A scale-dependent cascade model for the 1/f spectrum in the pristine solar wind

Context. The solar wind provides a natural laboratory for studying turbulent plasmas over a broad range of temporal and spatial scales. Its low-frequency magnetic spectrum often displays a 1/f range, whose physical origin and connection to nonlinear turbulent transfer remain open questions. Aims. We investigate whether the 1/f range can be interpreted as a turbulent range with scale-dependent energy transfer, and how this behavior differs from the inertial range. A central point of this work is that third-order structure functions can provide a useful estimate of the nonlinear energy transfer even when the inferred transfer rate is not scale independent. Methods. We used in situ Parker Solar Probe measurements to compute the energy transfer rate from the incompressible magnetohy-drodynamics third-order law, including expansion terms, and analyzed magnetic field increment statistics through probability density functions and structure functions. In particular, we used the third-order law as a diagnostic tool to investigate whether nonlinear energy transfers are present and how they scale with ℓ, rather than assuming a priori that the 1/f range behaves as a classical inertial range with constant flux. Results. The energy transfer decreases approximately as 1/τ (where τ is the time lag) within the 1/f range, in contrast with the nearly constant cascade rate expected in the inertial range. A scale-dependent model predicts an energy transfer across scales ɛ_ℓ ~ 1/ℓ, consistent with a k⁻¹ magnetic spectrum. The statistics of magnetic field increments show intermittent signatures, especially in the parallel component, whereas the perpendicular fluctuations are found to be quasi-Gaussian. Conclusions. These results suggest that the 1/f range can be interpreted as a non-conservative scale-dependent turbulent cascade, with implications for the interpretation of large-scale fluctuations in the solar wind and planetary magnetosheaths.