On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis.

Turbulent Rayleigh-Bénard convection in a 2D square cell is characterized by the existence of a large-scale circulation which varies intermittently. We focus on a range of Rayleigh numbers where the large-scale circulation experiences rapid non-trivial reversals from one quasi-steady (or meta-stable) state to another. In previous work [B. Podvin and A. Sergent, J. Fluid Mech. 766, 172201 (2015); B. Podvin and A. Sergent, Phys. Rev. E 95, 013112 (2017)], we applied proper orthogonal decomposition (POD) to the joint temperature and velocity fields at a given Rayleigh number, and the dynamics of the flow were characterized in a multi-dimensional POD space. Here, we show that several of those findings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of the embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specifically, the embedding theory confirms that the switches among meta-stable states are uncorrelated. It also shows that, despite the large number of degrees of freedom of the turbulent Rayleigh Bénard flow, a low dimensional description of its physics can be derived with low computational efforts, providing that a single global observable reflecting the symmetry of the system is identified. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established.

Determining the spectral signature of spatial coherent structures in an open cavity flow.

We applied to an open flow a proper orthogonal decomposition (POD) technique, on two-dimensional (2D) snapshots of the instantaneous velocity field, to reveal the spatial coherent structures responsible for the self-sustained oscillations observed in the spectral distribution of time series. We applied the technique to 2D planes out of three-dimensional (3D) direct numerical simulations on an open cavity flow. The process can easily be implemented on usual personal computers, and might bring deep insights regarding the relation between spatial events and temporal signature in (both numerical or experimental) open flows.