Lagrangian and Eulerian Chaos in Atmospheric Models

V. M. Ipatova and A. N. Filatov

Hydrometeorological Center of Russia, Bol’shoi Predtechenskii per. 9/13, Moscow, 123242 Russia

Received October 17, 1995; in final form, March 25, 1996

Abstract—The Eulerian and Lagrangian representations of motion are widely used in hydrodynamics. One and
the same flow can be described both by studying the fields of velocity, pressure, and so forth (the Eulerian
approach) and by considering the motion of fluid particles in the flow (the Lagrangian approach). Chaos can be
observed in both cases. However, its presence for one representation does not necessarily lead to that for the
other. The corresponding examples are given. The equation of a barotropic vortex is considered in a bounded
region. For the model under consideration, numerical experiments have shown the presence of chaotic motions
in the Lagrangian representation.

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