Mechanics and thermodynamics of a new minimal model of the atmosphere
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Mechanics and thermodynamics of a new minimal model of the atmosphere Gabriele Vissio1,2 , Valerio Lucarini3,4,a 1 2 3 4
CEN, Meteorological Institute, University of Hamburg, Hamburg, Germany Institute of Geosciences and Earth Resources (IGG) - National Research Council (CNR), Turin, Italy Department of Mathematics and Statistics, University of Reading, Reading, UK Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
Received: 20 August 2020 / Accepted: 26 September 2020 © The Author(s) 2020
Abstract The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere.
1 Introduction The climate is a nonequilibrium system whose dynamics is primarily driven by the uneven absorption of solar radiation, which is mainly absorbed near the surface and in the tropical latitudes, rather than aloft and in the mid-high latitudes, respectively. The system reacts to such an inhomogeneity in the local energy input through a complex set of instabilities and feedbacks affecting its dynamical processes and thermodynamic and radiative fluxes. Such processes lead to an overall reduction in the temperature gradients inside the system and allow for the establishment of approximate steady-state conditions [1,2]. An example of the re-equilibration mechanism can be described as follows. The large scale energy transport, which tends to reduce the temperature difference between low and high latitudes, is mainly performed by atmospheric disturbances in the form of synoptic and
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:807
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