Lagrangian and Eulerian chaos in atmospheric models

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.