This study explores the Faraday instability as a mechanism to enhance heat transfer in two-phase systems by exciting interfacial waves through resonance. The approach is particularly applicable to reduced-gravity environments where buoyancy-driven convection is ineffective. A reduced-order model, based on a weighted residual integral boundary layer method, is used to predict interfacial dynamics and heat flux under vertical oscillations with a stabilising thermal gradient. The model employs long-wave and one-way coupling approximations to simplify the governing equations. Linear stability theory informs the oscillation parameters for subsequent nonlinear simulations, which are then qualitatively compared against experiments conducted under Earth’s gravity. Experimental results show up to a 4.5-fold enhancement in heat transfer over pure conduction. Key findings include: (i) reduced gravity lowers interfacial stability, promoting mixing and heat transfer; and (ii) oscillation-induced instability significantly improves heat transport under Earth’s gravity. Theoretical predictions qualitatively validate experimental trends in wavelength-dependent enhancement of heat transfer. Quantitative discrepancies between model and experiment are rationalised by model assumptions, such as neglecting higher-order inertial terms, idealised boundary conditions, and simplified interface dynamics. These limitations lead to underprediction of interface deflection and heat flux. Nevertheless, the study underscores the value of Faraday instability as a means to boost heat transfer in reduced gravity, with implications for thermal management in space applications.

We consider laminar forced convection in a shrouded longitudinal-fin heat sink (LFHS) with tip clearance, as described by the pioneering study of (Sparrow, Baliga & Patankar 1978 J. Heat Trans. 100). The base of the LFHS is isothermal but the fins, while thin, are not isothermal, i.e. the conjugate heat transfer problem is of interest. Whereas Sparrow et al. numerically solved the fully developed flow and thermal problems for a range of geometries and fin conductivities, we consider the physically realistic asymptotic limit where the fins are closely spaced, i.e. the spacing is small relative to their height and the clearance above them. The flow problem in this limit was considered by (Miyoshi et al. 2024, J. Fluid Mech. 991, A2), and we consider the corresponding thermal problem. Using matched asymptotic expansions, we find explicit solutions for the temperature field (in both the fluid and fins) and conjugate Nusselt numbers (local and average). The structure of the asymptotic solutions provides further insight into the results of Sparrow et al.: the flow is highest in the gap above the fins, hence heat transfer predominantly occurs close to the fin tips. The new formulas are compared with numerical solutions and are found to be accurate for practical LFHSs. Significantly, existing analytical results for ducts are for boundaries that are either wholly isothermal, wholly isoflux or with one of these conditions on each wall. Consequently, this study provides the first analytical results for conjugate Nusselt numbers for flow through ducts.

The constant temperature and constant heat flux thermal boundary conditions, both developing distinct flow patterns, represent limiting cases of ideally conducting and insulating plates in Rayleigh–Bénard convection flows, respectively. This study bridges the gap in between, using a conjugate heat transfer (CHT) set-up and studying finite thermal diffusivity ratios $\kappa _s \! / \! \kappa _f$ to better represent real-life conditions in experiments. A three-dimensional Rayleigh–Bénard convection configuration including two fluid-confining plates is studied via direct numerical simulations given a Prandtl number ${Pr}=1$. The fluid layer of height $H$ and horizontal extension $L$ obeys no-slip boundary conditions at the two solid–fluid interfaces and an aspect ratio of ${\Gamma }=L/H=30$ while the relative thickness of each plate is ${\Gamma _s}=H_s/H=15$. The entire domain is laterally periodic. Here, different $\kappa _s \! / \! \kappa _f$ are investigated for moderate Rayleigh numbers $Ra=\left \{ 10^4, 10^5 \right \}$. We observe a gradual shift of the size of the characteristic flow patterns and their induced heat and mass transfer as $\kappa _s \! / \! \kappa _f$ is varied, suggesting a relation between the recently studied turbulent superstructures and supergranules for constant temperature and constant heat flux boundary conditions, respectively. Performing a linear stability analysis for this CHT configuration confirms these observations theoretically while extending previous studies by investigating the impact of a varying solid plate thickness $\Gamma _s$. Moreover, we study the impact of $\kappa _s \! / \! \kappa _f$ on both the thermal and viscous boundary layers. Given the prevalence of finite $\kappa _s \! / \! \kappa _f$ in nature, this work is a starting point to extend our understanding of pattern formation in geo- and astrophysical convection flows.

The ‘vorticity transport’ theory by G. I. Taylor states that, in two-dimensional (2-D) turbulent flows, it is not the momentum of the eddies which is conserved from one step of their random walk to the other (the so-called Reynolds–Prandtl analogy), but their vorticity, implying that the conservation laws for the time-averaged profiles for the velocity $u$ and concentration of a passive scalar $c$ must be different. This theory predicts that, across a 2-D wake or a jet, both fields (scaled by their maximal value) are exactly related to each other by $u=c^2.$ We reexamine critically this problem on hand of several experiments with plane and round turbulent jets seeded with high and low diffusing scalars, and conclude that the microscopic equations for $u$ and $c$ are identical, but that the differences between the $u$- and $c$-fields is a genuine mixing problem, sensitive to the dimensionality of the flow and to the intrinsic diffusivity of the scalar $D$, through the Schmidt number ($Sc=\nu /D$) dependence of the flow coarsening scale. We observe that $u=c^{\beta }$ with $\beta =2$ in plane jets irrespective of $Sc$, $\beta =3/2$ in round jets at $Sc=1$ and $\beta =1$ in round jets for $Sc\to \infty$. We explain why, because measurements dating back to the 1930s–40s were all made for heat transport in air ($Sc\approx 1$), agreement with Taylor‘s vision was only coincidental. The experiments and the new representation proposed here are strictly at odds with Reynolds’ analogy, although essentially an adaptation of it to eddies transporting momentum and mass, but liable to exchange mass with a smooth reservoir along their Brownian path.

Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid–fluid and solid–fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier–Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work, we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared with a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results, good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

Wall-resolved large-eddy simulations of flow over an axisymmetric body of revolution (DARPA SUBOFF bare model) at $ \it{Re}_L=1.1\times 10^6$ are performed to investigate wall pressure fluctuations under the combined effects of transverse curvature and varying pressure gradients. Due to the coexistence of convex and concave streamwise curvatures, the flow in the stern region features alternating zones of favourable and adverse pressure gradients (APGs). The simulation validates experimental findings by Balantrapu et al. (2023, J. Fluid Mech., vol. 960, A28), confirming that in APG-dominant axisymmetric boundary layers without streamwise curvatures, the root mean square wall pressure fluctuations ($p_{w,rms}$) decrease downstream alongside the wall shear stress ($\tau _w$), maintaining a constant ratio $p_{w,rms}/\tau _{w}$. This study further finds that when streamwise curvatures and strong streamwise pressure gradient variations present, this relationship breaks down, suggesting that $\tau _w$ is not the dominant contributor to wall pressure fluctuations. Instead, the local maximum Reynolds shear stress $-\rho \langle u_su_n\rangle _{max }$ emerges as a more robust pressure scaling parameter. Normalising the wall pressure spectra by $-\rho \langle u_su_n\rangle _{max }$ yields better collapse across the entire stern region compared to conventional inner or mixed scaling methods. The magnitude and location of $-\rho \langle u_su_n\rangle _{max }$ significantly influence the spectral levels of wall pressure fluctuations across different frequency bands. As the turbulence intensity and $-\rho \langle u_su_n\rangle _{max }$ shift away from the wall, outer-layer structures – with larger spatial and temporal scales – dominate the coherence of wall pressure fluctuations. This mechanism drives sustained attenuation of high-frequency pressure fluctuations and a simultaneous increase in both the streamwise and transverse correlation lengths of wall pressure fluctuations over the stern region.

Recently, Nagib et al. (Phys. Fluids, vol. 36, no. 7, 2024, 075145) used indicator functions of streamwise normal stress profiles to identify the valid wall-distance and Reynolds number ranges for two models in direct numerical sumulation (DNS) of channel and pipe flows. Since such functions are challenging to construct from experimental data, we propose a simpler, more robust method better suited to experiments. Applied to the two leading models – logarithmic and power-law – for normal stresses in the ‘fitting region’ of wall-bounded flows, this method is tested on prominent experimental data sets in zero-pressure-gradient (ZPG) boundary layers and pipe flows across a wide Reynolds number range ($Re_\tau$). Valid regions for the models appear only for $Re_\tau \gtrapprox 10{\,}000$, with a lower bound $y^+_{in} \sim (Re_\tau )^{0.5}$ and $y^+_{in} \gtrapprox 400$. The upper bound is a fixed fraction of the boundary layer thickness or pipe radius, independent of $Re_\tau$. The power-law model is found to hold over a broader range, up to $Y \approx 0.4$ in ZPG and $Y \approx 0.5$ in pipe flows, compared with the logarithmic trend, which is formulated to be coincident with the classical logarithmic region for the mean flow ($Y \lessapprox 0.15$). A slightly higher exponent ($0.28$) than that of Chen & Sreenivasan (J. Fluid Mech. vol. 933, 2022, A20; J. Fluid Mech. vol. 976, 2023, A21) extends the power-law model’s validity and correcting for outer intermittency in ZPG flows further broadens it. Projections to the near-wall region of both models yield nearly identical predictions of near-wall peak stress across the highest available $Re_\tau$. These findings, alongside results from Monkewitz & Nagib (J. Fluid Mech. vol. 967, 2023, A15) and Baxerras et al. (J. Fluid Mech. vol. 987, 2024, R8), highlight the importance of nonlinear eddy growth and residual viscous effects in wall-bounded flow modelling, informing potential refinements to the logarithmic model, such as those proposed by Deshpande et al. (J. Fluid Mech. vol. 914, 2021, A5).

Rayleigh–Taylor instability (RTI) caused by rarefaction waves not only features variable acceleration but also incorporates time-dependent density, which introduces great challenges in predicting the finger growth behaviours. In this work, we propose a model for predicting the single-mode finger behaviours by extending the Layzer potential-flow framework to account for time-dependent acceleration and density. Relative to the previous models, the present model can evaluate the effect of time-dependent density on finger growth, and can describe the growth behaviours of both bubbles and spikes in rarefaction-driven RTI flows. In addition, the time-dependent curvature of the finger tip as it evolves from its initial value to the quasi-steady value is quantified. To validate the model, rarefaction-tube experiments and numerical simulations are conducted across a wide range of initial conditions. The results show that the present model can accurately capture the amplitude growth and curvature evolution of bubbles and spikes across various density ratios. Moreover, both the present model and experiments demonstrate that the continuous density reduction in rarefaction-driven flows causes larger asymptotic velocities of bubbles and spikes, leading to higher Froude numbers relative to those under constant or time-dependent acceleration.

This study uses the diffusion analogy (Miyake, Sci. Rep., 5R-6, 1965, Univ. of Washington, Seattle, USA) to predict the full growth behaviour of internal boundary layers (IBLs) induced by a roughness change for neutrally – and especially stably – stratified boundary layers with finite thickness. The physics of the diffusion analogy shows that the streamwise variation of the IBL thickness is dictated by $\sigma _w/U$ at the interface, where $\sigma _w$ and $U$ represent wall-normal Reynolds stress and mean streamwise velocity, respectively. The existing variants of the model, summarised by Savelyev & Taylor (2005, Boundary-Layer Meteorol., vol. 115, pp. 1–25), are tailored to IBLs confined within the constant shear stress layer. To extend the applicability of the model to the outer region, we investigate the relation between $\sigma _w/U$ and $U/U_\infty$ in the outer region across varying stratification, where $U_\infty$ is the free-stream velocity. Our analysis reveals that wind tunnel data from a number of facilities collapse onto a master curve when $\sigma _w/U$ is premultiplied by a height-independent parameter, which is a function of the ratio of Monin–Obukhov length to the boundary layer thickness. The scaled $\sigma _w/U$ decreases inversely with $U/U_\infty$ in the surface layer, transitioning to a linear decrease as $U/U_\infty$ increases. The new model, which integrates these findings, along with the effects of streamline displacement and acceleration, captures the complete characteristics of IBLs as they develop within turbulent boundary layers of finite thickness.

Turbulent flows exhibit large intermittent fluctuations from inertial to dissipative scales, characterised by multifractal statistics and breaking the statistical self-similarity. It has recently been proposed that the Navier–Stokes turbulence restores a hidden form of scale invariance in the inertial interval when formulated for a dynamically (nonlinearly) rescaled quasi-Lagrangian velocity field. Here we show that such hidden self-similarity extends to the large-eddy-simulation (LES) approach in computational fluid dynamics (CFD). In particular, we show that classical subgrid-scale models, such as implicit or explicit Smagorinsky closures, respect the hidden scale invariance at all scales – both resolved and subgrid. In the inertial range, they reproduce the hidden scale invariance of Navier–Stokes statistics. These properties are verified very accurately by numerical simulations and, beyond CFD, turn LES into a valuable tool for fundamental turbulence research.

We present a theoretical framework for porous media gravity currents propagating over rigid curvilinear surfaces. By reducing the flow dynamics to low-dimensional models applicable on surfaces where curvature effects are negligible, we demonstrate that, for finite-volume releases, the flow behaviour in both two-dimensional and axisymmetric configurations is primarily governed by the ratio of the released viscous fluid volume to the characteristic volume of the curvilinear surface. Our theoretical predictions are validated using computational fluid dynamics simulations based on a sharp-interface model for macroscopic flow in porous media. In the context of carbon dioxide geological sequestration, our findings suggest that wavy cap rock geometries can enhance trapping capacity compared with traditional flat-surface assumptions, highlighting the importance of incorporating realistic topographic features into subsurface flow models.

In this work, we study the effectiveness of the time-localised principal resolvent forcing mode at actuating the near wall cycle of turbulence. This mode is restricted to a wavelet pulse and computed from a singular value decomposition of the windowed wavelet-based resolvent operator (Ballouz et al. 2024b, J. Fluid Mech. vol. 999, A53) such that it produces the largest amplification via the linearised Navier–Stokes equations. We then inject this time-localised mode into the turbulent minimal flow unit at different intensities, and measure the deviation of the system’s response from the optimal resolvent response mode. Using the most energetic spatial wavenumbers for the minimal flow unit – i.e. constant in the streamwise direction and once-periodic in the spanwise direction – the forcing mode takes the shape of streamwise rolls and produces a response mode in the form of streamwise streaks that transiently grow and decay. Though other works such as Bae et al. (2021 J. Fluid Mech. vol. 914, A3) demonstrate the importance of principal resolvent forcing modes to buffer layer turbulence, none instantaneously track their time-dependent interaction with the turbulence, which is made possible by their formulation in a wavelet basis. For initial times and close to the wall, the turbulent minimal flow unit matches the principal response mode well, but due to nonlinear effects, the response across all forcing intensities decays prematurely with a higher forcing intensity leading to faster energy decay. Nevertheless, the principal resolvent forcing mode does lead to significant energy amplification and is more effective than a randomly generated forcing structure and the second suboptimal resolvent forcing mode at amplifying the near-wall streaks. We compute the nonlinear energy transfer to secondary modes and observe that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into a structure twice-periodic in the spanwise direction; in the outer region, the streak breaks up into a structure that is once-periodic in the streamwise direction. In both regions, spanwise oscillations account for the dominant share of nonlinear energy transfer.

The breakup dynamics of viscous liquid bridges on solid surfaces is studied experimentally. It is found that the dynamics bears similarities to the breakup of free liquid bridges in the viscous regime. Nevertheless, the dynamics is significantly influenced by the wettability of the solid substrate. Therefore, it is essential to take into account the interaction between the solid and the liquid, especially at the three-phase contact line. It is shown that when the breakup velocity is low and the solid surface is hydrophobic, the dominant channel of energy dissipation is likely due to thermally activated jumping of molecules, as described by the molecular kinetic theory. Nevertheless, the viscous dissipation in the bulk due to axial flow along the bridge can be of importance for long bridges. In view of this, a scaling relation for the time dependence of the minimum width of the liquid bridge is derived. For high viscosities, the scaling relation captures the time evolution of the minimum width very well. Furthermore, it is found that external geometrical constraints alter the dynamic behaviour of low and high viscosity liquid bridges in a different fashion. This discrepancy is explained by considering the dominant forces in each regime. Lastly, the morphology of the satellite droplets deposited on the surface is qualitatively compared with that of free liquid bridges.