Irrotational monochromatic surface gravity waves possess a mean Lagrangian drift which transports mass and enhances mixing in the upper ocean. In the ocean, where many surface waves are present, it is commonly assumed that the mean Lagrangian drift can be computed independently for each wave component and summed. Here we show, using laboratory measurements and fully nonlinear simulations of two-dimensional steep focusing wave packets, that this assumption underpredicts the average transport in regions of wave focusing by up to $30\,\%$. To explain these enhancements, we derive a new exact method for constraining the local mean Lagrangian drift in general flows by working in the Lagrangian reference frame. From this method, we derive an expression for the local mean Lagrangian drift in deep-water narrow-banded wave fields governed by the nonlinear Schrödinger equation (NLSE) that predicts near-surface enhancements when waves focus and steepen. The theoretical predictions of the local transport agree with the laboratory measurements, particularly for smaller bandwidth packets where the NLSE approximation is most valid. These findings highlight that it is the local steepness of the wave field, not just the sum of the steepnesses of the linear (non-interacting) wave components, which sets the strength of these enhancements.

We investigate experimentally the collective settling dynamics of an initially planar ensemble of inertial particles in quiescent fluid. The experiments used a $10 \times 10$ horizontal array of spherical particles with diameter $d=4$ mm and initial centre-to-centre spacing $2d$. Five configurations were tested, including two homogeneous arrays of particles with density ratios $\rho _p/\rho _{\!f} = 1.14$ and 1.28, and three heterogeneous arrays that combined both particle types in distinct spatial arrangements. Particle trajectories were obtained using particle tracking velocimetry, and the induced flow was characterised with planar and stereo particle image velocimetry. The settling behaviour was strongly governed by the particle spatial arrangement and density contrast. Homogeneous arrays developed parachute-like settling structures with central particles lagging, whereas heterogeneous arrays amplified or inverted this structure. Lighter particles were entrained and accelerated within downdrafts generated by heavier neighbours, while heavier particles were slowed down in the presence of lighter ones. Flow measurements reveal that wake-induced shear and entrainment substantially alter the trajectories of lighter particles. Pair-dispersion statistics show that vertical relative spreading dominates the dynamics, with $R_z^2 \propto t^{3/2}$ over the measured interval, reflecting gravitational settling coupled with collective wake-mediated interactions. Lateral pair dispersion exhibits an early acceleration-driven ballistic regime ($R_L^2 \propto t^2$), followed by a progressive loss of velocity correlation consistent with a diffusive-like growth ($R_L^2 \propto t$). Vertical dispersion in homogeneous arrays was nearly independent of the initial lateral separation, $r_0$, but increased in heterogeneous systems, reflecting configuration-sensitive entrainment and shear.

We perform causal analysis on the low-dimensional Galerkin model for shear flow developed by Moehlis et al. (New J. Phys., vol. 6, 2004, 56). Our method integrates both equation-based analysis and the proposed Galerkin-based Granger causality (GGC) to investigate the effect of the nonlinear terms on the dynamics. Two types of quadratic interactions are identified: a fully triadic interaction and a modulated two-mode coupling. The propagation of these interactions through the nonlinear dynamics leads to a directed cause-and-effect network. Furthermore, the relative importance of each mode amplitude on the dynamics of the target mode is quantified. This analysis provides a deeper understanding of the nonlinear dynamics and distills control opportunities. To demonstrate the applicability of the proposed GGC to realistic flows where Galerkin projection is impractical, a turbulent lid-driven cavity flow is further studied. We foresee applications of the proposed causal analysis framework as valuable tools for Galerkin modelling – guiding investigations of modal causality, prediction uncertainty, model-order reduction and control design.

Boiling and bubble injection are effective strategies for enhancing heat transfer between solid boundaries and a working fluid in numerous industrial applications, including nuclear reactors and molten metal processing. Motivated by this, we conduct direct numerical simulations of a vertical, turbulent, differentially heated, bubble-laden channel flow. The Prandtl number $\textit{Pr}$, kept identical in both phases, is varied across three representative values – $0.07$ (liquid metals), $0.7$ (vapour) and $7$ (water) – to span thermal transport regimes across three orders of magnitude. The simulations are conducted at a friction Reynolds number $\textit{Re}_\tau =150$, void fraction $\alpha =5.4\,\%$ and a density ratio $\rho _r=0.1$ (defined as the bubble-to-carrier density). The bubbles substantially alter the hydrodynamic structure of the flow, amplifying turbulent fluctuations and mixing. Their interaction with the thermal boundary layers disrupts the characteristic streaky structures near the heated walls, fragmenting them into smaller and more chaotic patterns. To elucidate this mechanism, we examine the bubble-induced modifications to the temperature field and show that temperature becomes decorrelated from velocity. Consequently, the heat-transfer enhancement arises primarily from an increase in convective heat flux driven by intensified wall-normal velocity fluctuations. The thermal boundary layer is markedly thinned, and the Nusselt number nearly doubles across all examined cases.

Turbulent channel flow controlled by spanwise wall oscillations is studied using direct numerical simulations to improve how spanwise forcing reduces skin-friction drag. Harmonic wall oscillations generate a periodic transverse Stokes layer whose thickness $\delta$ is determined by the forcing period $T$. Although an optimal $T$ that maximises drag reduction is known to exist, its physical significance remains unclear. To elucidate it, we extend the spanwise Stokes layer by augmenting wall oscillation with an additional spanwise body force. In this formulation, $\delta$ and $T$ become decoupled and can be varied independently. The oscillating wall thus appears as a special and suboptimal case of spanwise forcing. Optimal performance is obtained for substantially smaller $T$ and larger $\delta$ than those of the classical Stokes layer. For the conditions examined, with Reynolds number and forcing amplitude held fixed, the maximum drag reduction increases by approximately one third, while the maximum net energy saving improves markedly from $-35\,\%$ to $+16\,\%$. These findings suggest that drag-reduction strategies based on spanwise forcing deserve renewed scrutiny: wall oscillation represents only one possible actuation method, and not necessarily the most effective one.