Cascade, cavitation, and mixed regime dynamics in Alfvén ion–acoustic turbulence: A Zakharov approach with applications to the upper solar atmosphere

Turbulence in the upper solar atmosphere and solar wind remains central to the understanding of coronal heating and energy transport. While Langmuir turbulence has been extensively classified into cascade-dominated, cavity-dominated, and mixed regimes, no comparable systematic framework exists for Alfvén turbulence, despite the ubiquity of Alfvénic fluctuations in the upper solar atmosphere. In this work, we extend the classification of turbulence to nondispersive Alfvén waves coupled with ion–acoustic fluctuations using the Zakharov and modified Zakharov systems in one dimension. Both analytical considerations and direct numerical simulations demonstrate that the turbulence character is strongly regulated at fixed amplitude and geometry primarily by the frequency mismatch ΔΩ=ω0−ωk, where ω0 is the driver frequency and ωk is the natural Alfvén wave frequency. ΔΩ serves as the key control parameter for turbulence character at fixed amplitude. For small ΔΩ, modulational instability is strong and cavitation dominates. For large ΔΩ, modulational growth is suppressed, and turbulence becomes cascade-dominated. Intermediate values of ΔΩ produce a mixed regime where cavitation and cascades coexist. This ΔΩ based framework unifies cavitation and cascade processes in Alfvénic systems and provides a possible reduced-model framework relevant to localized coronal heating processes: cavitation mediates localized energy deposition, while parametric decay processes redistribute energy toward larger spatial scales within the model domain.