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Abstract
Rational large Reynolds number matched asymptotic expansions of threedimensional nonlinear magnetohydrodynamic (MHD) states are the concern of this contribution. The nonlinear MHD states, assumed to be predominantly driven by a unidirectional shear, can be sustained without any linear instability of the base flow and hence are responsible for subcritical transition to turbulence. Two classes of nonlinear MHD states are found. The first class of nonlinear states emerged out of a nice combination of the purely hydrodynamic vortex/wave interaction theory by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641666) and the resonant absorption theories on Alfvén waves, developed in the solar physics community (e.g. Sakurai et al. Solar Phys., vol. 133, 1991, pp. 227245; Goossens et al. Solar Phys., vol. 157, 1995, pp. 75102). Similar to the hydrodynamic theory, the mechanism of the MHD states can be explained by the successive interaction of the roll, streak and wave fields, which are now defined both for the hydrodynamic and magnetic fields. The derivation of this 'vortex/Alfvén wave interaction' state is rather straightforward as the scalings for both of the hydrodynamic and magnetic fields are identical. It turns out that the leadingorder magnetic field of the asymptotic states appears only when a small external magnetic field is present. However, it does not mean that purely sheardriven dynamos are not possible. In fact, the second class of 'selfsustained sheardriven dynamo theory' shows a magnetic generation that is slightly smaller in size in the absence of any external field. Despite its small size, the magnetic field causes the novel feedback mechanism in the velocity field through resonant absorption, wherein the magnetic wave becomes more strongly amplified than the hydrodynamic counterpart.
Original language  English 

Pages (fromto)  176211 
Number of pages  36 
Journal  Journal of Fluid Mechanics 
Volume  868 
DOIs  
Publication status  Published  10 Jun 2019 
Keywords
 Dynamo theory
 Highspeed flow
 Nonlinear instability
Projects
 1 Finished

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