We study the conductive and convective states of phase-change of pure water in a rectangular container where two opposite walls are kept respectively at temperatures below and above the freezing point and all the other boundaries are thermally insula
ting. The global ice content at the equilibrium and the corresponding shape of the ice-water interface are examined, extending the available experimental measurements and numerical simulations. We first address the effect of the initial condition, either fully liquid or fully frozen, on the system evolution. Secondly, we explore the influence of the aspect ratio of the cell, both in the configurations where the background thermal-gradient is antiparallel to the gravity, namely the Rayleigh-Benard (RB) setting, and when they are perpendicular, i.e., vertical convection (VC). We find that for a set of well-identified conditions the system in the RB configuration displays multiple equilibrium states, either conductive rather than convective, or convective but with different ice front patterns. The shape of the ice front appears to be always determined by the large scale circulation in the system. In RB, the precise shape depends on the degree of lateral confinement. In the VC case the ice front morphology is more robust, due to the presence of two vertically stacked counter-rotating convective rolls for all the studied cell aspect-ratios.
We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidat
ing the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylors hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static point-like numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylors frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly non-homogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.
Convective flows coupled with solidification or melting in water bodies play a major role in shaping geophysical landscapes. Particularly in relation to the global climate warming scenario, it is essential to be able to accurately quantify how water-
body environments dynamically interplay with ice formation or melting process. Previous studies have revealed the complex nature of the icing process, but have often ignored one of the most remarkable particularity of water, its density anomaly, and the induced stratification layers interacting and coupling in a complex way in presence of turbulence and phase change. By combining experiments, numerical simulations, and theoretical modeling, we investigate solidification of freshwater, properly considering phase transition, water density anomaly, and real physical properties of ice and water phases, which we show to be essential for correctly predicting the different qualitative and quantitative behaviors. We identify, with increasing thermal driving, four distinct flow-dynamics regimes, where different levels of coupling among ice front, stably and unstably stratified water layers occur. Despite the complex interaction between the ice front and fluid motions, remarkably, the average ice thickness and growth rate can be well captured with the theoretical model. It is revealed that the thermal driving has major effects on the temporal evolution of the global icing process, which can vary from a few days to a few hours in the current parameter regime. Our model can be applied to general situations where the icing dynamics occurs under different thermal and geometrical conditions (e.g. cooling conditions or water layer depth).
The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multi-component reactions of second and higher orders, in a condition close to chemical equilibrium sustain
ed by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and remove relative correlations. We show that a unique control parameter, the Damkh{o}ler number ($Da_theta$) that can be constructed from the scalar Taylor micro-scale, the reactant diffusivity and the reaction rate characterises the functional dependence of fluctuations and correlations in a variety of conditions, i.e., at changing the reaction order, the Reynolds and the Schmidt numbers. The larger is such a Damkh{o}ler number the more depleted are the scalar fluctuations as compared to the fluctuations of a passive scalar field in the same conditions, and vice-versa the more intense are the correlations. A saturation in this behaviour is observed beyond $Da_theta simeq mathcal{O}(10)$. We provide an analytical prediction for this phenomenon which is in excellent agreement with direct numerical simulation results.
Inertialess anisotropic particles in a Rayleigh-Benard turbulent flow show maximal tumbling rates for weakly oblate shapes, in contrast with the universal behaviour observed in developed turbulence where the mean tumbling rate monotonically decreases
with the particle aspect ratio. This is due to the concurrent effect of turbulent fluctuations and of a mean shear flow whose intensity, we show, is determined by the kinetic boundary layers. In Rayleigh-Benard turbulence prolate particles align preferentially with the fluid velocity, while oblate ones orient with the temperature gradient. This analysis elucidates the link between particle angular dynamics and small-scale properties of convective turbulence and has implications for the wider class of sheared turbulent flows.
The orientational dynamics of inertialess anisotropic particles transported by two-dimensional convective turbulent flows display a coexistence of regular and chaotic features. We numerically demonstrate that very elongated particles (rods) align pre
ferentially with the direction of the fluid flow, i.e., horizontally close to the isothermal walls and dominantly vertically in the bulk. This behaviour is due to the the presence of a persistent large scale circulation flow structure, which induces strong shear at wall boundaries and in up/down-welling regions. The near-wall horizontal alignment of rods persists at increasing the Rayleigh number, while the vertical orientation in the bulk is progressively weakened by the corresponding increase of turbulence intensity. Furthermore, we show that very elongated particles are nearly orthogonal to the orientation of the temperature gradient, an alignment independent of the system dimensionality and which becomes exact only in the limit of infinite Prandtl number. Tumbling rates are extremely vigorous adjacent to the walls, where particles roughly perform Jeffery orbits. This implies that the root-mean-square near-wall tumbling rates for spheres are much stronger than for rods, up to $mathcal{O}(10)$ times at $Rasimeq 10^9$. In the turbulent bulk the situation reverses and rods tumble slightly faster than isotropic particles, in agreement with earlier observations in two-dimensional turbulence.
We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, $Pr simeq 480$, and at
Rayleigh numbers $Ra simeq 10^{8}$ and $Ra simeq 5 times 10^{8}$ in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle ($beta$) of the convection cell, the character of the flow can be changed from moderately turbulent, for $beta = 0^o$, to laminar and steady at $beta = 90^o$. The global heat transfer is found to be insensitive to the drastic reduction of turbulent intensity, with maximal relative variations of the order of $20%$ at $Ra simeq 10^{8}$ and $10%$ at $Ra simeq 5 times 10^{8}$, while the Reynolds number, based on the global root-mean- square velocity, is strongly affected with a decay of more than $85%$ occurring in the laminar regime. We show that the intensity of the heat flux in the turbulent regime can be only weakly enhanced by establishing a large scale circulation flow by means of small inclinations. On the other hand, in the laminar regime the heat is transported solely by a slow large scale circulation flow which exhibits large correlations between the velocity and temperature fields. For inclination angles close to the transition regime in-between the turbulent-like and laminar state, a quasi-periodic heat-flow bursting phenomenon is observed.
The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled point-like probes drifting in a flo
w. Such probes are characterised by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated by their intended course as the result of local sweeping of the fluid flow. The recorded time-series by these moving probes represent the simplest realisation of transect measurements in a fluid flow environment. We investigate the non trivial combination of Lagrangian and Eulerian statistical properties displayed by the transect time-series. We show that, as a result of the homogeneity and isotropy of the flow, the single-point acceleration statistics of the probes follows a predictable trend at varying the propulsion speed, a feature that is also present in the scalar time-derivative fluctuations. Further, by focusing on two-time statistics we characterize how the Lagrangian-to-Eulerian transition occurs at increasing the propulsion velocity. The analysis of intermittency of temporal increments highlights in a striking way the opposite trends displayed by the fluid velocity and passive scalars.
We present an investigation of the statistics of velocity gradient related quantities, in particluar energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic t
urbulent flow. The Refined Similarity Hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Re~400 with 2048^3 collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral-time-scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial-range.
Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-Benard turbulence are numerically analyzed. The working fluid is water. We focus on the temperature profiles, the center temperature, the Nusselt number, and o
n the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10^8) for fixed temperature difference (Delta) between top and bottom plates and as functions of Delta (non-Oberbeck-Boussinesqness) for fixed Ra with Delta up to 60 K. All results are consistent with the available experimental NOB data for the center temperature Tc and the Nusselt number ratio Nu_{NOB}/Nu_{OB} (the label OB meaning that the Oberbeck-Boussinesq conditions are valid). Beyond Ra ~ 10^6 the flow consists of a large diagonal center convection roll and two smaller rolls in the upper and lower corners. In the NOB case the center convection roll is still characterized by only one velocity scale.
