Direct numerical simulation (DNS) of temporally developing natural convection boundary layers is conducted at $ \textit{Pr} =4.16$ and $ \textit{Pr} =6$. Results are compared with an existing DNS dataset for $ \textit{Pr} =0.71$ (Ke et al. J. Fluid Mech. 964, 2023, p. A24) to enable a direct assessment of Prandtl number effects across the range $0.71\leqslant \textit{Pr} \leqslant 6$. The analysis reveals that the $ \textit{Pr}$ affects the flow through buoyancy forcing, which acts not only as the driving force but also modulates the local shear distribution via coupling with the momentum equation, thereby shifting the onset Rayleigh number of transition from the laminar regime. This transition is found to be characterised by the thermal boundary layer thickness $\delta _\theta$, which provides a robust prediction of the critical Rayleigh number across $ \textit{Pr}$, indicating a buoyancy instability consistent with the stability analysis (Ke et al. J. Fluid Mech. 988, 2024, p. A44; Ke et al. Intl J. Heat Mass Transfer 241, 2025, p. 126670). Further analysis in the turbulent regime suggests that while heat transfer becomes effectively independent of $ \textit{Pr}$, the near-wall turbulence structure remains sensitive to $ \textit{Pr}$ due to persistent buoyancy effects. The skin friction coefficient scaling shows clear transition from a linear scaling with the bulk Reynolds number in the weakly turbulent regime to a log-law-type scaling with the bulk Reynolds number in the ultimate turbulent regime (Grossmann & Lohse J. Fluid Mech. 407, 2000, pp. 27–56). The premultiplied velocity spectra confirms the development of near-wall streaks that are characteristic of canonical shear-driven turbulence in this ultimate turbulent regime, with their spanwise spacing systematically broadening with increasing $ \textit{Pr}$ due to persistent buoyancy effects; while the spectral signature of the outer plume-like region appears largely $ \textit{Pr}$-independent.

We investigated the influence of the slip velocity on particle migration in viscoelastic microchannel flows using a hybrid computational approach that coupled the lattice Boltzmann method with coarse-grained molecular dynamics. Our results demonstrate that the slip velocity changes lateral migration mechanisms by affecting the balance of inertial and elastic lift forces. In Newtonian fluids, forward slip drives particles toward the channel walls due to dominant inertial lift, while backward slip promotes migration toward the channel centreline. In viscoelastic fluids, however, slip-induced elastic lift forces arising from asymmetric polymer deformation around particles exceed inertial effects by an order of magnitude. This leads to a complete reversal of migration behaviour. We established that elastic lift scales linearly with the slip velocity and the block ratio, consistent with theoretical predictions, while polymer chain length influences elastic lift through a power-law dependence ($F_{e,s}^*\sim M^{1.66}$). These findings reveal that viscoelasticity-mediated slip effects provide a robust mechanism for particle manipulation in complex fluids. By connecting the microscopic polymer dynamics to macroscopic transport phenomena, our work offers new design principles for particle sorting and focusing applications in microfluidic systems.

Turbulence subject to axisymmetric expansion is experimentally investigated using opposed multiple-jet arrays. For each array, jet interaction generates decaying, nearly homogeneous and isotropic turbulence within a duct. The turbulent flows from the opposed arrays collide and spread radially, forming a mean-flow stagnation point with associated mean strain. Flow properties are examined using particle image velocimetry. The mean velocity gradient tensor, $\mathsf{A}_{\textit{ij}} = \partial \langle u_i \rangle / \partial x_{\!j}$, satisfies $\mathsf{A}_{\textit{xx}} : \mathsf{A}_{\textit{yy}} : \mathsf{A}_{zz} = -2 : 1 : 1$ with $\mathsf{A}_{\textit{xx}} \lt 0$, indicating axisymmetric expansion. Turbulence is strongly influenced by this expansion, becoming increasingly anisotropic towards the stagnation point, suggesting a cumulative effect of mean strain. The ratios of streamwise to transverse root-mean-square velocity fluctuations, $u_{\textit{rms}}/v_{\textit{rms}}$, and of their integral scales both increase relative to an isotropic state, consistent with rapid distortion theory (RDT). However, because the strain time scale is comparable to that of large-scale motions, deviations from RDT arise, including larger $u_{\textit{rms}}/v_{\textit{rms}}$ values and a steeper decay of energy spectra in the inertial subrange than the $-5/3$ law. The spectral slope change is opposite to that reported for axisymmetric contraction, suggesting a common mechanism for spectral modification in both strain types, since both are described by the same tensor form with opposite signs of $\mathsf{A}_{\textit{ij}}$. Consistently, the scaling exponents of velocity structure functions differ from predictions based on Kolmogorov’s second similarity hypothesis, even for low-order functions. These results confirm that axisymmetric mean strain significantly modifies turbulence properties, some of which are considered universal for other turbulent flows.

Underground gas storage is a critical technology in global efforts to mitigate climate change. In particular, hydrogen storage offers a promising solution for integrating renewable energy into the power grid. When injected into the subsurface, hydrogen’s low viscosity compared with the resident brine causes a bubble of hydrogen trapped beneath caprock to spread rapidly into an aquifer through release of a thin gas layer above the brine, complicating recovery. In long aquifers, the large viscous pressure drop between source and outlet induces significant pressure variations, potentially leading to substantial density changes in the injected gas. To examine the role of gas compressibility in the spreading dynamics, we use long-wave theory to derive coupled nonlinear evolution equations for the gas pressure and gas/liquid interface height, focusing on the limit of long domains, weak gas compressibility and low gas/liquid viscosity ratio. Simulations are supplemented with a comprehensive asymptotic analysis of parameter regimes. Unlike the near-incompressible limit, in which gas spreading rates are dictated by the source strength and viscosity ratio, and compressive effects are transient, we show how compression of the main gas bubble can generate dynamic pressure changes that are coupled to those in the thin gas layer that spreads over the liquid, with compressive effects having a sustained influence along the layer. This coupling allows compressibility to reduce spreading rates and gas pressures. We characterise this behaviour via a set of low-order models that reveal dominant scalings, highlighting the role of compressibility in mediating the evolution of the gas layer.

In this study, we investigate the transition from laminar to turbulent flow in boundary layers within nozzles used as standard flow meters. Experiments are conducted to analyse the effects of surface roughness, the radius of curvature at the nozzle throat and the level of free stream turbulence. The results indicate that, for industrial nozzles with standard roughness levels, surface roughness does not significantly influence the transition process. Additionally, tests on three different nozzles reveal that a smaller throat radius corresponds to a higher Reynolds number at the transition point. To understand this behaviour, we develop a theoretical model where the laminar boundary layer profiles are derived using an analytical formulation that accounts for compressibility and favourable pressure gradients in these nozzles. The stability characteristics of this boundary layer are examined within the framework of linear stability theory, assuming parallel flow. Since Tollmien–Schlichting waves are stabilised by the favourable pressure gradient, a spatial transient growth analysis is employed to explore the role of bypass mechanisms. Similar to the flat-plate boundary layer case, the optimal perturbations are identified as streaks. Due to the nozzle wall’s convex curvature, the highest growth is observed at low but non-zero frequencies, leading to unsteady streak formation. A transition model, based on the N-factor of optimal unsteady streaks, is used to estimate the onset of transition. This model successfully reproduces the experimentally observed effects of curvature and can be used to optimise the design of mass-flow-meter nozzles. Finally, the critical roughness size required to trigger a roughness-induced transition is estimated theoretically and compared with experimental observations. The impact of distributed roughness on transition is examined in relation to stability theory, showing that the tested roughness levels are ineffective in triggering transient growth mechanisms.

We present a theoretical analysis of a gyroscopic wave energy converter (GWEC), which generates electricity via the precession induced by the flywheel’s rotation and the pitch motion of a floating body. The coupled wave–body–gyroscope interaction problem is formulated under the assumptions of linear waves and resulting linear motions of both the floating body and the gyroscope. Within this framework, we identify the optimal control parameters that maximise the energy absorption efficiency. The analysis reveals that the GWEC can theoretically achieve the maximum energy absorption efficiency of 1/2 at any wave frequency through appropriate tuning of the flywheel’s rotational speed and the generator parameters. The derived theory is verified through numerical simulations in both the frequency and time domains. Furthermore, time-domain simulations incorporating the nonlinear gyroscopic response are conducted to assess the limitations of the linear gyroscopic model. These findings provide valuable insights for the future design of wave energy harvesting technologies.