pyrfu.pyrf.pid_4sc module#
- pyrfu.pyrf.pid_4sc.pid_4sc(r_mms, v_mms, p_mms, b_mms)[source]#
Compute Pi-D term using definition of [1] as :
\[Pi-D = - \Pi_{ij}D_{ij}\]with \(\Pi_{ij}\) the deviatoric part of the pressure tensor :
\[ \begin{align}\begin{aligned}\Pi_{ij} = P_{ij} - p\delta_{ij}\\p = \frac{1}{3}P_{ii}\end{aligned}\end{align} \]and \(D_{ij}\) the deviatoric part of the strain tensor :
\[ \begin{align}\begin{aligned}D_{ij} = \frac{1}{2}\left ( \partial_i u_j + \partial_j u_i \right ) - \frac{1}{3}\theta\delta_{ij}\\\theta = \nabla . u\end{aligned}\end{align} \]- Parameters:
r_mms (list of xarray.DataArray) – Time series of the position of the 4 spacecraft.
v_mms (list of xarray.DataArray) – Time series of the bulk velocities of the 4 spacecraft.
p_mms (list of xarray.DataArray) – Time series of the pressure tensor of the 4 spacecraft.
b_mms (list of xarray.DataArray) – Time series of the background magnetic field of the 4 spacecraft.
- Returns:
pid – Time series of the Pi-D.
- Return type:
References
[1]Yang, Y., Matthaeus, W. H., Parashar, T. N., Wu, P., Wan, M., Shi, Y., et al. (2017). Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence. Physical Review E, 95, 061201. doi : https://doi.org/10.1103/PhysRevE.95.061201