Numerical investigation of two-dimensional electro-thermo-hydrodynamic turbulence: Energy budget and scaling law analysis

Abstract

In fluid systems involving heat and mass transfers, convection is a fundamental phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient and/or an electric field. When the driving forces are large, the fluid system exhibits a chaotic behavior and even develops into turbulence. Modeling convection has given rise to the development of turbulence theory and energetic analysis for multi-physics systems. However, most of previous works have been limited to relatively simple thermal convection phenomena driven by solely buoyancy force. In this work, we formulate the energetic relation of the turbulent electro-thermo-hydrodynamic (ETHD) convection and develop a two-dimensional (2D) spectral solver for numerical analysis of ETHD turbulence for a variety of driving parameters (forces). From the numerical analysis, we find a modified scaling behavior of heat transfer by the electric force, and discover a new scaling behavior of the portion of kinetic energy contributed by buoyancy force as a function of a dimensionless forcing ratio. Finally, we show that the energy budget in the boundary layer of the 2D ETHD turbulence follows the scaling law previously found for the traditional 2D Rayleigh–Bénard Convection. This work marks the first step into energy budget and scaling law analysis of ETHD systems and significantly improve our understanding turbulent convection driven by both thermal and electric forces.