The vertical heated pipe is widely used in thermal engineering applications, as buoyancy can help drive a flow, but several flow regimes are possible: shear-driven turbulence, laminarised flow and convective turbulence. Steady velocity fields that maximise heat transfer have previously been calculated for heated pipe flow, but were calculated independently of buoyancy forces, and hence independently of the flow regime and time-dependent dynamics of the flow. In this work, a variational method is applied to find an optimal body force of limited magnitude $A_0$ that maximises heat transfer for the vertical arrangement, with the velocity field constrained by the full governing equations. In our calculations, mostly at Reynolds number ${\textit{Re}}=3000$, it is found that streamwise-independent rolls remain optimal, as in previous steady optimisations, but that the optimal number of rolls and their radial position is dependent on the flow regime. Surprisingly, while it is generally assumed that turbulence enhances heat transfer, for the strongly forced case, time dependence typically leads to a reduction. Beyond offering potential improvement through the targeting of the roll configuration for this application, wider implications are that optimisations under the steady flow assumption may overestimate improvements in heat transfer, and that strategies that simply aim to induce turbulence may not necessarily be efficient in enhancing heat transfer either. Including time dependence and the full governing equations in the optimisation is challenging but offers further enhancement and improved reliability in prediction.

Wettability quantifies the affinity of a liquid over a substrate and determines whether the surface is repellent or not. When both the liquid and the solid phases are made of the same chemical substance and are at thermal equilibrium, complete wetting is expected in principle, as observed, for instance, with drops of molten metals spreading on their solid counterparts. However, this is not the case for water on ice. Although there is a growing consensus on the partial wetting of water on ice and several estimates available for the value of the associated macroscopic contact angle, the question of whether these values correspond to the contact angle at mechanical and thermal equilibrium is still open. In the present paper, we address this issue experimentally and demonstrate the existence of such a macroscopic contact angle of water on ice, from measurements and theoretical arguments. Indeed, when depositing water droplets on smooth polycrystalline ice layers with accurately controlled surface temperatures, we observe that spreading is unaffected by thermal effects and phase change close enough to the melting point (namely, for undercoolings below 1 K) so that conditions of thermal equilibrium are closely approached. Whereas the short time motion of the contact line is driven by an inertial-capillary balance, the evolution towards mechanical equilibrium is described by a viscous-capillary dynamics and is therefore capillary – and not thermally – related. Moreover, we show that the resulting contact angle remains constant for undercoolings below 1 K. In this way, we show the existence of a non-zero macroscopic contact angle of water on ice under conditions of mechanical and thermal equilibrium, which is very close to $12^\circ$. We anticipate this key finding will significantly improve the understanding of capillary flows in the presence of phase change, which is of special interest in the realm of ice morphogenesis and glaciology, and will also be beneficial with the aim of developing numerical methods for resolving triple-line dynamics.

In this paper, a freely falling circular cylinder attached by a splitter plate in an infinite fluid domain under gravity is investigated numerically. The kinematic modes and wake patterns are summarised, and their parametric sensitivity with the dimensionless plate length ($L^\ast$), the Galileo number ($Ga$) and the cylindric-fluid density ratio ($\rho ^\ast$) is studied. The kinematic modes of a freely falling circular cylinder with a splitter plate can be classified into six types: the steady falling, the steady oblique falling, the small vibration oblique falling, the zigzag oblique falling, the locked falling and the chaotic falling. In the meantime, the wake patterns can be summarised into five types: the steady wake, the 2S wake, the 2P + nS wake, the 2P + 2S wake, and the chaotic wake. The effect of the length of the splitter plate on the vortex shedding characteristics represented by the Strouhal number is also discussed. Further investigation reveals that the attachment of a splitter plate of different lengths to the rear not only influences the kinematic mode and the vortex shedding of the circular cylinder, but also allows the passive and precise control of its falling posture and trajectory. Finally, through theoretical analysis, scaling laws are proposed to estimate the turn angle $\alpha$ and the drift angle $\beta$. The present study can deepen the understanding of similar natural phenomena, such as gliding birds and falling maple seeds, and provide valuable reference for engineering design of drag-reduction devices or air-dropped objects.

The flow instabilities in shock-wave–boundary-layer interactions at Mach 6 are comprehensively investigated through compression corner and incident shock cases. The boundary of global stability and the characteristics of globally unstable modes are determined by global stability analysis. In resolvent analysis, cases are categorized into flat plate, no separation, small separation and large separation flows. The optimal response shifts from the first mode in the flat plate case to streaks after the amplification in the interaction region. The amplification of streaks and the first mode (oblique mode) are both attributed to the Görtler instability. Meanwhile, the second mode exhibits minimal growth and higher Mack’s modes appear within the separation bubble. Rounded corner case and linear stability analysis are utilized to further validate the amplification mechanism of the oblique mode.

The turbulent transport of momentum, energy and passive scalar is investigated in the flow around a rectangular cylinder of aspect ratio 5 : 1 – a geometry representative of separating and reattaching flows from sharp-edged bodies. The study is based on direct numerical simulation (DNS) conducted at Reynolds numbers up to ${\textit{Re}} = 14\,000$, based on the cylinder thickness, with Schmidt number fixed at ${\textit{Sc}} = 0.71$. At this Reynolds number, the flow exhibits features of asymptotic high-${\textit{Re}}$ behaviour. Budgets of mean momentum, Reynolds stresses, mean scalar and scalar fluxes provide a detailed view of the underlying transport mechanisms. The mean momentum balance elucidates the role of turbulence in entraining free stream fluid, promoting shear-layer reattachment, sustaining backflow in the recirculation region and regulating wake dynamics through large-scale vortex shedding. The leading-edge shear layer is the main site of turbulence production, with energy injected into streamwise fluctuations and redistributed to cross-flow components by pressure–strain interactions. As ${\textit{Re}}$ increases, vertical fluctuations increasingly return energy to the mean upward flow, stabilising the separation bubble height. Turbulent transport dominates scalar redistribution. Scalar fluxes are primarily generated by interactions between Reynolds stresses and scalar gradient, and modulated by pressure-scalar gradient effects. An a priori evaluation of eddy-viscosity and diffusivity models quantifies the misalignment between modelled and DNS-resolved stress and flux tensors, as well as the inhomogeneity of eddy transport coefficients. This analysis deepens the understanding of transport phenomena in bluff-body flows approaching the asymptotic regime, and underpins the validation and improvement of turbulence models for separating and reattaching flows.

The interaction between deep oceanic currents and an ice base is critical to accurately predict global ice melting rates, yet predictions are often affected by inaccuracies due to inadequate dynamical modelling of the ice–water interface morphology. To improve current predictive models, we numerically investigate the evolution of the ice–water interface under a subsurface turbulent shear-dominated flow, focusing on the time and length scales that govern both global and local morphological features. Based on our previous work (Perissutti, Marchioli & Soldati 2024 Intl J. Multiphase Flow 181, 105007), where we confirmed the existence of a threshold Reynolds number below which only streamwise-oriented topography forms and above which a larger-scale spanwise topography emerges and coexists with the streamwise structures, we explore three orders of magnitude for the Stefan number (the ratio of sensible heat to latent heat). We examine its impact on ice melting and its role in shaping the interface across the two distinct morphodynamic regimes. We identify characteristic time scales of ice melting and demonstrate that the key features of ice morphodynamics scale consistently with the Stefan number and the Péclet number (the ratio of heat advection to diffusion) in both regimes. These scaling relationships can be leveraged to infer the main morphodynamic characteristics of the ice–water interface from direct numerical simulation datasets generated at computationally feasible values of Péclet and Stefan numbers, enabling the incorporation of morphodynamics into geophysical melting models and thereby enhancing their predictive accuracy.

Motivated by the need for a better understanding of the melting and stability of floating ice bodies, we experimentally investigated the melting of floating ice cylinders. Experiments were carried out in a tank, with ice cylinders with radii between 5 and 12 cm, floating horizontally with their axis perpendicular to gravity. The water in the tank was at room temperature, with salinities ranging from 0 to 35 g l−1. These conditions correspond to Rayleigh numbers in the range 10$^5\lesssim$ Ra $\lesssim$ 10$^9$. The relative density and thus the floating behaviour was varied by employing ice made of H$_2$O–D$_2$O mixtures. In addition, we explored a two-layer stable stratification. We studied the morphological evolution of the cross-section of the cylinders and interpreted our observations in the context of their interaction with the convective flow. The cylinders only capsize in fresh water but not when the ambient is saline. This behaviour can be explained by the balance between the torques exerted by buoyancy and drag, which change as the cylinder melts and rotates. We modelled the oscillatory motion of the cylinders after a capsize as a damped nonlinear oscillator. The downward plume of the ice cylinders follows the expected scalings for a line-source plume. The plume’s Reynolds number scales with Rayleigh number in two regimes, namely Re $\propto$ Ra$^{1/2}$ for Ra $\lt \mathcal{O}(10^7)$ and Re $\propto$ Ra$^{1/3}$ for Ra $\gt \mathcal{O}(10^7)$, and the heat transfer (non-dimensional as Nusselt number) scales as Nu $\propto$ Ra$^{1/3}$. Although the addition of salt substantially alters the solutal, thermal and momentum boundary layers, these scaling relations hold irrespectively of the initial size or the water salinity. While important differences exist between our experiments and real icebergs, our results can qualitatively be connected to natural phenomena occurring in fjords and around isolated icebergs, especially with regard to the melting and capsizing behaviour in stratified waters.