The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for turbulence-resolving integral simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three-component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier–Stokes with relatively simple closure approximations. Evidence from direct numerical simulations (DNS) suggests that TRIS can theoretically resolve $35\,\%{-}40\,\%$ of the turbulent skin friction enhancement for friction Reynolds numbers between $180$ and $5200$, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in ${\sim}1$ minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of $395$ and $590$ show that TRIS generates a relatively accurate representation of the flow, while highlighting discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modelling, motivating extension to more general flow configurations such as boundary layers on immersed objects.

The aerodynamic sound generated by the oblique collision of two vortex rings is featured by the asymmetric emission associated with the octupole mode, which differs from the symmetric emission associated with the quadrupole mode observed in the coaxial collision of two vortex rings. This distinctive feature of aerodynamic sound is closely related to the tilting and reconnecting of the vortex rings. While previous studies have explored the effects of reconnecting on aerodynamic sound, this study specifically addresses the impact of vortex ring tilting. We propose a novel vortex sound formula to quantitatively assess the role of tilting in aerodynamic sound generation. The proposed formula relates the far-field sound pressure to equivalent circulations and vorticity centroids by referring to Truesdell’s consistency conditions for vorticity moments. The variations of the equivalent circulations and vorticity centroids in the oblique collision of two vortex rings under different configurations are analysed based on the numerical solution of the Navier–Stokes equations in the source region. It is found that the tilting of vortex rings results in a rapid change of the equivalent circulation associated with the vorticity in the collision direction. However, the change caused by titling is almost out of phase with that caused by reconnecting and deforming. The vortex tilting significantly reduces the aerodynamic sound associated with the longitudinal quadrupole and octupole modes, which is opposite to the role of vortex reconnecting that was reported in the oblique collision of vortex rings.

Stochastic resonance (SR) is universal phenomenon, where noise amplifies a weak periodic signal in bistable nonlinear systems, with wide applications in biology, climate science, engineering etc., although in fluid dynamics it remains underexplored. Recently, we unexpectedly found SR above non-modal elastic instability onset in an inertialess viscoelastic channel flow, where it emerges on the top of a chaotic streamwise velocity power spectrum $E_u$ due to its interaction with white-noise spanwise velocity power spectrum $E_w$ and weak elastic waves. These three conditions necessary for SR emergence differ from those required for the classical SR emergence mentioned above. Here, we consider SR in an inertialess viscoelastic channel flow with a smoothed inlet causing order of magnitude lower noise intensity than in our former studies. Our observations reveal that SR appears at the same conditions mentioned above, where SR is found just upon the instability onset in a lower subrange of a transition regime, in contrast, here, SR persists across all flow regimes – transition, elastic turbulence and drag reduction. Furthermore, we provide experimental evidence that SR, presented by a sharp peak in $E_u$, manifests as either a standing or propagating wave in the $x$-direction, with a rather uniform amplitude of streamwise velocity fluctuations and zero propagation velocity in the $z$-direction. These findings reveal a new mechanism underpinning the transition to a chaotic channel flow of viscoelastic fluids and establish SR as a robust framework for understanding complex flow dynamics. This work opens new avenues for exploring SR in other nonlinear systems and practical applications such as mixing enhancement and flow control in industrial and biological contexts.

An analysis is presented of the suspensions of small, electrified particles in a gas. Two limits of interest for the electrodynamic particulate suspension technique are considered, corresponding to large and small values of the ratio $t_{coll}/t_s$ of the mean time between particle collisions to the viscous adaptation time required for the particles to reach their terminal velocities. The effect of the particle inertia can be neglected when this ratio is large, and only the distribution of particle charges at each point of the suspension needs to be computed. The way this distribution approaches an equilibrium form, determined elsewhere in the continuum regime when the mean free path of the particles is small compared with the suspension size, is described, as well as the connection between continuum regime and quasi-neutrality of the suspension. In the opposite case when $t_{coll}/t_s$ is small, the inertia of the particles plays an important role, and the joint distribution of particle charges and velocities is required. A Boltzmann equation is proposed for this distribution function, taking advantage of the fact that the charges of the particles have little effect on the redistribution of momentum and energy in the collisions. The equilibrium distribution function in the continuum regime is computed approximately, and hydrodynamic equations for the particle phase analogous to the Euler equations for a monoatomic gas are derived. The simplification of these equations when the particle inertia is negligible at the scale of the suspension is worked out.

This work explores the use of a shallow surface hump for passive control and stabilisation of stationary crossflow (CF) instabilities. Wind tunnel experiments are conducted on a spanwise-invariant swept-wing model. The influence of the hump on the boundary layer stability and laminar–turbulent transition is assessed through infrared thermography and particle image velocimetry measurements. The results reveal a strong dependence of the stabilisation effect on the amplitude of the incoming CF disturbances, which is conditioned via discrete roughness elements at the wing leading edge. At a high forcing amplitude, weakly nonlinear stationary CF vortices interact with the hump and result in an abrupt anticipation of transition, essentially tripping the flow. In contrast, at a lower forcing amplitude, CF vortices interact with the hump during linear growth. Notable stabilisation of the primary CF disturbance and considerable transition delay with respect to the reference case (i.e. without hump) is then observed. The spatial region just downstream of the hump apex is shown to be key to the stabilisation mechanism. In this region, the primary CF disturbances rapidly change spanwise orientation and shape, possibly driven by the pressure gradient change-over caused by the hump and the development of CF reversal. The amplitude and shape deformation of the primary CF instabilities are found to contribute to a long-lasting suboptimal growth downstream of the hump, eventually leading to transition delay.

Researchers have long debated which spatial arrangements and swimming synchronisations are beneficial for the hydrodynamic performance of fish in schools. In our previous work (Seo and Mittal, Bioinsp. Biomim., Vol. 17, 066020, 2022), we demonstrated using direct numerical simulations that hydrodynamic interactions with the wake of a leading body -caudal fin carangiform swimmer could significantly enhance the swimming performance of a trailing swimmer by augmenting the leading-edge vortex (LEV) on its caudal fin. In this study, we develop a model based on the phenomenology of LEV enhancement, which utilises wake velocity data from direct numerical simulations of a leading fish to predict the trailing swimmer’s hydrodynamic performance without additional simulations. For instance, the model predicts locations where direct simulations confirm up to 20 % enhancement of thrust. This approach enables a comprehensive analysis of the effects of relative positioning, phase difference, flapping amplitude, Reynolds number and the number of swimmers in the school on thrust enhancement. The results offer several insights regarding the effect of these parameters that have implications for fish schools as well as for bio-inspired underwater vehicle applications.

A drop of an electrically conducting non-magnetic fluid of radius $R$, electrical conductivity $\kappa$, density $\rho _i$ and viscosity $\eta _i$ is suspended in a non-conducting medium of density $\rho _o$, viscosity $\eta _o$ and subject to an oscillating magnetic field of magnitude $H_0$ and angular frequency $\omega$. Oscillating eddy currents are induced in the drop due to Faraday’s law. The Lorentz force density, the cross product of the current density and the magnetic field, is the superposition of a steady component and an oscillating component with frequency $2 \omega$. The characteristic velocity due to the Lorentz force density is $(\mu _0 H_0^2 R/\eta _i)$ times a function of the dimensionless parameter $\beta = \sqrt {\mu _0 \kappa \omega R^2}$, the square root of the ratio of the frequency and the current relaxation rate. Here, $\mu _0$ is the magnetic permeability. The characteristic velocities for the steady and oscillatory components increase proportional to $\beta ^{4}$ for $\beta \ll 1$, and decrease proportional to $\beta ^{-1}$ for $\beta \gg 1$. The steady flow field consists of two axisymmetric eddies in the two hemispheres with flow outwards along the magnetic field axis and inwards along the equator. The flow in the drop induces a biaxial extensional flow in the surrounding medium, with compression along the magnetic axis and extension along the equatorial plane. The oscillating component of the velocity depends on $\beta$ and the Reynolds number ${Re}_\omega$ based on the frequency of oscillations. For ${Re}_\omega \gg 1$, the amplitude of the oscillatory velocity decreases proportional to ${Re}_\omega ^{-1}$ for $\beta \ll 1$, and proportional to ${Re}_\omega ^{-1/2}$ for $\beta \gg 1$.

Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces a quantum implicit representation of vortex filaments in turbulence, employing a levelset method that models the filaments as the intersection of the real and imaginary zero iso-surfaces of a complex scalar field. Describing the fluid field via the scalar field offers distinct advantages in capturing complex structures, topological properties and fluid dynamics, while opening new avenues for innovative solutions through quantum computing platforms. The representation is reformulated into an eigenvalue problem for Hermitian matrices, enabling the conversion of velocity fields into complex scalar fields that embed the vortex filaments. The resulting optimisation is addressed using a variational quantum eigensolver, with Pauli operator truncation and deep learning techniques applied to improve efficiency and reduce noise. The proposed quantum framework achieves a near-linear time complexity and a exponential storage reduction while maintaining a balance of accuracy, robustness and versatility, presenting a promising tool for turbulence analysis, vortex dynamics research, and machine learning dataset generation.

We present results of three-dimensional direct numerical simulations of turbulent Rayleigh–Bénard convection of dilute polymeric solutions for Rayleigh number ($Ra$) ranging from $10^6$ to $ 10^{10}$, and Prandtl number $Pr=4.3$. The viscoelastic flow is simulated by solving the incompressible Navier–Stokes equations under the Boussinesq approximation coupled with the finitely extensible nonlinear elastic Peterlin constitutive model. The Weissenberg number ($Wi$) is either $Wi=5$ or $Wi=10$, with the maximum chain extensibility parameter $L=50$, corresponding to moderate fluid elasticity. Our results demonstrate that both heat transport and momentum transport are reduced by the presence of polymer additives in the studied parameter range. Remarkably, the specific parameters used in the current numerical study give similar heat transfer reduction values as observed in experiments. We demonstrate that polymers have different effects in different regions of the flow. The presence of polymers stabilises the boundary layer, which is found to be the primary cause of the overall heat transfer reduction. In the bulk region, the presence of polymers slows down the flow by increasing the effective viscosity, enhances the coherency of thermal plumes, and suppresses the small-scale turbulent fluctuations. For small $Ra$, the heat transfer reduction in the bulk region is associated with plume velocity reduction, while for larger $Ra$, it is caused by the competing effects of suppressed turbulent fluctuations and enhanced plume coherency.