We analyse the pressure-driven radial flow of a shear-thinning fluid between two parallel plates. Complex fluid rheology may significantly affect the hydrodynamic features of such non-Newtonian flows, which remain not fully understood, compared with Newtonian flows. We describe the shear-thinning rheology using the Ellis model and present a theoretical framework for calculating the pressure distribution and the flow rate–pressure drop relation. We first derive a closed-form expression for the pressure gradient, which allows us to obtain semi-analytical expressions for the pressure, velocity and flow rate–pressure drop relation. Specifically, we provide the corresponding asymptotic solutions for small and large values of the dimensionless flow rates. We further elucidate the entrance length required for the radial velocity of a shear-thinning fluid to reach its fully developed form, showing that this length approximates the Newtonian low-Reynolds-number value at low shear rates, but may strongly depend on the fluid’s shear-thinning rheology and exceed the Newtonian value at high shear rates. We validate our theoretical results with finite-element numerical simulations and find excellent agreement. Furthermore, we compare our semi-analytical, asymptotic and finite-element simulation results for the pressure distribution with the experimental measurements of Laurencena & Williams (Trans. Soc. Rheol. vol. 18, 1974, pp. 331–355), showing good agreement. Our theoretical results using the Ellis model capture the interplay between the shear-thinning and the zero-shear-rate effects on the pressure drop, which cannot be explained using a simple power-law model, highlighting the importance of using an adequate constitutive model to accurately describe non-Newtonian flows of shear-thinning fluids.

Particle suspensions in confined geometries can become clogged, which can have a catastrophic effect on function in biological and industrial systems. Here, we investigate the macroscopic dynamics of dense suspensions in constricted geometries. We develop a minimal continuum two-phase model that allows for variation in particle volume fraction. The model comprises a ‘wet solid’ phase with material properties dependent on the particle volume fraction, and a seepage Darcy flow of fluid through the particles. We find that spatially varying geometry (or material properties) can induce emergent heterogeneity in the particle fraction and trigger the abrupt transition to a high-particle-fraction ‘clogged’ state.

Waves transport particles in the direction of wave propagation with the Stokes drift. When the Earth’s rotation is accounted for, waves induce an additional (Eulerian-mean) current that reduces drift and is known as the anti-Stokes drift. This effect is often ignored in oceanic particle-tracking simulations, despite being important. Although different theoretical models exist, they have not been validated by experiments. We conduct laboratory experiments studying the surface drift induced by deep-water waves in a purpose-built rotating wave flume. With rotation, the Lagrangian-mean drift deflects to the right (counterclockwise rotation) and reduces in magnitude. Compared with two existing steady theoretical models, measured drift speed follows a similar trend with wave Ekman number but is larger. The difference is largely explained by unsteadiness on inertial time scales. Our results emphasise the importance of considering unsteadiness when predicting and analysing the transport of floating material by waves.

Drops in a shear flow experience shear-induced diffusion due to drop–drop interactions. Here, the effects of medium viscoelasticity on shear-induced collective diffusivity are numerically investigated. A layer of viscous drops suspended in a viscoelastic fluid was simulated, fully resolving each deforming drop using a front-tracking method. The collective diffusivity is computed from the spreading of the drop layer with time, specifically a one-third scaling, as well as using an exponentially decaying dynamic structure factor of the system of drops. Both methods led to matching results. The surrounding viscoelasticity was shown to linearly reduce the diffusion-led spreading of the drop layer, the effect being stronger for less deformable drops (low capillary number). Because of the competition between the increasing effect with capillary number (Ca) and the decreasing effect with Weissenberg number (Wi), collective diffusivity vanishes at very low Ca and high enough Wi. The physics behind the hindering effects of viscoelasticity on shear-induced diffusion is explained with the help of drop–drop interactions in a viscoelastic fluid, where shear-induced interaction leads to trapping of drops into tumbling trajectories at lower Ca and higher Wi due to viscoelastic stresses. Using the simulated values, phenomenological correlations relating the shear-induced gradient diffusivity with Wi and Ca were found.

The dynamics of self-excited shock train oscillations in a back pressured axisymmetric duct was investigated to deepen the understanding of the isolator/combustor coupling in high-speed propulsion systems. The test article consisted of an internal compression inlet followed by a constant area isolator, both having a circular cross-section. A systematic back pressure variation was implemented by using a combination of aerodynamic and physical blockages at the isolator exit. High bandwidth two-dimensional pressure field imaging was performed at $8\,{\rm kHz}$ repetition rate within the isolator for different back pressure settings. The acquisition rate was considerably higher than the dominant frequency of the shock train oscillations across the different back pressure settings. The power spectral density of the pressure fluctuations beneath the leading shock foot exhibited broadband low frequency oscillations across all back pressures that resembled the motions of canonical shock–boundary layer interaction units. A node in the vicinity of reattachment location that originated the pressure perturbations within the separation shock was also identified, which further ascertained that the leading shock low frequency motions were driven by the separation bubble pulsations. Above a threshold back pressure, additional peaks appeared at distinct higher frequencies that resembled the acoustic modes within the duct. However, none of the earlier expressions of the resonance acoustic frequency within a straight duct agreed with the experimentally observed value. Cross-spectral analyses suggested that these modes were caused by the shock interactions with upstream propagating acoustic waves that emanate from the reattachment location, originally proposed for transonic diffusers by Robinet & Casalis (2001) Phys. Fluids 13, 1047–1059. Feedback interactions described using one-dimensional stability analysis of the shock perturbations by obliquely travelling acoustic waves (Robinet & Casalis 2001 Phys. Fluids 13, 1047–1059) made favourable comparisons on the back pressure threshold that emanated the acoustic modes as well as the acoustic mode frequencies.

In recent years, integrating physical constraints within deep neural networks has emerged as an effective approach for expediting direct numerical simulations in two-phase flow. This paper introduces physics-informed neural networks (PINNs) that utilise the phase-field method to model three-dimensional two-phase flows. We present a fully connected neural network architecture with residual blocks and spatial parallel training using the overlapping domain decomposition method across multiple graphics processing units to enhance the accuracy and computational efficiency of PINNs for the phase-field method (PF-PINNs). The proposed PINNs framework is applied to a bubble rising scenario in a three-dimensional infinite water tank to quantitatively assess the performance of PF-PINNs. Furthermore, the computational cost and parallel efficiency of the proposed method was evaluated, demonstrating its potential for widespread application in complex training environments.

Numerical studies on the statistical properties of irregular waves in finite depth have to date been based on models founded on weak nonlinearity; as a consequence, only lower-order (usually third-order) nonlinear interactions have thus far been investigated. The present study performs numerical simulations with a fully nonlinear, spectrally accurate model to investigate the statistics of irregular, unidirectional wave fields in finite water depth initially given by a Texel, Marsen and Arsloe spectrum. A series of random unidirectional wave fields are considered, covering a wide range of water depth. The wave spectrum and statistical properties, including the probability density function of the surface elevation, exceedance probability of wave crests and occurrence probability of extreme (rogue) waves, are investigated. The importance of full nonlinearity in comparison with third-order results is likewise evaluated. The results show that full nonlinearity increases kurtosis and enhances the occurrence probability of large wave crests and rogue waves substantially, in both deep water and finite water depth. Therefore, we propose that full nonlinearity may contribute significantly to the formation of rogue waves. Furthermore, to account for the effects of higher-order nonlinearity on modulational instability, we analyse the relationship between the Benjamin–Feir index (BFI) and maximal excess kurtosis. Our results show a strong linear relationship i.e. $({\mathcal{K}}_{max}-3)\propto {\textrm{BFI}}$, in contrast to $({\mathcal{K}}_{max}-3)\propto {\textrm{BFI}}^2$ based on the assumptions of weak nonlinearity, a narrow-banded spectrum and deep-water conditions. Above, $\mathcal{K}_{max}$ is the maximal kurtosis.

A deep reinforcement learning method for training a jellyfish-like swimmer to effectively track a moving target in a two-dimensional flow was developed. This swimmer is a flexible object equipped with a muscle model based on torsional springs. We employed a deep Q-network (DQN) that takes the swimmer’s geometry and dynamic parameters as inputs, and outputs actions that are the forces applied to the swimmer. In particular, an action regulation was introduced to mitigate the interference from complex fluid–structure interactions. The goal of these actions is to navigate the swimmer to a target point in the shortest possible time. In the DQN training, the data on the swimmer’s motions were obtained from simulations using the immersed boundary method. During tracking a moving target, there is an inherent delay between the application of forces and the corresponding response of the swimmer’s body due to hydrodynamic interactions between the shedding vortices and the swimmer’s own locomotion. Our tests demonstrate that the swimmer, with the DQN agent and action regulation, is able to dynamically adjust its course based on its instantaneous state. This work extends the application scope of machine learning in controlling flexible objects within fluid environments.

In this study, the statistical properties and formation mechanisms of particle clusters that consider the influence of particle–wall interactions in particle-laden wall turbulence are systematically investigated through wind tunnel experiments. In the experiments, two particle release modes, including particle top-releasing mode (Case 1) and particle locally laying mode (Case 2), were adopted to establish varying conditions with different particle–wall interaction strengths. The Voronoï diagram method was employed to identify the particle clusters, and the impact of particle–wall interactions on the characteristics of the clusters was analysed. The results indicate that particle–wall interaction is the predominant factor in the formation of particle clusters in the near-wall region. Under Case 1 and Case 2, the maximum concentration of particles in the clusters could reach nearly five times the average particle concentration; however, the clusters with large particle numbers ($N_C\gt 5$) in Case 1 tended to form near the wall and the vertical velocities of these clusters were greater than the average velocities of all particles. In contrast, under Case 2, clusters with large particle numbers exhibited a higher probability of occurrence further from the wall and the vertical velocities of these clusters were lower than the average velocity of all particles. Furthermore, this study found that the presence of particle clusters in these flows significantly alters the flow field properties surrounding them, implying that a region of high strain and low vorticity constitutes an essential but non-sufficient condition for the generation of particle clusters in wall turbulence.