Nonlinear development of phase-mixed alfvén waves |
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| Authors: | L Nocera E R Priest J V Hollweg |
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| Institution: | 1. Department of Applied Mathematics , St Andrews University , Scotland;2. Space Science Centre , DeMerritt Hall, Durham, New Hampshire, U.S.A. |
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| Abstract: | Abstract We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983). We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δvy exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber ka are damped over a timescale kuRe 0|δ vy/vA |?2, Re 0 being the Reynolds number corresponding to the Braginskij viscosity coefficient η0 and vA the Alfvén speed. Dissipation is most effective where β = (vs /vA) 2 ≈ 1, vs being the speed of sound. |
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| Keywords: | Coronal heating nonlinear analysis nonlinear MHD waves |
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