Energy analysis of 2D electro-thermo-hydrodynamic turbulent convection

Turbulent convection is ubiquitous in fluid systems. In particular, multi-physical convection problems involve mass, heat, and particle transfer. When the particles are charged and driven by a high-voltage electric field, both buoyancy and electric forces contribute to driving and maintaining the convection. In this work, we perform numerical analysis using a high-fidelity Fourier-Chebyshev spectral solver. We further derive the dynamical systems governing the kinetic energy, the enstrophy, the potential energy, and the electric energy analytically. Using the simulated data, we apply a long short-term memory recurrent neural network to predict the chaotic time series of domain-average energy terms. Finally, we perform a data-driven modal decomposition to show the coherent structures that contain energy and enstrophy in 2D turbulent convection.