Phase dependent advection-diffusion in drift wave - zonal flow turbulence

Paper in proceeding, 2016

In magnetically confined plasmas, drift wave turbulence is believed to be responsible for the anomalous transport and the generation of inherent sheared zonal flows providing a self-regulating mechanism that may control the turbulence itself. The coupled system of drift wave-zonal flow (DW-ZF) is one of the key points in the evasive explanation of the low to high confinement (L-H) transition in fusion plasmas. In plasma turbulence a large number of non-linearly interacting modes are present which yield an enormous complexity and dynamic richness. However, the nonlinear mode coupling processes allows for coherent structures (sheared flow, acoustic modes, etc.) to be formed which can even grow in the presence of random fields or cascade to smaller scales, this is a manifestation of the self-organization process with predator-prey dynamics. A powerful and yet simple mathematical framework for describing the self-organisation phenomena was developed by Kuramoto [1]. The Kuramoto model describes the phase dynamics of a system of stochastic limit-cycle oscillators revolving at arbitrary intrinsic frequencies and coupled through the sine of their phase differences. Furthermore, under certain conditions they spontaneously lock into a common frequency. Most often in modelling, the dynamics of the phases is neglected and the so-called random-phase approximation (RPA) is used. However, one could expect that the phase dynamics can play a role in the self-organisation and the formation of coherent structures. In this work we present a study on the importance of a collective phase dynamic on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. The model is built on the stochastic passive advection-diffusion of a scalar [2] while using the predator-prey model with stochastic oscillators representing the DW-ZF interaction [3]. Our findings show the occurrence of modulational behaviour prior to the synchronisation state, and that the synchronization of the phases can result in a significant change in the dynamics of the fluctuation energy and the saturation state.