Nonlinear evolution of a large‐amplitude circularly polarized Alfvén wave: Low beta

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Abstract
The nature of turbulent cascades arising from the parametric instabilities of a monochromatic field‐aligned large‐amplitude circularly polarized Alfvén wave is investigated via direct numerical simulation for the case of low plasma β and no wave dispersion. The magnetohydrodynamic code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Anisotropic turbulent cascades, similar to those found in early incompressible two‐dimensional simulations, occur after nonlinear saturation of the parallel propagating decay instability. The turbulent spectrum can be divided into three regimes: the lowest wave numbers are dominated by lower sideband remnants of the parametric process, intermediate wave numbers display nearly incompressible dynamics, and the highest wave numbers are dominated by acoustic turbulence.