Time-dependent oscillating viscoelastic Rayleigh-Bénard convection: Viscoelastic kinetic energy budget analysis

Numerical simulations of viscoelastic Rayleigh-B\'enard convection (VRBC) are conducted to investigate time-dependent oscillating convection leading to the formation of reverse flowing cells. A viscoelastic kinetic-energy budget method is used to analyze the energy transport and a parametric analysis for the reversal flow dynamics. The emergence of the reversal convection can be explained by potential energy transfer between flow and fluid elasticity. The image shows periodic total kinetic energy (${E}_{t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l}$), energy exchange rate (${\mathrm{\ensuremath{\Phi}}}_{G}$), and buoyancy flux (${\mathrm{\ensuremath{\Phi}}}_{F}$) time evolution in VRBC from the local view, during a half-period of a reverse process for Phan-Thien-Tanner (PTT) fluid.