Chaotic transport by Rossby waves in shear flow

Abstract

Transport and mixing properties of Rossby waves in shear flow are studied using tools from Hamiltonian chaos theory. The destruction of barriers to transport is studied analytically, by using the resonance overlap criterion and the concept of separatrix reconnection, and numerically by using Poincaré sections. Attention is restricted to the case of symmetric velocity profiles with a single maximum; the Bickley jet with velocity profile sech2 is considered in detail. Motivated by linear stability analysis and experimental results, a simple Hamiltonian model is proposed to study transport by waves in these shear flows. Chaotic transport, both for the general case and for the sech2 profile, is investigated. The resonance overlap criterion and the concept of separatrix reconnection are used to obtain an estimate for the destruction of barriers to transport and the notion of banded chaos is introduced to characterize the transport that typically occurs in symmetric shear flows. Comparison between the analytical estimates for barrier destruction and the numerical results is given. The role of potential vorticity conservation in chaotic transport is discussed. An area preserving map, termed standard nontwist map, is obtained from the Hamiltonian model. It is shown that the map reproduces the transport properties and the separatrix reconnection observed in the Hamiltonian model. The conclusions reached are used to explain experimental results on transport and mixing by Rossby waves in rotating fluids.