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 (${{\boldsymbol{Z}}}^{\pm }$) 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 ${\mathrm{PSD}}_{2{\rm{D}}}({k}_{\parallel },{k}_{\perp })$ and the spatial correlation function ${\mathrm{CF}}_{2{\rm{D}}}({r}_{\parallel },{r}_{\perp }).$ 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 (${{\boldsymbol{Z}}}^{\pm }$), and the distribution of residual energy ${E}_{{\rm{R}}},$ Alfvén ratio ${R}_{{\rm{A}}}$, and Elsässer ratio ${R}_{{\rm{E}}}$ in the $({k}_{\parallel },{k}_{\perp })$ space. The spectra ${\mathrm{PSD}}_{2{\rm{D}}}({k}_{\parallel },{k}_{\perp })$ of ${\boldsymbol{B}}$, ${\boldsymbol{V}}$, and ${{\boldsymbol{Z}}}_{\mathrm{major}}$ (the larger of ${{\boldsymbol{Z}}}^{\pm }$) show a similar pattern that ${\mathrm{PSD}}_{2{\rm{D}}}({k}_{\parallel },{k}_{\perp })$ 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 ${\boldsymbol{B}}$, ${\boldsymbol{V}}$, and ${{\boldsymbol{Z}}}_{\mathrm{major}},$ the spectrum ${\mathrm{PSD}}_{2{\rm{D}}}({k}_{\parallel },{k}_{\perp })$ of ${{\boldsymbol{Z}}}_{\mathrm{minor}}$ is distributed mainly along the k⊥ axis. Close to the k⊥ axis, $| {E}_{{\rm{R}}}| $ becomes larger while ${R}_{{\rm{A}}}$ becomes smaller, suggesting that the dominance of magnetic energy over kinetic energy becomes more significant at small k∥. ${R}_{{\rm{E}}}$ is larger at small k∥, implying that ${\mathrm{PSD}}_{2{\rm{D}}}({k}_{\parallel },{k}_{\perp })$ of ${{\boldsymbol{Z}}}_{\mathrm{minor}}$ is more concentrated along the k⊥ direction as compared to that of ${{\boldsymbol{Z}}}_{\mathrm{major}}.$ The residual energy condensate at small k∥ is consistent with simulation results in which ${E}_{{\rm{R}}}$ is spontaneously generated by Alfvén wave interaction.