Coarse-grained continuous descriptions for lipid bilayers are typically based on minimising the Helfrich energy. Such models consider the fluid properties of these structures only implicitly and have been shown to nicely reproduce equilibrium properties. Model extensions that also address the dynamics of these structures are surface (Navier–)Stokes–Helfrich models. They explicitly account for membrane viscosity. However, these models also usually treat the lipid bilayer as a homogeneous continuum, neglecting the molecular degrees of freedom of the lipids. Here, we derive refined models that consider in addition a scalar order parameter representing the molecular alignment of the lipids along the surface normal. Starting from hydrodynamic surface liquid crystal models, we obtain a hydrodynamic surface Landau–Helfrich model for asymmetric lipid bilayers and a surface Beris–Edwards model for symmetric lipid bilayers. The fully ordered case for both models leads to the known surface (Navier–)Stokes–Helfrich models. Besides more detailed continuous models for lipid bilayers, we therefore also provide an alternative derivation of surface (Navier–)Stokes–Helfrich models. The impact on the dynamics is demonstrated by numerical simulations.

The inner–outer interaction model (IOIM), first proposed by Marusic et al. (Science, 2010, vol. 329, pp. 193–196), has proven to be an effective turbulence model for canonical and non-canonical wall-bounded flows, where a reference velocity signal from the logarithmic region acts as the input for predicting near-wall velocity fluctuations. Its most recent iteration by Baars et al. (Phys. Rev. Fluids, 2016, vol. 1, p. 054406) further proposes a user-independent scale separation point, refining model parameters. In this study, we compared the long-perceived universal IOIM’s parameters, including the linear transfer kernel, amplitude modulation coefficients and the universal signal for a range of Reynolds and Mach numbers, where mathematical relationships between the parameters are proposed. We observed that while the universal signals exhibit a high degree of similarity, particularly near the wall, the amplitude modulation coefficients and linear transfer kernels display Reynolds and Mach number effects, where varying the reference location also causes them to exhibit significant changes. We have found transformations to collapse amplitude modulation coefficients for incompressible flows and differing reference locations, improving modelling via the IOIM across flow parameters. Despite this, compressibility effects cannot be suitably accounted for currently and remain a future challenge for the IOIM framework.

A recent study by Zhang et al. (2024, J. Fluid Mech., vol. 979, A43) introduced an effective control strategy, namely streamwise-uniform spanwise equally distributed injection/suction slots on the pressure (unstable) wall, to enhance passive scalar transport in spanwise rotating plane Poiseuille flows (RPPFs). In this work, we employ direct numerical simulations to further investigate the scalar transport increase rate ($\textit{STI}$) under different slot configurations. Two distinct configurations are investigated, namely uniform-width slots, where injection and suction slots share identical dimensions, and non-uniform-width slots, where their widths vary independently. The former is to examine the effect of slot width, whereas the latter is devoted to distinguishing the individual roles of injection versus suction. While the slot widths change, the root mean square wall-normal velocity is maintained at a fixed minimal value. For uniform configurations, $ \textit{STI}$ increases monotonically with slot width, nearly doubling as the width grows from $\pi /8$ to $\pi /2$. In contrast, non-uniform configurations exhibit a complex, non-monotonic dependence on slot dimensions. Spectral, quadrant and zonal-conditional quadrant analyses reveal that injection and suction slots play distinct roles in modulating near-wall dynamics. Injection enhances ejection events ($Q2$), promoting local plume detachment, and facilitating the formation of large-scale ascending plume currents. Suction, conversely, strengthens sweep events ($Q4$), suppressing plume detachment while intensifying descending currents. This dual mechanism organises turbulent structures into more stable large-scale structures, thereby improving scalar transport efficiency. A decomposition of $ \textit{STI}$ based on clustering analysis confirms that the enhancement stems primarily from increased occurrence possibilities and improved transport capacities of dominant clusters. These findings establish flow stabilisation through selective slot control as an effective mechanism for enhancing passive scalar transport in RPPFs.

This work investigates experimentally and numerically the dynamics of rigid particles with two orthogonal symmetry planes settling under gravity in a highly viscous fluid at a Reynolds number much smaller than one. Joshi & Govindarajan (2025 Phys. Rev. Lett. 134(1), 014002), showed theoretically that for such shapes, the dynamics are qualitatively different for different signs of the product of two rotational–translational mobility coefficients, evaluated with respect to the particle centre of mass in a symmetric reference frame. However, upon examining a particle’s shape, it is not immediately evident if this product is negative, positive or zero. In this paper, we demonstrate how to estimate these coefficients and the sign of their product from experiments, using special initial orientations, and also numerically, based on the Stokes equations. Especially interesting are the ‘settlers’ – such particles that reorient and approach a stationary stable orientation, and we focus our study on this class of shapes. We show experimentally that cones, crescent moons, arrowheads and open flat rings are the settlers, and we evaluate from the experiments their rotational–translational mobility coefficients. Then, we reconstruct each experimental shape as a rigid conglomerate of many touching beads, and use the precise Hydromultipole code to calculate the mobility coefficients for the conglomerate. The numerical and experimental values are close enough to determine that the particles are the settlers, and to estimate the characteristic reorientation time scales. Our findings apply to non-Brownian micro-objects in water-based solutions – experimentally by the similarity principle and theoretically based on the Stokes equations. The reorientation of sedimenting rigid particles to a stationary stable configuration in a relatively short time might be used for environmental, biological, medical or industrial applications.

Contrary to accepted turbulence folklore, which holds that no mathematical relation exists between the Navier–Stokes equations (NSEs) and the multifractal model (MFM) of Parisi and Frisch, we develop a theory that reconciles the MFM with Leray’s weak solutions of Navier–Stokes analysis. From a combination of Euler invariant scaling and the NSEs set in a three-dimensional box of side $L$, we also derive the Paladin–Vulpiani scale $\eta_{h,pav}$ which is related to the Reynolds number Re by $L\eta _{h,\textit{pa}v}^{-1} = \textit{Re}^{1/(1+h)}$, and which acts as a mediator between the two theories. This is achieved by considering $L^{2m}$-norms of the velocity gradient to find a correspondence between $m$ and the local scaling exponent $h$ in the multifractal model. The parameter $m$ acts as if it were the sliding focus control on a telescope which allows us to zoom in and out on different structures. The range $1 \leqslant m \leqslant \infty$ is equivalent to $-{{ {2}/{3}}} \leqslant h_{\textit{min}} \leqslant {{{1}/{3}}}$, which lies precisely in the region where Bandak et al. (Phys. Rev. E, 2022, vol. 105, p. 065113; Phys. Rev. Lett., 2024, vol. 132, p. 104002) have suggested that thermal noise makes the NSEs inadequate and generates spontaneous stochasticity. The implications of this are discussed.

Flow around a submerged cylinder near a free surface reveals that adjusting the Froude number and gap ratio influences the underwater jet pattern, vortex shedding frequency and free-surface deformation. The jet typically separates near the trough, leading to vorticity concentration and breaking waves that dissipate wave energy. Antarctic orcas collaborate to generate deep depression waves, breaking ice and washing seals from floes. Orcas raise their heads and tap their tails downward when approaching ice, which may benefit strong wave generation. We investigate the wave-generating hydrodynamics using a towing tank and particle image velocimetry. A scaled model with an elliptical body and wedge-shaped tail was tested under Froude number similarity. Experiments covered towing speeds of $0.3- 0.7\,\textrm{ms}^{-1}$, combining different body ($10^\circ$/$0^\circ$/$-10^\circ$) and tail angles ($30^\circ$/$0^\circ$/$-30^\circ$), at chord-based Reynolds numbers of $17\,030- 40\,506$. Four wake regimes are identified: small-scale vortex emergence triggered by capillary waves; extensive wave breaking due to flow separation at the trough; smooth depression wave caused by jet reattachment and downward advection of wake vortices; and large-scale vortex impingement generated by wake vortex perturbations. Under the pitched posture, the jet attaches successively to the solid surface and the trough via the Coandâ effect, suppressing flow separation, creating the most pronounced wave. The strong jet maintained a low-potential-energy state of the wave and led to large ice floes flipping and fracturing through the bending effect, while smaller ice floes were overwashed. This study suggests a novel flow-control strategy for objects near the free surface through jet attachment.

Neural network observers (NNOs) are proposed for online estimation of fluid flows, addressing a key challenge in flow control: obtaining flow states online from a limited set of sparse and noisy sensor data. For this task, we propose a generalisation of the classical Luenberger observer. In the present framework, the estimation loop is composed of subsystems modelled as neural networks (NNs). By combining flow information from selected probes and a neural network surrogate model (NNSM) of the flow system, we train NNOs capable of fusing information to provide the best estimation of the states, that can in turn be fed back to a neural network controller (NNC). The NNO capabilities are demonstrated for three nonlinear dynamical systems. First, a variation of the Kuramoto–Sivashinsky (KS) equation with control inputs is studied, where variables are sparsely probed. We show that the NNO is able to track states even when probes are contaminated with random noise or with sensors at insufficient sample rates to match the control time step. Then, a confined cylinder flow is investigated, where velocity signals along the cylinder wake are estimated by using a small set of wall pressure sensors. In both the KS and cylinder problems, we show that the estimated states can be used to enable closed-loop control, taking advantage of stabilising NNCs. Finally, we present a legacy dataset of a turbulent boundary layer experiment, where convolutional NNs are employed to implement the models required for the estimation loop. We show that, by combining low-resolution noise-corrupted sensor data with an imperfect NNSM, it is possible to produce more accurate and robust estimates. Our approach presents better robustness to noise when compared with direct reconstructions via super-resolution NNs and predictions from graph NNs and Fourier neural operators.

This work presents a predictive two-point statistical closure framework for turbulence formulated in physical space. A closure model for ensemble-averaged, incompressible homogeneous isotropic turbulence (HIT) is developed as a starting point to demonstrate the viability of the approach in more general flows. The evolution equation for the longitudinal correlation function is derived in a discrete form, circumventing the need for a Fourier transformation. The formulation preserves the near-exact representation of the linear terms, a defining feature of rapid distortion theory. The closure of the nonlinear higher-order moments follows the phenomenological principles of the eddy-damped quasi-normal Markovian (EDQNM) model of Orszag (J. Fluid Mech., vol. 41, 1970, pp. 363–386). Several key differences emerge from the physical-space treatment, including the need to evaluate a matrix exponential in the evolution equation and the appearance of triple integrals arising from the non-local nature of the pressure–Poisson equation. This framework naturally incorporates non-local length-scale information into the evolution of turbulence statistics. Verification of the physical-space two-point closure is performed by comparison with direct numerical simulations of statistically stationary forced HIT and with classical EDQNM predictions and experimental data for decaying HIT. Finally, extensions to inhomogeneous and anisotropic turbulence are discussed, emphasising advantages in applications where spectral methods are ill-conditioned, such as compressible flows with discontinuities.