Using pore-resolved direct numerical simulation (DNS), we investigate passive scalar transport at a unit Schmidt number in a turbulent flow over a randomly packed bed of spheres. The scalar is introduced at the domain’s free-slip top boundary and absorbed by the bed, which maintains a constant and uniform scalar value on the sphere surfaces. Eight cases are analysed, which are characterised by friction Reynolds numbers of ${\textit{Re}}_\tau \in [150, 500]$ and permeability Reynolds numbers of ${\textit{Re}}_{{\kern-1pt}K} \in [0.4, 2.8]$, while flow depth-to-sphere-diameter ratios vary within $h/D \in \{ 3, 5, 10 \}$ and the roughness Reynolds numbers lie within $k_s^+ \in [20,200]$. For cases with comparable ${\textit{Re}}_\tau$, the permeable wall behaviour enhances scalar absorption, as indicated by increases in the Sherwood number and the scalar roughness function $\Delta c^+$ over ${\textit{Re}}_{{\kern-1pt}K}$. At progressively higher ${\textit{Re}}_{{\kern-1pt}K}$, the scalar absorption diverges increasingly from the momentum absorption, as its distribution peaks deeper below the crests of the sphere pack and spreads over a wider vertical region. The fixed-value scalar boundary condition emphasises certain similarities between the scalar and velocity fields. Near-interface scalar fluctuations are correlated with streamwise velocity fluctuations, and the turbulent Schmidt number remains close to its value in the free-flow region. Compared with zero-flux scalar boundary conditions, prescribing a uniform scalar value on the sphere surfaces reduces spatial heterogeneity within the pore space, thereby limiting both dispersive transport and the form-induced production of temporal scalar fluctuations.

We join the theories that describe the orientation, treated as a tensor, of liquid crystals and the agitation of inelastic grains to obtain a mathematical model of non-spherical particles contained in a quasi-2D square box and driven into dissipative collisions through the vibration of two of the four flat walls, in the absence of gravity and mean flow. The particle agitation induces spatial inhomogeneities in the density and the isotropic–nematic transition to take place somewhere inside the box, if the particle shape is sufficiently far from spherical. We show quantitative agreement between the theory and discrete numerical simulations of ellipsoids of different length-to-diameter ratio. We need to fit two dimensionless parameters that were not previously available or determined in different configurations. These parameters, of order unity and weakly dependent on the shape of the particles, are indicative of the resistance to alignment distortion associated with entropic elasticity.

Recently, data-driven methods have shown great promise for discovering governing equations from simulation or experimental data. However, most existing approaches are limited to scalar equations, with few capable of identifying tensor relationships. In this work, we propose a general data-driven framework for identifying tensor equations, referred to as symbolic identification of tensor equations (SITE). The core idea of SITE – representing tensor equations using a host–plasmid structure – is inspired by the multidimensional gene expression programming approach. To improve the robustness of the evolutionary process, SITE adopts a genetic information retention strategy. Moreover, SITE introduces two key innovations beyond conventional evolutionary algorithms. First, it incorporates a dimensional homogeneity check to restrict the search space and eliminate physically invalid expressions. Second, it replaces traditional linear scaling with a tensor linear regression technique, greatly enhancing the efficiency of numerical coefficient optimization. We validate SITE using two benchmark scenarios, where it accurately recovers target equations from synthetic data, showing robustness to noise and flexible expressive capability. Furthermore, SITE is applied to identify constitutive relations directly from molecular simulation data, which are generated without reliance on macroscopic constitutive models. It adapts to both compressible and incompressible flow conditions and successfully identifies the corresponding macroscopic forms, highlighting its potential for data-driven discovery of tensor equation.

One of the challenges with modelling subsurface flows is the uncertainty in measurements of geological properties, mostly due to limited resolution in observation methods. Many subsurface flows can be modelled as a gravity current, which, for uniform material properties and power-law injection rate, has a well-characterised similarity solution. The similarity solution forms a dynamical attractor that is typically approached rapidly from a host of initial conditions. Here, we consider the impact of transverse variations to the permeability field by performing a perturbation analysis of the self-similar spreading. This treats the response as perturbations to the self-similar flow. We restrict our focus to permeability fields that vary laterally, or across the flow, starting with the simple case of a sinusoidal perturbation to a uniform permeability. At early times, the height and nose position of the current are determined by the local permeability, and deviations to the height and nose grow at the same rate as the mean, and proportional to the amplitude, of the permeability variation. The transition between the early and late time regimes is governed by the wavelength of the permeability. At late times, lateral spreading between high and low permeability streaks is dominant; the height deviations decay, and the nose deviations approach a steady state. The magnitudes of both depend on the product of the wavelength and amplitude of the permeability. The single mode sets the groundwork for examining more complex, multimodal permeabilities, which are more representative of real geological structures.

Fully resolving turbulent flows remains challenging due to a turbulent systems’ multiscale complexity. Existing data-driven approaches typically demand expensive retraining for each flow scenario and struggle to generalize beyond their training conditions. Leveraging the universality of small-scale turbulent motions (Kolmogorov’s K41 theory), we propose a scale-oriented zonal generative adversarial network (SoZoGAN) framework for high-fidelity, zero-shot turbulence generation across diverse domains. Unlike conventional methods, SoZoGAN is trained exclusively on a single dataset of moderate-Reynolds-number homogeneous isotropic turbulence (HIT). The framework employs a zonal decomposition strategy, partitioning turbulent snapshots into subdomains based on scale-sensitive physical quantities. Within each subdomain, turbulence is synthesized using scale-indexed models pretrained solely on the HIT database. A SoZoGAN demonstrates high accuracy, cross-domain generalizability and robustness in zero-shot super-resolution of unsteady flows, as validated on untrained HIT, turbulent boundary layer and channel flow. Its strong generalization, demonstrated for homogeneous and inhomogeneous turbulence cases, suggests potential applicability to a wider range of industrial and natural turbulent flows. The scale-oriented zonal framework is architecture-agnostic, readily extending beyond generative adversarial networks to other deep learning models.

We study the force exerted by the uniform flow of a Bingham fluid around two- and three-dimensional particles in the regime of slow creeping flow and relatively weak yield stress. Matched asymptotic expansions are employed to couple a viscously dominated Stokes flow close to the particle with a far field in which the yield stress and viscous stresses are comparable. The far-field region is therefore modelled as a Bingham fluid driven by a point force at the origin (i.e. a viscoplastic Stokeslet). It features the full nonlinearity of the viscoplastic rheology, and its solution is computed through direct numerical simulation. Asymptotic matching then leads to a quasi-analytical expression for the drag force in terms of the dimensionless Bingham number ${\textit{Bi}}$, which measures the magnitude of the yield stress relatively to viscous effects at the particle scale. We deploy this methodology to determine the drag force on a sphere in three dimensions, and circular and elliptic cylinders in two dimensions, confirming our asymptotic predictions by comparison with full numerical simulations of the motion. We also generalise the three-dimensional result to arbitrary particles. The viscoplastic correction to the Newtonian drag in three dimensions scales as ${\textit{Bi}}^{1/2}$. In two dimensions, however, the effects of viscoplasticity are non-negligible at leading order. The drag varies with $[\ln (1/{\textit{Bi}})]^{-1}$, but this asymptotic result is only approached very slowly. Instead, an accurate representation of the drag is derived in terms of a single algebraic relation between the drag and the Bingham number.

We present an acoustic characterisation of a model-scale wind turbine using large eddy simulation and the acoustic analogy. The analysis is representative of medium-sized turbines with low tip Mach number (${\sim} 0.10$). The fluid dynamic analysis revealed: a turbulent boundary layer over the blades, together with a trailing edge vortex sheet; a complex near-wake structure, including tip and root vortices; an intermediate wake with vortex instabilities triggering leap-frogging and vortex grouping mechanisms; and a far wake characterised by fully developed turbulence. Two primary noise generation mechanisms were identified. The unsteady pressure field over the turbine surface generates tonal noise at the blade passing frequency and a high-frequency broadband noise, associated with the trailing edge vortex sheet (linear-noise contribution). The turbulent wake generates broadband low-frequency noise, driven by the complex fluid-dynamic processes outlined previously (nonlinear noise contribution). The linear part of the noise was found to dominate over the nonlinear one in the acoustic far field, while the opposite is true in the acoustic near field. As a composition of the two contributions to the noise, the directivity exhibits a non-symmetric dipole shape oriented along the flow direction, with lobes recovering symmetry moving from the near to the far field. Finally, analysis of the acoustic decay rates reveals that the linear term in the near field decays according to an $r^{-(n+1)}$ law within the rotor plane, where n is the number of blades, consistent with recent findings on the acoustics of rotating sources.

We investigate the scale-by-scale transfers of energy, enstrophy and helicity in homogeneous and isotropic polymeric turbulence using direct numerical simulations. The study relies on the exact scale-by-scale budget equations, derived from the governing model equations, that fully capture the back-reaction of polymers on the fluid dynamics. Polymers act as dynamic sinks and sources and open alternative routes for interscale transfer whose significance is modulated by their elasticity, quantified through the Deborah number (${\textit{De}}$). Polymers primarily deplete the nonlinear energy cascade at small scales, by attenuating intense forward and inverse transfer events. At sufficiently high ${\textit{De}}$, a polymer-driven flux emerges and dominates at small scales, transferring on average energy from larger to smaller scales, while allowing for localised backscatter. For enstrophy, polymers inhibit the stretching of vorticity, with fluid–polymer interactions becoming the primary enstrophy source at high ${\textit{De}}$. Accordingly, an analysis of the small-scale flow topology reveals that polymers promote two-dimensional straining states and enhance the occurrence of shear and planar extensional flows, while suppressing extreme rotation events. Helicity, injected at large scales, exhibits a transfer mechanism analogous to energy, being dominated by nonlinear dynamics at large scales and by polymer-induced fluxes at small scales. Polymers enhance the breakdown of small-scale mirror symmetry, as indicated by a monotonic increase in relative helicity with ${\textit{De}}$ across all scales.

Contact between fluctuating, fluid-lubricated soft surfaces is prevalent in engineering and biological systems, a process starting with adhesive contact, which can give rise to complex coarsening dynamics. One representation of such a system, which is relevant to biological membrane adhesion, is a fluctuating elastic interface covered by adhesive molecules that bind and unbind to a solid substrate across a narrow gap filled with a viscous fluid. This flow is described by the stochastic elastohydrodynamic thin film equation, which incorporates thermal fluctuations into the description of viscous nanometric thin-film flow coupled to elastic membrane deformation. The average time it takes the fluctuating elastic membrane to adhere is predicted by the rare event theory, increasing exponentially with the square of the initial gap height. When the forces arising from spring-like adhesive molecules are included in the simulations, thermal fluctuations initiate phase separation of domains of bound and unbound molecules. The coarsening process of these unbound pockets displays close similarities to classical Ostwald ripening; however, the inclusion of hydrodynamics affects power-law growth. In particular, we identify a new bending-dominated coarsening regime, which is slower than the well-known tension-dominated case.

An experimental study is performed to control flow separation from a two-dimensional curved ramp using a spanwise pulsed blowing slit jet placed near the separation point of the baseline flow. The momentum-thickness-based Reynolds number $ \textit{Re}_{\theta}$ is 5700. Four control parameters are investigated, including the velocity ratio $\overline{U_{J,c}^{*}}$, duty cycle dc, dimensionless excitation frequency $f_{e}^{{*}}$ and jet blowing angle $\alpha$. The control mechanisms are found to differ from small to large jet angle. Empirical scaling analysis for $\alpha \leq 55^{\circ}$ unveils that $\Delta \overline{C_{p,e}}=f_{1}(\overline{U_{J,c}^{*}}, { d}c, f_{e}^{*}, \alpha , Re_{\theta })$ may be reduced to $\Delta \overline{C_{p,e}}/\varPi (\tau )=f_{2}(\xi )$, where $f_{1}$ and $f_{2}$ are different functions, $\Delta \overline{C_{p,e}}$ is the variation in the pressure coefficient at the end of the ramp under control, $\varPi (\tau )$ is a function of dimensionless duration $\tau$ at which the jet is closed within one excitation period, $\Delta \overline{C_{p,e}}/\varPi (\tau )$ represents the control efficiency, and $\xi$ is a scaling factor that is physically the energy ratio per unit area of the blowing jet to the mainstream. This scaling law is also found to be valid for steady jet control. Several interesting inferences can be made from this scaling law, which provides important insight into the physics of flow separation control.

Analytical expressions for the mean wall-normal velocity and wall shear stress in compressible boundary layers are derived by integrating the mean continuity and momentum equations. In the constant-density limit, the momentum integral formulation recovers the classical Kármán–Pohlhausen equation for incompressible boundary-layer flows. In compressible regimes, particularly under strong pressure gradients, streamwise density gradients are shown to play a crucial role in shaping boundary-layer dynamics. The derived analytical equations are validated against high-fidelity direct numerical simulation data, demonstrating both accuracy and robustness. Furthermore, the analytical equations offer insights into the physical mechanisms of compressible boundary layers, particularly the influence of density gradients. The effect of compressibility on the wall-normal velocity is explicitly demonstrated, highlighting the distinct behaviour of compressible boundary layers compared with incompressible flows. Finally, an analytical expression for the skin-friction coefficient is developed, revealing its close connection to the mean wall-normal velocity at the boundary-layer edge.

Not all particulate matter carried by fluid flows has constant buoyancy. In some cases, the buoyancy of a particle can change dynamically based on the local flow. We refer to this phenomenon as ‘active buoyancy.’ Although actively buoyant particles are found throughout nature, their dynamics is not well understood, particularly when they are also highly inertial. Motivated by the problem of the transport of firebrands in wildfires, whose effective buoyancy is modulated by conductive and convective heat transfer to the surrounding fluid, we conducted a series of experiments to investigate the effects of active buoyancy on particle settling in quiescent fluid. We find that, depending on the control parameters, active buoyancy can either hinder or enhance settling, in some cases to a large extent. The details of this settling modulation, however, cannot be simply captured by any single control parameter. Analysis of the trajectories of the falling particles showed that they fall along nearly sinusoidal paths even though the particle Reynolds number is higher than expected for this regime, suggesting that active buoyancy may act to stabilise their wakes. Our results suggest both that models of actively buoyant particles such as firebrands must account for the effects of active buoyancy and that there is still much to be understood about the behaviour of these complex particles.