On reversals in 2D turbulent Rayleigh-Bénard convection: insights from embedding theory and comparison with Proper Orthogonal Decomposition analysis

International audienceTurbulent 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 (Podvin and Sergent JFM 2015, Podvin and Sergent PRE 2017), we applied Proper Orthogonal Decomposition (POD) to the joint temperature and velocity elds at a given Rayleigh number and the dynamics of the ow were characterized in a multi-dimensional POD space. Here, we show that several of those ndings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specically, embedding theory conrms 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 Benard ow, a low dimensional description of its physics can be derived with low computational eorts, providing that a single global observable reecting the symmetry of the system is identied. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established. 2 We use Rayleigh-Bénard turbulent convection simulations to compare the properties of quasi-stationary states and transitions (reversals) previously identied via Principal Orthogonal Decomposition (POD) to those obtained via embedding the global angular momentum of the system. Our main result is to show that we can map POD properties on the attractor reconstructed via embedding techniques. Specically, the embedding technique conrms that the switches among dierent meta-stable states are uncorrelated. Moreover, a local stability indicator can be used to distinguish and classify the dierent metastable states. The low computational costs of embedding analysis suggests to use this procedure whenever a global observable reecting the symmetry of the system can be identied, while the POD should be preferred when such information is not available