Shell models of magnetohydrodynamic turbulence

Plunian F., Stepanov R., Frick P. Shell Models of Magnetohydrodynamic Turbulence // Physics Reports, 2013. V.523.N.1. P.1-60. DOI
Abstract:
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a generalmathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decayingMHD turbulence, dynamo action, Alfvén waves and the Hall effect.

Download (PDF, Неизвестный)

Written by

Suspendisse sodales elit quis diam varius sit amet condimentum odio fringilla. Nunc pellentesque est velit. Suspendisse ut dapibus erat. Vivamus pharetra arcu vitae libero luctus commodo. Vestibulum sapien magna, blandit sed elementum eget, faucibus sit amet risus. Proin dapibus velit posuere ligula accumsan in sollicitudin tellus euismod. Nam quis turpis augue, at scelerisque magna. Integer eu enim arcu. Aenean pretium pretium nibh id porttitor.

Комментариев нет.

Оставить комментарий

Сообщение