_{\textit{local}} \lt 0$ (lower velocity gradient) around the particle’s stagnation points, reducing suspension viscosity relative to the particle-free liquid. The interaction between local flow and polymers intensifies with increasing $c$. Highly stretched polymers impede local flow, reducing $\Delta \textit{De}_{\textit{local}}$, while $\Delta \textit{De}_{\textit{local}}$ increases in regions with collapsed polymers. Initially, increasing $c$ aligns $\Delta \textit{De}_{\textit{local}}$ and local polymer stretch with far-field values, diminishing particle–polymer interaction effects. However, beyond a certain $c$, a new mechanism emerges. At low $c$, fluid three particle radii upstream exhibits $\Delta \textit{De}_{\textit{local}} \gt 0$, stretching polymers beyond their undisturbed state. As $c$ increases, however, $\Delta \textit{De}_{\textit{local}}$ in this region becomes negative, collapsing polymers and resulting in increasingly negative stress from particle–polymer interactions at large $\textit{De}$ and time. At high $c$, this negative interaction stress scales as $c^2$, surpassing the linear increase of particle-free polymer stress, making dilute sphere concentrations more effective at reducing the viscosity of viscoelastic liquids at larger $\textit{De}$ and $c$.

We experimentally and theoretically examine the maximum spreading of viscous droplets impacting ultra-smooth solid surfaces, where viscosity plays a dominant role in governing droplet spreading. For low-viscosity droplets, viscous dissipation occurs mainly in a thin boundary layer near the liquid–solid interface, whereas for high-viscosity droplets, dissipation is expected to extend throughout the droplet bulk. Incorporating these dissipation mechanisms with energy conservation principles, two distinct theoretical scaling laws for the maximum spreading factor ($\beta _m$) are derived: $\beta _m \sim ({\textit{We}}/ {\textit{Oh}})^{1/6}$ for low-viscosity regimes (${\textit{Oh}} \lesssim 0.1$) and $\beta _m \sim \textit{Re}^{1/5}$ for high-viscosity regimes (${\textit{Oh}} \gt 1$), where $\textit{We}$, $\textit{Re}$ and $\textit{Oh}$ are the Weber, Reynolds and Ohnesorge numbers, respectively. Both scaling laws show good agreement with the experimental data for their respective validity ranges of $\textit{Oh}$. Furthermore, to better model experimental data at vanishing $\textit{Re}$, we introduce a semi-empirical scaling law, $\beta _m \sim (A + {\textit{We}}/ {\textit{Oh}})^{1/6}$, where $A$ is a fitting parameter accounting for finite spreading ($\beta _m \approx 1$) at negligible impact velocities. This semi-empirical law provides an effective description of $\beta _m$ for a broad experimental range of $10^{-3} \leqslant {\textit{Oh}} \leqslant 10^0$ and $10^1 \leqslant {\textit{We}} \leqslant 10^3$.

This study investigates the effects of dissipation and the associated self-heating in cone jets of ionic liquids with high electrical conductivities. A numerical model based on the leaky-dielectric formulation that incorporates conservation of energy and temperature-dependent properties (restricted to the viscosity and the electrical conductivity) is developed and compared with isothermal numerical solutions and experimental data for four ionic liquids. The numerical solutions show that self-heating leads to significant temperature increases (up to 446 K) along the cone jet, dramatically enhancing the electrical conductivity and reducing the viscosity. The model reproduces the experimental values of the current for the ionic liquids studied. While isothermal solutions follow established scaling laws, the solutions including self-heating exhibit liquid-specific behaviours due to the unique temperature dependencies of the conductivity and viscosity. Self-heating creates a strong positive feedback between the electric current and the electrical conductivity, resulting in much higher electrospray currents compared with the isothermal solution. Ohmic dissipation dominates over viscous dissipation. Strong self-heating and the opposite effects of temperature on the electrical conductivity and the viscosity, increase the disparity between the two dissipation modes. This work demonstrates the importance of accounting for self-heating in the modelling and analysis of experimental data of cone jets of ionic liquids and other highly conductive liquids. First-principles modelling and case-specific experimental characterisation are necessary to describe these systems, as the traditional scaling laws break down when self-heating is significant.

A mechanical heart valve is a durable device used to replace damaged ones inside a living heart, aiming for regulated blood flow to avoid the risks of cardiac failure or stroke. The modern bileaflet designs, featuring two semicircular leaflets, aim to improve blood flow control and minimise turbulence as compared to the older models. However, these valves require lifelong anticoagulation therapy to prevent blood clots, increasing bleeding risks and necessitating regular monitoring. Turbulence within the valve can lead to complications such as haemolysis (damage to red blood cells), thrombosis, platelet activation and valve dysfunction. It also contributes to energy loss, increased cardiac workload, and endothelial damage, potentially impairing the valve efficiency and increasing the risk of infective endocarditis. To address these challenges, a design-modified St Jude Medical (SJM) valve with streamlined edges was conceptualised and assessed using direct numerical simulations. Results show that the streamlined design minimises abrupt blood flow alterations and reduces turbulence-inducing vortices. Compared to existing SJM valves, the new design ensures smoother flow transitions, reduces flow disturbances, and reduces pressure drop. It significantly decreases shear stress, drag and downstream turbulence, enhancing haemodynamic efficiency. These improvements lower the risk of complications such as haemolysis and thrombosis, offering a safer and more efficient option for valve replacement, establishing the potential of edge streamlining in advancing mechanical heart valve technology, and favouring patient outcomes.

This study connected flow structure and morphological changes in and around a rectangular vegetation patch. The emergent patch was constructed in an 8 cm sand bed. Two patch densities were tested, using a regular configuration of rigid dowels. Near the leading edge of the patch, enhanced turbulence levels produced sediment erosion. Some of the eroded sediment was carried into the patch, forming an interior deposition dune. The denser patch resulted in a smaller dune due to stronger lateral flow diversion and weaker interior streamwise velocity. After the leading-edge dune, in the fully developed region of the patch, vortices formed in the shear layers along the patch lateral edges. Elevated turbulence at the patch edge produced local erosion. For the dense patch, material eroded from the edge was transported into the patch to form a flow-parallel ridge, and there was no net sediment loss/gain by the patch. For the sparse patch, material eroded from the edge was transported away from the patch, resulting in a net loss of sediment from the patch. In the wake of both patches, deposition occurred near the wake edges and not at the wake centreline, which was attributed to the weak lateral transport associated with the weakness of the von Kármán vortex street. Specifically, the lateral transport length scale was less than half the width of the patch. The increasing bedform height within the wake progressively weakened and narrowed the von Kármán vortex street, illustrating an important feedback from morphological evolution to the flow structure. Despite significant local sediment redistribution, the patch did not induce channel-scale sediment transport.

This study investigates the onset of linear instabilities and their later nonlinear interactions in the shear layer of an initially laminar jet using high-fidelity simulations. We present a quantitative analysis of the vortex-pairing phenomenon by computing the spatial growth rates and energy budget of the dominant frequencies. Compared with a turbulent jet, the hydrodynamic instabilities and vortex pairing are enhanced in an initially laminar jet. Using local linear theory, we identify the fundamental as the frequency with the largest spatial growth rate, and its exponential growth causes the shear layer to roll up into vortices. Visualisations and conditional $x$–$t$ plots reveal that fundamental vortices pair to form subharmonic vortices, which then merge to produce second subharmonic vortices. The energy transfer during this process is evaluated using the spectral turbulent kinetic energy equation, focusing on dominant coherent structures identified through spectral proper orthogonal decomposition. Spectral production and nonlinear transfer terms show that the fundamental frequency gains energy solely from the mean flow, while subharmonics gain energy both linearly from the mean flow and nonlinearly through backscatter from the fundamental frequency. Our results confirm Monkewitz’s theoretical model of a resonance mechanism between the fundamental and subharmonic, which supplies energy to the subharmonic. We highlight the energetic versus dynamical importance of tonal frequencies. The second subharmonic corresponds to the largest spectral peak, while the fundamental, though the fourth largest spectral peak, is dynamically dominant, as it determines all other spectral peaks and supplies energy to the subharmonics through a reverse energy cascade.

This work investigates the receptivity mechanisms of a NACA0008 airfoil to a $\textit{Tu}=2.5\,\%$ level of free-stream turbulence (FST) through a direct numerical simulation (DNS) and an associated linearised simulation on the same mesh. By comparing velocity perturbation fields between the two simulations, the study reveals that the streaky structures that degenerate into turbulent spots are predominantly influenced by nonlinear convective terms, rather than the linear amplification of inflow perturbations around the laminar base flow. A power spectral analysis shows differences in the energy distribution between the DNS and linearised simulation, with the DNS containing more energy at higher wavenumbers, for structures located near the airfoil’s leading edge. Representative wavenumbers are identified through modal analysis, revealing a dynamics dominated by streak-like structures. The study employs the Nek5000 numerical solver to distinguish between linear and nonlinear receptivity mechanisms over the NACA0008 airfoil, highlighting their respective contributions to the amplification of perturbations inside the boundary layer. In the high FST case studied, it is observed that the energy of the incoming turbulence is continuously transferred into the boundary layer along the length of the wing. The nonlinear interactions generate streaks with higher spanwise wavenumbers compared with those observed in purely linearised simulations. These thinner streaks align with the spanwise scales identified as susceptible to secondary instabilities. Finally, the procedures presented here generalise the workflow of previous works, allowing for the assessment of receptivity for simulations with arbitrary mesh geometries.

At all scales, porous materials stir interstitial fluids as they are advected, leading to complex (and chaotic) distributions of matter and energy. Of particular interest is whether porous media naturally induce chaotic advection in Darcy flows at the macroscale, as these stirring kinematics profoundly impact basic processes such as solute transport and mixing, colloid transport and deposition and chemical, geochemical and biological reactivity. While the prevalence of pore-scale chaotic advection has been established, and many studies report complex transport phenomena characteristic of chaotic advection in heterogeneous Darcy flow, it has also been shown that chaotic dynamics are prohibited in a large class of Darcy flows. In this study we rigorously establish that chaotic advection is inherent to steady three-dimensional (3-D) Darcy flow with anisotropic and heterogeneous hydraulic conductivity fields. These conductivity fields generate non-trivial braiding of streamlines, leading to both chaotic advection and (purely advective) transverse macro-dispersion. We establish that steady 3-D Darcy flow has the same topology as unsteady 2-D flow and use braid theory to establish a quantitative link between transverse dispersivity and Lyapunov exponent in heterogeneous Darcy flow. Our main results show that chaotic advection and transverse dispersion occur in both anisotropic weakly heterogeneous and in heterogeneous weakly anisotropic conductivity fields, and that the quantitative link between these phenomena persists across a broad range of conductivity fields. As the ubiquity of macroscopic chaotic advection has profound implications for the myriad processes hosted in porous media, these results call for re-evaluation of transport and reaction methods in these systems.

We study convection in a volumetrically heated fluid which is cooled from both plates and is under rotation through the use of direct numerical simulations. The onset of convection matches similar systems and predictions from asymptotic analysis. At low rotation rates, the fluid becomes more organised, enhancing heat transport and increasing boundary layer asymmetry, whereas high rotation rates suppress convection. Velocity and temperature statistics reveal that the top unstably stratified boundary layer exhibits behaviour consistent with other rotating convective systems, while the bottom boundary shows a unique interaction between unstable stratification and Ekman boundary layers. Additional flow statistics such as energy dissipation are analysed to rationalise the flow behaviour.

We study the stationary, intermittent and nonlinear dynamics of nominally ideally expanded, natural and forced supersonic twin-rectangular turbulent jets using spectral modal decomposition. We decompose large-eddy simulation data into four reflectional symmetry components about the major and minor axes. In the natural jet, spectral proper orthogonal decomposition (SPOD) uncovers two resonant instabilities antisymmetric about the major axis. Known as screech tones, the more energetic of the two is a steady flapping instability, while the other is an intermittent double-flapping instability. We test the hypothesis that symmetry breaking can be leveraged for control design. Time-periodic forcing symmetric about the major and minor axes is implemented using a plasma actuation model, and succeeds in removing screech from a different symmetry component. We investigate the spectral peaks of the forced jet using an extension of bispectral mode decomposition (BMD), where the bispectrum is bounded by unity and which conditionally recovers the SPOD. We explain the appearance of harmonic peaks as three sets of triadic interactions between reflectional symmetries, forming an interconnected triad network. BMD modes of active triads distil coherent structures comprising multiple coupled instabilities, including Kelvin–Helmholtz, core and guided-jet modes (G-JM). Downstream-propagating core modes can be symmetric or antisymmetric about the major axis, whereas upstream-propagating G-JM responsible for screech closure (Edgington-Mitchell et al. J. Fluid Mech.945, 2022, p. A8) are antisymmetric only. The dependence of G-JM on symmetry hence translates from the azimuthal symmetry of the round jet to the dihedral group symmetry of the twin-rectangular jet, and explains why the twin jet exhibits antisymmetric but not symmetric screech modes.

Elasto-inertial turbulence (EIT) has been demonstrated to be able to sustain in two-dimensional (2-D) channel flow; however the systematic investigations on 2-D EIT remain scarce. To address this gap, this study conducts direct numerical simulations of 2-D EIT at a modest Reynolds number ($Re=2000$) to examine its statistical characteristics and dynamic mechanisms. Meanwhile, this paper explores the similarities and differences between 2-D EIT with the maximum drag reduction (MDR) state in three-dimensional (3-D) flow. We demonstrate that statistical characteristics of 2-D EIT follow distinct trends compared to those in viscoelastic drag-reducing turbulence as nonlinear elasticity increases. These differences can be attributed to two different underlying dynamical processes: the gradual suppression of inertial turbulence in 3-D flow, and the progressive enhancement of EIT in 2-D flow. Also, we present the role of pressure, energy budget and spectral characteristics of 2-D EIT, which show significant similarities to those in the MDR state, thus providing compelling evidence for the 2-D nature of EIT. More strikingly, we identify an anomalous Reynolds stress in 2-D EIT that contributes negatively to flow resistance, which differs from the extremely small but positive Reynolds stress observed in the MDR state. Although with small values of Reynolds stress, the correlation analysis indicates clearly moderate positive correlation between the streamwise and normalwise velocity fluctuations rather than their being uncorrelated. Moreover, quadrant analysis of velocity fluctuations reveals the predominance of motions in the first and third quadrants, which are closely associated with the typical polymer extension sheet-like structures.

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.