Articles | Volume 13, issue 2
Nonlin. Processes Geophys., 13, 125–133, 2006
https://doi.org/10.5194/npg-13-125-2006
Nonlin. Processes Geophys., 13, 125–133, 2006
https://doi.org/10.5194/npg-13-125-2006

  04 May 2006

04 May 2006

Energy-conserving and Hamiltonian low-order models in geophysical fluid dynamics

A. Gluhovsky A. Gluhovsky
  • Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana, USA

Abstract. Arbitrary truncations in the Galerkin method commonly used to derive low-order models (LOMs) may violate fundamental conservation properties of the original equations, causing unphysical behaviors in LOMs such as unbounded solutions. To avoid these, energy-conserving LOMs are developed in the form of coupled Volterra gyrostats, based on analogies between fluid dynamics and rigid body mechanics. Coupled gyrostats prove helpful in retaining in LOMs the Hamiltonian structure of the original equations. Examples of Hamiltonian LOMs describing 2-D and 3-D Rayleigh-Bénard convection are presented, including the celebrated Lorenz model and its 3-D analog.