Analyzing the transition-to-turbulence in Rayleigh-Benard flows through latent space representations

In the cusp of turbulence, Rayleigh-Benard flows exhibit both large-scale convective structures, as well as small-scale eddies. As the Rayleigh number is increased more scales become activated, synchronization properties between field components are lost, and, ultimately, the flow is dominated by the small-scale structures. By generating compressed latent representations of the phase space at each Rayleigh number via convolutional autoencoders we can track how the change in the number of degrees of freedom of the system, showing how during transition the rate of change is not linear. We then use these representations to analyze the properties of the flow. In particular, we estimate the entropy of the system and show how it grows as the system transitions to turbulence and the number of possible states increases.