Spectral anisotropy of Elsässer variables in two-dimensional wave-vector space as observed in the fast solar wind turbulence

Intensive studies have been conducted to understand the anisotropy of solar wind turbulence. However, the anisotropy of Elsässer variables ($Z^{\pm }$) 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 ${PSD}_{2D}(k_{\parallel },k_{\perp })$ and the spatial correlation function ${CF}_{2D}(r_{\parallel },r_{\perp }).$ 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 ($Z^{\pm }$), and the distribution of residual energy $E_R,$ Alfvén ratio $R_A$, and Elsässer ratio $R_E$ in the $(k_{\parallel },k_{\perp })$ space. The spectra ${PSD}_{2D}(k_{\parallel },k_{\perp })$ of $B$, $V$, and $Z_{major}$ (the larger of $Z^{\pm }$) show a similar pattern that ${PSD}_{2D}(k_{\parallel },k_{\perp })$ 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 $Z_{major},$ the spectrum ${PSD}_{2D}(k_{\parallel },k_{\perp })$ of $Z_{minor}$ is distributed mainly along the k_⊥ axis. Close to the k_⊥ axis, $|E_R|$ becomes larger while $R_A$ becomes smaller, suggesting that the dominance of magnetic energy over kinetic energy becomes more significant at small k_∥. $R_E$ is larger at small k_∥, implying that ${PSD}_{2D}(k_{\parallel },k_{\perp })$ of $Z_{minor}$ is more concentrated along the k_⊥ direction as compared to that of $Z_{major}.$ The residual energy condensate at small k_∥ is consistent with simulation results in which $E_R$ is spontaneously generated by Alfvén wave interaction.