Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2102.10576

Bifurcation analysis of two-dimensional Rayleigh--Bénard convection using deflation

Nicolas Boullé·Vassilios Dallas·Patrick E. Farrell
View original source ↗Read source document ↗Export metadata ↓

Abstract

We perform a bifurcation analysis of the steady states of Rayleigh--Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialisation strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this non-linear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the disconnected branches we find contains an S-shaped curve with hysteresis, which is the origin of a flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyse the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.

Explore related subjects

physics.flu-dyncs.NAmath.NAphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nicolas Boullé, Vassilios Dallas, Patrick E. Farrell. 2022-04-22. Bifurcation analysis of two-dimensional Rayleigh--Bénard convection using deflation. https://doi.org/10.1103/physreve.105.055106

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Cross-helicity and chaotic dynamics of full-disc solar magnetic field

Using the results of laboratory experiments and direct numerical simulations, as well as observations of the full-disc solar magnetic field and sunspot number dynamics, it is demonstrated that cross-helicity can dominate the decaying part of the frequency power spectra of the magnetic field generated by a magnetohydrodynamic (MHD) dynamo in chaotic/turbulent swirling flows for sufficiently strong MHD turbulence (including the solar dynamo). The theoretical consideration is based on a Kolmogorov-like phenomenology within the framework of the distributed chaos concept. It is also shown that the solar full-disc magnetic field for the last two solar cycles with weak magnetic activity exhibits deterministic chaotic behavior concentrated around the equator.

physics.flu-dyn↗
arXiv2026

Manifestation of spurious currents and interface regularization in wind turbulence over fast-propagating waves

Accurate simulation of wind turbulence over fast-propagating waves requires interface-capturing methods that suppress numerical artifacts while accurately resolving momentum transfer across the interface. In high wave-age regimes, numerical errors at the air-water interface can reach magnitudes comparable to the physical flow, directly affecting predicted turbulence statistics. This study examines widely used interface-capturing techniques to evaluate how curvature estimation and flux discretization influence wind-wave simulations through the resulting spurious currents and interface regularization. A systematic assessment is performed using static and translating droplet benchmarks, together with solitary and monochromatic wave cases, to identify and quantify the dominant numerical error mechanisms. In addition, comparison with experimental measurements reveals how these primary error sources manifest in coupled wind-wave simulations. These findings clarify the numerical origin of the observed discrepancies and underscore the importance of accurate curvature and flux treatment in high wave-age regimes, without which numerical artifacts risk being misattributed to genuine wind-wave physics.

physics.flu-dyn↗
arXiv2026

A reconfigurable multi-axis cyber-physical framework for multi-regime fluid--structure interaction experiments

Fluid--structure interaction (FSI) experiments are typically built around mechanical dynamics and constraints imposed by the physical apparatus, so changing mass, stiffness, damping, or allowable motion often requires hardware reconfiguration. Here we present a reconfigurable cyber-physical framework in which these properties are instead assigned through software-defined dynamics. The system provides three translational and one rotational degree of freedom, each independently configurable as prescribed, load-responsive, or locked, with operating roles that can also be reassigned during a running experiment. Measured forces and torques are incorporated into real-time virtual dynamic models, while a common supervisory architecture coordinates multi-axis motion, mode switching, synchronized data acquisition, and diagnostic positioning. The prescribed-motion pathway is validated using a pitching hydrofoil by comparison with published thrust and power scaling trends, while the load-responsive pathway is evaluated using an active-heave/passive-pitch benchmark that reproduces the expected frequency-dependent resonant response over the tested conditions. The same platform is then reconfigured for intra-cycle active--passive pitching, coordinated vertical-axis turbine-surrogate motion, force-driven passive surge, and automated multilayer stereoscopic particle image velocimetry. These results demonstrate that distinct FSI boundary conditions and measurement requirements can be implemented within a common motion, sensing, and control architecture. By treating mechanical roles and constraints as software-defined experimental variables, the framework provides a reusable basis for reconfigurable FSI experiments without redesigning the underlying platform for each application.

physics.flu-dyn↗