부산대학교 도서관

Summary: ``We consider the Nambu and Hamiltonian representations ofRayleigh-Bénard convection with a nonlinear thermal heating effectproportional to the Eckert number $(Ec)$. The model that we use is anextension of the classical Lorenz-63 model with four kinematic and sixthermal degrees of freedom. The conservative parts of the dynamicalequations which include all nonlinearities satisfy Liouville's theoremand permit a conserved Hamiltonian $H$ for arbitrary $Ec$. For $Ec=0$two independent conserved functions exist; one of these is associatedwith unavailable potential energy and is also present in the Lorenz-63truncation. This function $C$ which is a Casimir of the noncanonicalHamiltonian system is used to construct a Nambu representation of theconserved part of the dynamics. The thermal heating effect can berepresented either by a second canonical Hamiltonian or as a gradient(metric) system using the time derivative $\dot C$ of the Casimir. Theresults demonstrate the impact of viscous heating in the total energybudget and in the Lorenz energy cycle for kinetic and availablepotential energy.''