Spectral Anisotropy of Elsässer Variables in Two Dimensional Wave-vector Space as Observed in the Fast Solar Wind Turbulence

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Intensive studies have been conducted to understand the anisotropy of solar wind turbulence. However, the anisotropy of Elsässer variables (Z±) in 2D wave-vector space has yet to be investigated. Here we first verify the transformation based on the projection-slice theorem between the power spectral density PSD₂D(k∥,k⊥) and the spatial correlation function CF₂D (r∥,r⊥). Based on the application of the transformation to the magnetic field and the particle measurements from the WIND spacecraft, we investigate the spectral anisotropy of Elsässer variables (Z±), and the distribution of residual energy Eᵣ, Alfvén ratio Rₐ and Elsässer ratio Rₑ in the (k∥,k⊥) space. The spectra PSD₂D(k∥,k⊥) of B, V, and Zmajor (the larger of Z±) show a similar pattern that PSD₂D(k∥,k⊥) is mainly distributed along a ridge inclined toward the k⊥ axis. This is probably the signature of the oblique Alfvénic fluctuations propagating outwardly. Unlike those of B, V, and Zmajor, the spectrum PSD₂D(k∥,k⊥) of Zminor is distributed mainly along the k⊥ axis. Close to the k⊥ axis, | Eᵣ| becomes larger while Rₐ becomes smaller, suggesting that the dominance of magnetic energy over kinetic energy becomes more significant at small k∥. Rₑ is larger at small k∥, implying that PSD₂D(k∥,k⊥) of Zminor is more concentrated along the k⊥ direction as compared to that of Zmajor. The residual energy condensate at small k∥ is consistent with simulation results in which Eᵣ is spontaneously generated by Alfvén wave interaction.