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

Abstract

Intensive studies have been conducted to understand the anisotropy of solar wind turbulence. However, the anisotropy of Elsässer variables (${\text{Z}}^{\pm }$) 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 (${\text{Z}}^{\pm }$), 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 $\text{B}$, $\text{V}$, and ${\text{Z}}_{major}$ (the larger of ${\text{Z}}^{\pm }$) show a similar pattern that PSD${}_{2D}(k_{\parallel },k_{\perp })$ is mainly distributed along a ridge inclined toward the $k_{\perp }$ axis. This is probably the signature of the oblique Alfvénic fluctuations propagating outwardly. Unlike those of $\text{B}$, $\text{V}$, and ${\text{Z}}_{major}$, the spectrum PSD${}_{2D}(k_{\parallel },k_{\perp })$ of ${\text{Z}}_{minor}$ is distributed mainly along the $k_{\perp }$ axis. Close to the $k_{\perp }$ axis, $\left|E_R\right|$ becomes larger while R${}_A$ becomes smaller, suggesting that the dominance of magnetic energy over kinetic energy becomes more significant at small $k_{\parallel }$. R${}_E$ is larger at small $k_{\parallel }$, implying that PSD${}_{2D}(k_{\parallel },k_{\perp })$ of ${\text{Z}}_{minor}$ is more concentrated along the $k_{\perp }$ direction as compared to that of ${\text{Z}}_{major}$. The residual energy condensate at small $k_{\parallel }$ is consistent with simulation results in which E${}_R$ is spontaneously generated by Alfvén wave interaction.