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.