Effective transport barriers in nontwist systems

TL;DR

This paper investigates transport barriers in nontwist systems, specifically in fluids and plasmas with zonal flows, using symplectic nontwist maps to analyze how these barriers form and break down.

Contribution

It introduces a detailed analysis of transport barriers in nontwist maps, highlighting the role of high stickiness structures and their dependence on control parameters.

Findings

Identification of high stickiness structures near broken shearless curves

Use of escape time and transmissivity to measure stickiness

Application of finite-time rotation number and Lyapunov exponent as phase space indicators

Abstract

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. Using a symplectic nontwist maps, which model such zonal flows, we investigate these barriers. In particular, the standard nontwist map, a paradigm of nontwist systems, is used to analyze the parameter dependence of the transport through a broken shearless barrier. Varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Several diagnostics are used: stickiness is measured by escape time and transmissivity plots, while barriers that separate different regions of stickiness are identified by employing two indicators in the phase space, the finite-time rotation number and the finite-time Lyapunov exponent.