부산대학교 도서관

Summary: ``We consider the Nambu and Hamiltonian representations of Rayleigh-Bénard convection with a nonlinear thermal heating effect proportional to the Eckert number $(Ec)$. The model that we use is an extension of the classical Lorenz-63 model with four kinematic and six thermal degrees of freedom. The conservative parts of the dynamical equations which include all nonlinearities satisfy Liouville's theorem and permit a conserved Hamiltonian $H$ for arbitrary $Ec$. For $Ec=0$ two independent conserved functions exist; one of these is associated with unavailable potential energy and is also present in the Lorenz-63 truncation. This function $C$ which is a Casimir of the noncanonical Hamiltonian system is used to construct a Nambu representation of the conserved part of the dynamics. The thermal heating effect can be represented either by a second canonical Hamiltonian or as a gradient (metric) system using the time derivative $\dot C$ of the Casimir. The results demonstrate the impact of viscous heating in the total energy budget and in the Lorenz energy cycle for kinetic and available potential energy.''