The connection between the drag and vorticity dynamics for viscous flow over a bluff body is explored using the Josephson–Anderson (J–A) relation for classical fluids. The instantaneous rate of work on the fluid, associated with the drag force, is related to the vorticity flux across the streamlines of a background potential flow. The vorticity transport itself is examined by aid of the Huggins vorticity-flux tensor. The analysis is performed for three flows: flow over a sphere at Reynolds numbers $Re=200,3700$, and flow over a prolate spheroid at $Re=3000$ and $20^{\circ }$ incidence. In these flows, the vorticity transport shifts the flow away from and towards the ideal potential flow, with a net balance towards the former effect thus making an appreciable contribution to the drag. The J–A relation is first demonstrated for the flow over a sphere at $Re=200$. The drag power injection is related to the viscous flux of azimuthal vorticity from the wall into the fluid, and the advection of vorticity by the detached shear layer. In the wake, the azimuthal vorticity is advected towards the wake centreline and is annihilated by viscous effects, which contributes a reduction in drag. The analysis of the flow over a sphere at $Re=3700$ is reported for the impulsively started and stationary stages, with emphasis on the effects of unsteady two-dimensional separation and turbulent transport in the transitional wake. The turbulent flux in the wake enhances the transport of mean azimuthal vorticity towards the wake centreline, and is the main driver of the recovery of enthalpy between the rear point of the sphere and far downstream. The rate of work on the fluid by the drag force for a prolate spheroid is mostly due to the transport of vorticity along the separated boundary layers. Primary and secondary separation contribute oppositely to the power injection by the drag force, while the large-scale vortices only re-distribute vorticity without a net contribution. A mechanism for secondary separation is proposed based on the theory of vortex-induced separation.

This study investigates the interactions between flexural-gravity waves and interfacial waves in a two-layer fluid, focusing on wave blocking. Both liquid layers are of finite depth bounded on top by a viscoelastic thin plate. Both liquids are incompressible and inviscid, and their flows are two-dimensional and potential. Linear wave theory and a linear equation of a thin floating viscoelastic plate of constant thickness are used. We analyse the phenomenon of wave blocking and Kelvin–Helmholtz (KH) instability in a two-layer fluid with a discontinuous background mean flow. A quartic dispersion relation for frequency as a function of wavenumber and other parameters of the problem is derived. Two cases of uniform current and layers moving with different velocities are studied. Wave blocking occurs when roots of the dispersion relation coalesce without accounting for plate viscosity, leading to zero group velocity. Our findings indicate that wave blocking can occur for both flexural-gravity and interfacial waves under various frequency and current speed conditions, provided that plate viscosity is absent. The role of different parameters and the flow velocities of the upper and lower layers are investigated in the occurrence of wave blocking and KH instability. The loci of the roots of the dispersion relation involving plate viscosity depict that no root coalescence occurs irrespective of the values of wavenumber and frequency in the presence of plate viscosity. The amplitude ratio of the interfacial wave elevation to that of floating viscoelastic plate deflection exhibits the dead-water phenomenon as a density ratio approaches unity.

A numerical study is presented on flow-induced vibration of a circular cylinder, under the effect of a downstream stationary cylinder-induced proximity interference. The interference-induced various types of gap-flow regimes and characteristics of vibration and gap-flow rate $Q^*_g$ are presented, by considering various non-dimensional gaps $G^* = 0.1{-}2.5$ and reduced velocities $U^* = 3{-}20$ at a constant Reynolds number $Re = 100$, mass ratio $m^*= 2$ and damping ratio $\zeta = 0.005$. Decreasing $G^*$ or increasing proximity leads to the four gap-flow regimes: bi-directional gap flow at $G^* \geqslant 1.0$, uni-directional non-orthogonal gap flow at $G^* = 1.5{-}1.0$, uni-directional orthogonal gap flow at $G^* \leqslant 0.5$ and uni-directional one-sided gap flow at $G^* \leqslant 0.3$. Further, the respective regimes at larger $U^*$ are associated with proximity-induced modified vortex-induced vibration (PImVIV), proximity-induced galloping (PIG), transitional PImVIV–PIG, and proximity-induced staggered vibration (PISV). Quantitative presentation of maximum gap-flow rate $Q^*_{{g,max}}$, phase $ \phi _g$ (between $Q^*_{g}$ and displacement $y^*$) and phase portraits ($Q^*_{g}$ versus $y^*$) provides clear demarcation between the various gap-flow regimes. Flow mechanisms are presented for the PImVIV, PIG and PISV responses. For the PIG, the mechanism is presented for the first time on generation of galloping instability, asymptotically increasing $A^*$ and existence of optimum gap $G^* = 0.5$ for the maximum amplitude. This work is significant as it provides new insights into the proximity interference-induced gap-flow dynamics between two cylinders, associated flow mechanism for both vibration mitigation and enhancement and promising potential applications for energy harvesting.

This study investigates the transport of particles in turbulent channel flow with friction Reynolds number $Re_\tau = 1000$ by direct numerical simulation. We focus on how large-scale flow structures, namely the $Qs$ structures (Lozano-Durán et al. 2012, J. Fluid Mech., vol. 694, pp. 100–130), affect the wall-normal transport of particles. Despite occupying less than $10\,\%$ of the physical domain, our results highlight the critical role played by $Qs$ structures in the particle transport, namely that the particle number and momentum flux inside the $Qs$ structures are substantially higher than outside. The fraction of particle wall-normal momentum flux inside $Qs$ structures is considerably larger than their volume fraction, suggesting highly efficient transport inside the $Qs$ structures. This prominent role played by $Qs$ structures in the transport of inertial particles is more effective by diminishing the inertia of particles. Notably, the long-distance transport of particles in the wall-normal direction is driven primarily by the continuous effect of $Qs$ structures. In summary, our findings advance the understanding of the effects of $Qs$ structures on particle transport, and demonstrate their significant role in the process.

The electromagnetically driven magnetised spherical Couette flow is studied experimentally, theoretically and numerically in the laminar regime. The working fluid, Galinstan, is contained in the spherical gap between two concentric spheres at rest. The electromagnetic stirring is primarily generated due to the interaction of a direct current, which is injected through two ring-shaped electrodes located at the equatorial zone of each sphere, and a dipolar magnetic field produced by a permanent magnet located inside the inner sphere. The flows were explored experimentally for a Reynolds number ranging from 450 to 2230 and a Hartmann number of 240. Ultrasound Doppler velocimetry and particle image velocimetry were used to characterise the flow. For low Reynolds numbers, given the symmetry of the problem, a one-dimensional analytic solution is obtained in the equatorial plane from the magnetohydrodynamic equations. The analytical solution reproduces the main characteristics of the flow. In addition, a full three-dimensional numerical model is able to reproduce both the analytical solution and the experimental measurements. To the best knowledge of the authors, this is the first time experimental results of the magnetised spherical Couette flow have been reported with electromagnetic forcing using a liquid metal as the working media.

Viscoplastic fluids exhibit yield stress, beyond which they flow viscously, while at lower stress levels they behave as solids. Despite their fundamental biological and medical importance, the hydrodynamics of swimming in viscoplastic environments is still evolving. In this study, we investigate the swimming of an ellipsoidal squirmer and the associated tracer diffusion in a Bingham viscoplastic fluid. The results illustrate that neutral squirmers in viscoplastic fluids experience a reduction in swimming speed and an increase in power dissipation as the Bingham number increases, with swimming efficiency peaking at moderate Bingham numbers. As the aspect ratio of a squirmer increases, ellipsoidal squirmers exhibit significantly higher swimming speeds in viscoplastic fluids. The polar and swirling modes can either enhance or reduce swimming speed, depending on the specific scenarios. These outcomes are closely related to the confinement effects induced by the yield surface surrounding the swimmer, highlighting how both swimmer shape and swimming mode can significantly alter the yield surface and, in turn, modify the swimming hydrodynamics. In addition, this study investigates the influence of viscoplasticity on swimmer-induced diffusion in a dilute suspension. The plasticity enforces the velocity far from the swimmer to be zero, thus breaking the assumptions used in Newtonian fluids. The diffusivity reaches its maximum at intermediate aspect ratios and Bingham numbers, and increases with the magnitude of the squirmer’s dipolarity. These findings are important to understand microscale swimming in viscoplastic environments and the suspension properties.