Projects per year
Abstract
This paper aims to numerically verify the large Reynolds number asymptotic theory of magnetohydrodynamic (MHD) flows proposed in the companion paper Deguchi (J. Fluid Mech., vol. 868, 2019, pp. 176–211). To avoid any complexity associated with the chaotic nature of turbulence and flow geometry, nonlinear steady solutions of the viscous resistive MHD equations in plane Couette flow have been utilised. Two classes of nonlinear MHD states, which convert kinematic energy to magnetic energy effectively, have been determined. The first class of nonlinear states can be obtained when a small spanwise uniform magnetic field is applied to the known hydrodynamic solution branch of plane Couette flow. The nonlinear states are characterised by the hydrodynamic/magnetic roll–streak and the resonant layer at which strong vorticity and current sheets are observed. These flow features, and the induced strong streamwise magnetic field, are fully consistent with the vortex/Alfvén wave interaction theory proposed in the companion paper. When the spanwise uniform magnetic field is switched off, the solutions become purely hydrodynamic. However, the second class of ‘selfsustained sheardriven dynamos’ at the zero external magnetic field limit can be found by homotopy via the forced states subject to a spanwise uniform current field. The discovery of the dynamo states has motivated the corresponding large Reynolds number matched asymptotic analysis in the companion paper. Here, the reduced equations derived by the asymptotic theory have been solved numerically. The asymptotic solution provides remarkably good predictions for the finite Reynolds number dynamo solutions.
Original language  English 

Pages (fromto)  830858 
Number of pages  29 
Journal  Journal of Fluid Mechanics 
Volume  876 
DOIs  
Publication status  Published  10 Oct 2019 
Keywords
 highspeed flow
 nonlinear instability
 ynamo theory
Projects
 1 Finished

Towards a mathematical description of magnetohydrodynamic turbulence
Australian Research Council (ARC)
1/04/17 → 31/03/21
Project: Research