Nambu representation of an extended Lorenz model with viscous heating

Blender, R. and Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 (2013) Nambu representation of an extended Lorenz model with viscous heating. Physica D: Nonlinear Phenomena, 243 (1). 86 - 91. ISSN 0167-2789

Abstract/Summary

We consider the Nambu and Hamiltonian representations of Rayleigh-B\'{e}nard convection with a nonlinear thermal heating effect proportional to the Eckert number (Ec). The model we use is an extension of the classical Lorenz-63 model with 4 kinematic and 6 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 Casimir functions exist, one of these is associated with unavailable potential energy and is also present in the Lorenz-63 truncation. This Casimir $C$ is used to construct a Nambu representation of the conserved part of the dynamical system. 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71521
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Viscous heating
Publisher	Elsevier
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