The stability of monochromatic large‐amplitude Alfvén waves is investigated via MHD numerical simulations. In a compressible medium, such as the heliospheric environment, these waves are subject to the parametric decay instability. The mother wave decays in a compressive mode, that soon steepens and dissipates thermal energy, and in a backscattered Alfvénic mode with lower amplitude and frequency, thus starting an inverse cascade. This well known process is shown here to be very robust, since it occurs basically unchanged regardless of the dimensionality of the spatial domain and, above all, even linear or arc‐polarized waves in oblique propagation, most often found in solar wind data, appear to behave in the same way. This physical process could help to explain the observed radial decrease of cross helicity in the fast polar wind, as measured by Ulysses.

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