Reconstructing Rayleigh–Bénard flows out of temperature-only measurements using nudging

Abstract

Nudging is a data assimilation technique that has proved to be capable of reconstructing several highly turbulent flows from a set of partial spatiotemporal measurements. In this study, we apply the nudging protocol on the temperature field in a Rayleigh–Bénard convection system at varying levels of turbulence. We assess the global, as well as scale by scale, success in reconstructing the flow and the transition to full synchronization while varying both the quantity and quality of the information provided by sparse measurements either on the Eulerian or Lagrangian domain. We assess the statistical reproduction of the dynamic behavior of the system by studying the spectra of the nudged fields as well as the correct prediction of heat transfer properties as measured by the Nusselt number. Furthermore, we analyze the results in terms of the complexity of solutions at various Rayleigh numbers and discuss the more general problem of predicting all state variables of a system given partial or full measurements of only one subset of the fields, in particular, temperature. This study sheds new light on the correlation between the velocity and temperature in thermally driven flows and on the possibility to control them by acting on the temperature only.

CDAnet: A Physics‐Informed Deep Neural Network for Downscaling Fluid Flows

“…In the literature, researchers have tried to examine the use of temperature information only to recover the full system state (Agasthya et al., 2022; Charney et al., 1969). This approach, however, is not supported by theory (Farhat, Jolly, & Titi, 2015), and computational evidence (Altaf et al., 2017) provides a concrete example showing divergence of the downscaled fields from the true system state.…”

“…The low-resolution pressure and velocity fields are input to the network that predicts the temperature, pressure and velocities at a higher spatial and temporal resolutions. The results shown correspond to Ra = 10 5 and (S, T ) = (16,8).…”

“…In the literature, researchers have tried to examine the use of temperature information only to recover the full system state (Charney et al, 1969;Agasthya et al, 2022).…”

“…the case of (S, T ) = (16, 8). The snapshots indicate that the predicted solutions are qualitatively similar to the true solutions for all time steps.…”