Projects per year
Abstract
Subcritical instabilities (i.e. finiteamplitude instabilities that occur without any linear instability) in magnetohydrodynamic (MHD) flows are studied by computing finiteamplitude equilibrium solutions of viscous–resistive MHD equations. The plane Couette flow magnetised by a uniform spanwise current is used as a model flow. Solutions are found for broad sub and superAlfvénic flow regimes by controlling the magnetic Mach number, but their existence is greatly influenced by the magnetic Prandtl number. When that number is unity, and the walls are perfectly insulating, the solution branch found in the superAlfvénic regime cannot be continued towards the subAlfvénic regime; the boundary between those regimes is called the Chandrasekhar state, where Chandrasekhar (Proc. Natl Acad. Sci. USA, vol. 42, 1956, pp. 273–276) proved the nonexistence of a linear ideal instability. Thus, the result may seem to suggest that the Chandrasekhar theorem holds even when diffusivity and nonlinearity are present. This is certainly true, but only when the perturbation magnetic field on the boundary is small. The boundary effects add more complexity to the nonlinear analysis of the Chandrasekhar state. The Chandrasekhar theorem is known to work for flows bounded by perfectly conducting walls. However, somewhat paradoxically, when the walls are perfectly conducting, our largeReynoldsnumber computational results show that the nonlinear solutions do exist in the Chandrasekhar state. We give a theoretical reasoning for this curious phenomenon, using a largeReynoldsnumber asymptotic analysis. For small magnetic Prandtl numbers, we also show that the solution can be continued for infinitesimally small magnetic Mach number, where the flow is significantly subAlfvénic.
Original language  English 

Article number  A20 
Number of pages  23 
Journal  Journal of Fluid Mechanics 
DOIs  
Publication status  Published  10 Jan 2020 
Projects
 1 Finished

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