We explored the dynamics of Taylor–Couette flows within square enclosures, focusing primarily on the turbulence regime and vortex behaviour at varying Reynolds numbers. Laboratory experiments were conducted using particle image velocimetry for Reynolds numbers $Re_{\varDelta }\in [0.23, 4.6]\times 10^3$ based on the minimum gap $\varDelta /d = 1/16$, $1/8$ and $1/4$, where $d$ is the cylinder diameter, or $Re\in [1.8, 9.8]\times 10^3$ based on $d/2$. At lower $Re$, the flow was dominated by well-defined Taylor and Görtler vortices, while higher $Re$ led to a turbulent state with distinct motions. Space–time radial velocity analysis revealed persistent Taylor vortices at lower $Re$, with larger gaps but increased turbulence, and irregular motions at higher $Re$, with smaller gaps. Velocity spectra reveal that the energy distribution is maintained at frequencies lower than the integral-type frequency $f_I$ across varying $\varDelta$ due to the dominance of large vortices. However, there is a monotonic increase in energy at higher frequencies beyond $f_I$. The reduced characteristic frequency $f_I\varDelta /\omega _ir_i \sim 1/10$ indicates that these motions scale linearly with angular velocity, and inversely with the gap. Proper orthogonal decomposition (POD) and spectral POD were used to distinguish between Taylor and Görtler vortices, showing the effects of gap size and the associated energy cascade. Linear stability analysis included as complementary support revealed primary instability of the Taylor vortex, which is similar to the circular enclosure, along with multiple corner modes that are unique to the geometry.

Long-duration and time-resolved particle image velocimetry measurements were conducted in rough-wall open channel flows (OCFs), with the friction Reynolds number ranging from 642 to 2034. The primary objective is to investigate the impacts of various turbulent motions at different scales on the mean wall-shear stress ($\langle \tau _w \rangle$). To achieve this aim, a physical decomposition of $\langle \tau _w \rangle$ was initially performed utilizing the double-averaged methodology proposed by Nikora et al. (2019 J. Fluid Mech. 872, 626–664). This method enabled the breakdown of $\langle \tau _w \rangle$ into three distinct constituents: viscous, turbulent and dispersive stress segments. The findings underscore the substantial roles that turbulent and dispersive stresses play, accounting for over 75 % and 9 % of $\langle \tau _w \rangle$, respectively. Subsequently, a scale decomposition was further applied to analyse the contributions of coherent motions at different scales to $\langle \tau _w \rangle$. Adopting typical cutoff streamwise wavelengths ($\lambda _x = 3h$ and $10h$), the contribution of large-scale motions (LSMs) and very large-scale motions (VLSMs) to the overall wall-shear stress was quantified. It was revealed that turbulent motions with $\lambda _x \gt 3h$ and $\lambda _x \gt 10h$ contribute more than 40 % and 18 % of $\langle \tau _w \rangle$, respectively. The scale decomposition of the wall-shear stress and the contribution from LSMs and VLSMs exhibit evident dependencies on the Reynolds number. The contribution of LSMs and VLSMs to $\langle \tau _w \rangle$ is lower in rough OCFs compared with those of smooth counterparts. Secondary currents induced by the rough wall are hypothesised to be responsible for the reduced strength of LSMs and VLSMs and decreases in their contribution to $\langle \tau _w \rangle$.

A linear stability model based on a phase-field method is established to study the formation of ripples on the ice surface. The pattern on horizontal ice surfaces, e.g. glaciers and frozen lakes, is found to be originating from a gravity-driven instability by studying ice–water–air flows with a range of water and ice thicknesses. Contrary to gravity, surface tension and viscosity act to suppress the instability. The results demonstrate that a larger value of either water thickness or ice thickness corresponds to a longer dominant wavelength of the pattern, and a favourable wavelength of 90 mm is predicted, in agreement with observations from nature. Furthermore, the profiles of the most unstable perturbations are found to be with two peaks at the ice–water and water–air interfaces whose ratio decreases exponentially with the water thickness and wavenumber.

In this work, a systematic study is carried out concerning the dynamic behaviour of finite-size spheroidal particles in non-isothermal shear flows between parallel plates. The simulations rely on a hybrid method combining the lattice Boltzmann method with a finite-difference solver. Fluid–particle and heat–particle interactions are accounted for by using the immersed boundary method. The effect of particle Reynolds number ($\textit{Re}_p=1{-}90$), Grashof number (${Gr}=0{-}200$), initial position and initial orientation of the particle are thoroughly examined. For the isothermal prolate particle, we observed that above a certain Reynolds number, the particle undergoes a pitchfork bifurcation; at an even higher Reynolds number, it returns to the centre position. In contrast, the hot particle behaves differently, with no pitchfork bifurcation. Instead, the Reynolds and Grashof numbers can induce oscillatory tumbling or log-rolling motions in either the lower or upper half of the channel. Heat transfer also plays an important role: at low Grashof numbers, the particle settles near the lower wall, while increasing the Grashof number shifts it towards the upper side. Moreover, the presence of thermal convection increases the rotational speed of the particle. Surprisingly, beyond the first critical Reynolds number, the equilibrium position of the thermal particle shifts closer to the centreline compared with that of a neutrally buoyant isothermal particle. Moreover, higher Grashof numbers can cause the particle to transition from tumbling to log-rolling or even a no-rotation mode. The initial orientation has a stronger influence at low Grashof numbers, while the initial position shows no strong effect in non-isothermal cases.

This study investigates noise generation from co-rotating rotors arranged in a side-by-side configuration. The analysis examines the effects of different phase delays and separation distances. A simple mathematical model is developed to provide insight into constructive and destructive noise interference. An experimental campaign was carried out to validate the proposed analytical model. Furthermore, the study introduces a space–time proper orthogonal decomposition technique to separate broadband and tonal components. Subsequently, wavelet analysis is applied to the tonal component, revealing a transition to chaos via intermittency, characterised by the local birth and decay of periodic oscillations. This phenomenon highlights the intricate and fascinating chaotic nature of interference transitions. The chaotic behaviour of the tonal component is related to the macro time scale of pressure fluctuations, and has been incorporated into the mathematical model. This model has several applications, including its potential use in the development of active control systems and the design of quieter distributed propulsion systems.

Microswimmers display an intriguing ability to navigate through fluids with spatially varying viscosity, a behaviour known as viscotaxis, which plays a crucial role in guiding their motion. In this study, we reveal that the orientation dynamics of chiral squirmers in fluids with uniform viscosity gradients can be elegantly captured using the Landau–Lifshitz–Gilbert equations, originally developed for spin systems. Remarkably, we discover that chiral swimmers demonstrate negative viscotaxis, tracing spiral trajectories as they move. Specifically, a chiral squirmer with a misaligned source dipole and rotlet dipole exhibits a steady-state spiral motion – a stark contrast to the linear behaviour observed when the dipoles are aligned. This work provides fresh insights into the intricate interplay between microswimmer dynamics and fluid properties.

This paper investigates linear and nonlinear evolution of a radiating mode in a supersonic boundary layer in the presence of an impinging sound wave. Of special interest is the case where the sound wave has wavenumber and frequency twice those of the radiating mode, and so the two share the same phase speed and hence the critical layer. In this case, a radiating mode is sensitive to a small-amplitude sound wave due to effective interactions taking place in their common critical layer. The sound wave influences the development of the radiating mode through the mechanism of subharmonic parametric resonance, which is often referred to as Bragg scattering. Amplitude equations are derived to account for this effect in the two regimes where non-equilibrium and non-parallelism play a leading-order role, respectively. A composite amplitude equation is then constructed to account for both of these effects. These amplitude equations are solved to quantify the impact of the impinging sound wave on linear and nonlinear instability characteristics of the radiating mode. Numerical results show that the incident sound makes the amplification and attenuation of the radiating mode highly oscillatory. With sufficiently high intensity, the impinging sound enhances the radiating mode. For a certain range of moderate intensity, the impinging sound inhibits the growth of the radiating mode and may eliminate the singularity, which would form in the absence of external acoustic fluctuations. The far-field analysis shows that the incident sound alters the Mach wave field of the radiating mode significantly, rendering its pressure contours spiky and irregular.

We analyse moment and probability density function (PDF) statistics of a passive scalar $\Theta$ at a Prandtl number of $Pr=0.71$ in a turbulent jet. For this, we conducted a direct numerical simulation at a Reynolds number of $Re=3500$ and, further, employed Lie symmetries applied to the multi-point moment equations, generalising recent work (Nguyen & Oberlack 2024b under review with Flow Turbul. Combust.) that focused on pure hydrodynamics. It is shown that the symmetry theory also provides highly precise results for free shear flows for all the quantities mentioned and statistical symmetries again play a key role. The scalar statistics are partly similar to the $U_z$ velocity statistics, and in particular, as in the above-mentioned work, a significant generalisation of the classical scalings has been derived so that a variation of the scaling laws solely controlled by the inflow is possible. An exponential behaviour of the scaling prefactors with the moment orders $m$ and $n$ for scalar and velocity is also discovered for any mixed moments. Instantaneous $\Theta$-moments and mixed $U_z$-$\Theta$-moments exhibit a Gaussian distribution with variation of the scaled radius $\eta =r/(z-z_0)$. Therein, the coefficient in the Gauss exponent is nonlinear with varying moment orders $m$ and $n$. The scalar PDF statistics are clearly different from the velocity statistics, i.e. already deviate from the Gaussian distribution on the jet axis, as is observed for the $U_z$ statistics, and become clearly skewed and heavy tailed for increasing $\eta$.

We investigate suspensions of non-Brownian, millimetric monodisperse spherical particles floating at quasi-two-dimensional fluid interfaces, from dilute to dense concentrations. Building upon the phase diagram in the capillary number ($Ca$) and areal fraction ($\phi$) constructed by Shin & Coletti (2024 J. Fluid Mech. 984, R7), we analyse the dynamics of both aggregation and dispersion. In the capillary-driven clustering regime ($Ca \lt 1$), strong inter-particle bonds yield large, fractal-like clusters that grow by hit-and-stick collisions. In the drag-driven break-up regime ($Ca \gt 1$, $\phi \lt 0.4$), turbulent fluctuations overcome capillarity and result in particles moving similarly to passive tracers and forming clusters by random adjacency. In the lubrication-driven clustering regime ($Ca \gt 1$, $\phi \gt 0.4$), the close inter-particle proximity amplifies lubrication forces and results in large, crystal-like clusters. Above a threshold concentration that depends on $Ca$, self-similar percolating clusters span the entire domain. The particle transport exhibits a classic ballistic-to-diffusive transition, with the long-time diffusivity hindered by the reduced fluctuating energy at high concentrations. Nearby particles separate at initially slow rates due to strong capillary attraction, and then follow a super-diffusive dispersion regime. In dense suspensions, the process is characterised by the time scale associated with inter-particle collisions and by the energy dissipation rate defined by the lubrication force between adjacent particles. Our results provide a framework for predicting particle aggregation in interfacial suspensions such as froth flotation and pollutant dispersion, and may inform the design of advanced materials through controlled colloidal self-assembly.

The scattering of surface waves by structures intersecting liquid surfaces is fundamental in fluid mechanics, with prior studies exploring gravity, capillary and capillary–gravity wave interactions. This paper develops a semi-analytical framework for capillary–gravity wave scattering by a fixed, horizontally placed, semi-immersed cylindrical barrier. Assuming linearised potential flow, the problem is formulated with differential equations, conformal mapping and Fourier transforms, resulting in a compound integral equation framework solved numerically via the Nyström method. An effective-slip dynamic contact line model accounting for viscous dissipation links contact line velocity to deviations from equilibrium contact angles, with fixed and free contact lines of no dissipation as limiting cases. The framework computes transmission and reflection coefficients as functions of the Bond number, slip coefficient and barrier radius, validating energy conservation and confirming a $90^\circ$ phase difference between transmission and reflection in specific limits. A closed-form solution for scattering by an infinitesimal barrier, derived using Fourier transforms, reveals spatial symmetry in the diffracted field, reduced transmission transitioning from gravity to capillary waves and peak contact line dissipation when the slip coefficient matches the capillary wave phase speed. This dissipation, linked to impedance matching at the contact lines, persists across a range of barrier sizes. These results advance theoretical insights into surface-tension-dominated fluid mechanics, offering a robust theoretical framework for analysing wave scattering and comparison with future experimental and numerical studies.