The incipient cavitation of a pair of unequal strength counter-rotating vortices undergoing the long-wavelength Crow instability is examined with high-speed video, acoustic measurements and volumetric particle tracking velocimetry. This work expands upon the previous studies of Chang & Ceccio (J. Acoust. Soc. Am., vol. 130, 2011, pp. 3209–3219) and Chang et al. (Phys. Fluids, vol. 24, 2012, 014107). Volumetric velocimetry results presented by Knister et al. (J. Fluid Mech., 2026) were used to predict the core pressures of the stretched secondary vortices. These data are combined with free-stream nuclei measurements to predict the rates of cavitation inception, which compared well with the directly measured inception rates. The acoustic emissions of incipient cavitation events are also related to the vortex properties and the nuclei content of the water. The reduced pressure in the stretched vortices is shown to be related primarily to the reduction in the core radius of the secondary vortex and not due to axial jetting or straining. The measured vortex dynamics indicates that the process leading to the pressure drop in the secondary vortex core is a transient process but not more rapid than the development of the Crow instability. In conclusion, these results show that a relatively simple model of cavitation inception in a stretched secondary vortex captures the essential physics connecting the nuclei population and the underlying vortical flow field, enabling prediction of the resulting observed inception rates. These results also indicate that the reduced pressures in vortical flow leading to inception are primarily due to the reduction in the core of the vortices and not due to substantive axial jetting. The pressure drop in the vortex cores is accordingly a transient process, but despite the appearances of cavitation inception it does not proceed faster than the development of the Crow instability in the secondary vortices.

The hydrodynamics of vortex-induced vibration of a flexible pipe in bidirectionally sheared flows are investigated through combined experimental and numerical approaches. Such bidirectionally sheared flows are inspired by subsurface currents induced by internal solitons widely occurring in the ocean, which feature oppositely directed flow velocities along the flexible pipe. Experiments are conducted in an ocean basin using a tensioned pipe with distributed strain sensors, and numerical simulations are conducted by a validated strip method based framework. The mean in-line displacement, mean drag, shear force and bending moment are characterised. The mean in-line displacement, maximised over the spanwise direction, exhibits an approximately quadratic dependence on the maximum velocity in bidirectionally sheared flow. In contrast, the mean drag coefficient remains nearly unchanged with increasing flow velocity. Both trends are cross-validated via experiments and simulations. Furthermore, empirical expressions are proposed to describe the influence of background flow velocities on the shear force and bending moment. Excitation and added mass coefficients associated with dominant frequency response and time-varying hydrodynamic coefficients considering multi-frequency responses are extracted and analysed. The results show that the phase difference between the cross-flow and in-line responses retains an antisymmetric distribution, whereas the excitation coefficients exhibit quasi-symmetric patterns around the mid-span. The time-dependent added mass coefficient is strongly correlated with the wake pattern, with negative values occurring predominantly during P + S and 2P vortex shedding patterns. Moreover, spectral proper orthogonal decomposition is employed to link the dominant vortex-induced vibration frequencies of the flexible pipe with the surrounding flow field. The results indicate a clear transition in which the dominant flow field frequency follows the Strouhal frequency at lower velocity, but aligns with the structural vibration frequency at higher velocity associated with the occurrence of the lock-in phenomenon.

The equivalent source method (ESM) is one of the fundamental methods for reconstructing the far-field acoustic pressure and identifying the sources in aeroacoustics. However, it suffers from disturbances of near-field hydrodynamic pressure. We propose a hierarchical ESM (HESM) to suppress the disturbance by filtering out hydrodynamic pressure. The hydrodynamic pressure is filtered out using a frequency-domain convection operator. This operator replaces the prescribed convection velocity in Taylor’s frozen flow hypothesis with an adaptive complex convection velocity. The complex convection velocity is adapted in an iterative way to take into account the multiscale convection and spatial amplification of hydrodynamic pressure. The hydrodynamic pressure associated reconstruction error can thus be suppressed. The proposed HESM is compared with the Ffowcs Williams–Hawkings analogy method and the ESM that directly uses the pressure and the filtered pressure with the widely used uniform convection velocity. The use of complex convection velocity-based hydrodynamic pressure filtering mitigates the overprediction of acoustic pressure and enables precise reconstruction of both acoustic pressure directivity and spectra.

We investigate the stability of the flow past two side-by-side square cylinders (at Reynolds number 200 and gap ratio 1) using tools from dynamical systems theory. The flow is highly irregular due to the complex interaction between the flapping jet emanating from the gap and the vortices shed in the wake. We first perform spectral proper orthogonal decomposition (SPOD) to understand the flow characteristics. We then conduct Lyapunov stability analysis by linearising the Navier–Stokes equations around the irregular base flow and find that it has two positive Lyapunov exponents. The covariant Lyapunov vectors (CLVs) are also computed. Contours of the time-averaged CLVs reveal that the footprint of the leading CLV is in the near-wake, whereas the other CLVs peak further downstream, indicating distinct regions of instability. SPOD of the two unstable CLVs is then employed to extract the dominant coherent structures and oscillation frequencies in the tangent space. For the leading CLV, the two dominant frequencies match closely with the prevalent frequencies in the drag coefficient spectrum and correspond to instabilities due to vortex shedding and jet-flapping. The second unstable CLV captures the subharmonic instability of the shedding frequency. Global linear stability analysis (GLSA) of the time-averaged flow identifies a neutral eigenmode that resembles the leading SPOD mode of the first CLV, with a very similar structure and frequency. However, while GLSA predicts neutrality, Lyapunov analysis reveals that this direction is unstable, exposing the inherent limitations of the GLSA when applied to chaotic flows.

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as complex as quasi-time-periodic solutions. Approximations of these states can be computed efficiently using a quasi-linear model, consistent with the large-Reynolds-number asymptotic analysis. The quasi-linear structure is key to producing multiscale critical layers that generate vortices obeying Taylor’s frozen-flow hypothesis.

We present three-dimensional direct numerical simulations of turbulent Rayleigh–Bénard convection in a closed rectangular box whose width $L_y$ and length $L_x$ are 0.8 and 2.4 times the height $H$, respectively. The Rayleigh number $\textit{Ra}$ varies from $10^5$ to $10^{10}$, and the Prandtl number is unity. The advantages of the present configuration are: (a) a relatively stable unidirectional large-scale circulation, consisting of two counter-rotating rolls, fills the cell and fixes the thermal plume ejection- and shear-dominated regions, in contrast to those in closed cylindrical cells. (b) The regions of plume ejection are essentially independent of the sidewalls so that their autonomous existence can be studied. This is because there is some space, or ‘fetch’, for the velocity and thermal boundary layers to develop along the length. (c) This geometry allows one to study the influence of locally thin and thick boundary layers (which follow larger or smaller plume activity) on the scaling of convection properties. In regions of larger plume activity (defined by an incessant movement of plumes), the temperature fluctuation as well as the normalised thermal and viscous dissipation rates decay more slowly with $\textit{Ra}$ than in regions of lower activity. Both viscous and thermal boundary layers thin down rapidly with increasing distance from the plume ejection region. The local thicknesses of both boundary layers decline more rapidly with $\textit{Ra}$ in the ejection region than in regions of impact and shear, where they are similar to each other. Despite these details, the global heat transport laws are practically the same as those in other configurations of low to moderate aspect ratios.

Accurate prediction of the hydrodynamic coefficients of non-spherical particles in wall-confined flows is crucial for understanding particle–fluid interactions and reliable modelling of particle motion. Under strong wall confinement, the hydrodynamic coefficients exhibit a highly nonlinear dependence on the Reynolds number, wall distance and particle orientation – posing significant modelling challenges. In this study, we propose a multi-stage physics-informed machine-learning (MSPIML) framework for modelling the drag, lift and pitching torque coefficients of a wall-bounded prolate spheroid over the explored parameter space. In the first stage, a physics-informed mixture-of-experts (PIMoE) model predicts the drag coefficient by intelligently blending empirical correlations with a data-driven statistical expert. The resulting high-fidelity drag coefficient is then injected as an auxiliary input to a second-stage model, either a deep neural network (DNN) or an additional MoE, that predicts lift and pitching torque coefficients, thereby leveraging the strong physical coupling among the three coefficients. Trained on a comprehensive dataset of 720 direct numerical simulations covering wide ranges of Reynolds number, wall distance and particle orientation, the optimal PIMoE–DNN and PIMoE–MoE configurations achieve relative errors below 2.2 % for drag, 11.4 % for lift and 7.0 % for pitching torque while maintaining excellent generalisation across the entire parameter space. Moreover, the Shapley additive explanations analysis confirms that the MSPIML framework correctly captures the physical dependencies: dominant influence of Reynolds number and strong pitching torque dependence on the drag coefficient. The MSPIML framework provides an interpretable and efficient approach to the prediction of hydrodynamic coefficients and offers substantial potential for dynamic modelling of non-spherical particles in multiphase flows.

A mathematical model for the deposition of particles from a thin sessile droplet undergoing diffusion-limited evaporation in four different modes of evaporation, namely the constant contact radius (CR), constant contact angle (CA), stick–slide (SS), and stick–jump (SJ) modes, is formulated and analysed. Explicit expressions are obtained for the flow and concentration of particles within the droplet, as well as the evolutions of the mass of particles in the bulk of the droplet and in a distributed deposit and/or in one or more ring deposits on the substrate. It is shown that the nature of the deposit depends on both the local evaporative flux and the motion of the contact line. In particular, for a droplet undergoing diffusion-limited evaporation, the flow is outwards towards the contact line in both the CR and CA modes, however, the receding contact line in the CA mode results in a qualitatively different deposit from that in the CR mode, specifically a switch from a ring deposit in the CR mode to a near-uniform deposit in the CA mode. This contrasts with the behaviour of a droplet undergoing spatially uniform evaporation in the CA mode, in which the flow is radially inwards resulting in a peak deposit. For a droplet evaporating in the SS or SJ modes, the final deposit is a combination of the deposit types associated with the CR and CA modes. The present model is validated by finding good agreement between the theoretical predictions for the deposit and previous experimental results.