# Lorenz's Model of Global Atmospheric Circulation

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This attractor arises from Lorenz's model of global atmospheric circulation (known as Lorenz–84). It models the behavior of the Earth's atmosphere on each hemisphere by averaging conditions at different latitudes, enabling a reduction to just three variables, as opposed to the alternative of solving a large number of simultaneous hydrodynamic equations. The model implies an equilibrium between the energy of westerly wind currents and the energy transported toward the poles. As a consequence, heat transfer in each hemisphere generates a global decrease in temperature in the direction of the North and South Poles and also predicts that westerly winds will be weaker.

Contributed by: Enrique Zeleny (September 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The variables are dimensionless; is the velocity of the mean of west wind in mid-latitudes, while and are amplitudes of poleward heat transport, with energies and , and decreasing energy . Linear terms represent atmospheric dissipation. The system is determined by the differential equations

where allows damping for the west wind and for energy exchange. The rest of the parameters are positive: is the mean value of the west wind's velocity or temperature difference equator-to-pole, and and are thermal driving forces. Finally, the time unit is equivalent to five days.

Reference

[1] T. Tél and M. Gruiz, *Chaotic Dynamics: An Introduction Based on Classical Mechanics*, Cambridge, UK: Cambridge University Press, 2006.

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