arXiv subjects

Florian Rein

Publications and source records attributed to Florian Rein.

4 recordsLinked to original sources

arXiv2026

Suppression of Rayleigh-B\'enard convection and restratification by horizontal convection

We investigate the competition between horizontal convection (HC) and Rayleigh-B\'enard convection (RBC) in a fluid layer subject to a uniform destabilizing buoyancy flux at the bottom and a horizontally varying buoyancy distribution at the top. The RBC forcing imposes negative horizontal mean vertical buoyancy gradients at the top and bottom of the fluid layer. But if the HC forcing is sufficiently strong then the volume averaged vertical buoyancy gradient, $\langle b_z \rangle$, is positive i.e.~opposite in sign to destabilizing RBC buoyancy gradients at the boundaries. If $\langle b_z \rangle>0$ we say that the layer has been ''restratified''. Using scaling analysis based on power integrals together with two-dimensional direct numerical simulations at Rayleigh numbers up to $10^{10}$, we identify two cases: a neutral stratification state, in which HC first offsets RBC so that $\langle b_z \rangle = 0$, and a strong stratification regime, in which HC dominates and $\langle b_z \rangle$ is opposite in sign, and greater in magnitude, than the prescribed destabilizing vertical buoyancy gradient at the layer boundaries. For the range of parameters explored in this study, we derive scaling laws for the onset of these regimes in terms of the horizontal and vertical flux Rayleigh numbers, $\RaH$ and $\RaV$, finding $\RaHN \sim \RaV^{4/5}$ for the neutral state and $\RaHstrg \sim \RaV$ for the onset of strong stratification. The results highlight the controlling role of the top boundary layer in setting the mean stratification and clarify the conditions under which HC suppresses RBC. These findings are relevant to geophysical environments such as subglacial lakes, and the oceans of Snowball Earth and icy moons, where bottom heating and horizontal buoyancy variations jointly shape ocean stratification.

physics.flu-dyn↗

arXiv2025

Instability triggered by mixed convection in a thin fluid layer

We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends on the Prandtl number as well as the normalized flux difference ($f$) and decreases with the aspect ratio ($\epsilon$), following a $\epsilon f^{-1}$ power law. Using 3D initial value and 2D eigenvalue calculations, we identify a dominant 3D mode characterized by two transverse standing waves attached to the domain edges. We characterize the dominant mode's frequency and transverse wave number as functions of the Rayleigh number and aspect ratio. An analytical asymptotic solution for the base state in the bulk is obtained, valid over most of the domain and increasingly accurate for lower aspect ratios. A local stability analysis, based on the analytical base state, reveals oscillatory transverse instabilities consistent with the global instability characteristics. The source term for this most unstable mode appears to be interactions between vertical shear and horizontal temperature gradients.

physics.flu-dyn↗

arXiv2025

Experimental study of the convection in a thin cylindrical gas layer with imposed bottom and top fluxes and imposed side temperature

We investigate convection in a thin cylindrical gas layer with an imposed flux at the bottom and a fixed temperature along the side, using a combination of direct numerical simulations and laboratory experiments. The experimental approach allows us to extend by two orders of magnitude the explored range in terms of flux Rayleigh number. We identify a scaling law governing the root-mean-square horizontal velocity and explain it through a dimensional analysis based on heat transport in the turbulent regime. Using particle image velocimetry, we experimentally confirm, for the most turbulent regimes, the presence of a drifting persistent pattern consisting of radial branches, as identified by Rein et al. (2023, J. Fluid Mech. 977, A26). We characterise the angular drift frequency and azimuthal wavenumber of this pattern as functions of the Rayleigh number. The system exhibits a wide distribution of heat flux across various time scales, with the longest fluctuations attributed to the branch pattern and the shortest to turbulent fluctuations. Consequently, the branch pattern must be considered to better forecast important wall heat flux fluctuations, a result of great relevance in the context of nuclear safety, the initial motivation for our study.

physics.flu-dyn↗

arXiv2024

Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection. The second one is driven by vertical heat transfers analogous to Rayleigh Benard convection. We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.

physics.flu-dyn↗