pyrfu.pyrf.pid_4sc module#

pyrfu.pyrf.pid_4sc.pid_4sc(r_mms, v_mms, p_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:
Returns:

pid – Time series of the Pi-D.

Return type:

xarray.DataArray

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

pyrfu.pyrf.pid_4sc.pid_4sc_err(r_mms, v_mms, p_mms, errv_mms, errp_mms)[source]#

Compute error propagation for Pi-D term using definition of [1] as :

\[Pi-D = - \Pi_{ij}D_{ij}\]

with \(\Pi_{ij}\) the deviatoric part of the pressure tensor : .. math:

\Pi_{ij} = P_{ij} - p\delta_{ij}

p = \frac{1}{3}P_{ii}

and \(D_{ij}\) the deviatoric part of the strain tensor : .. math:

D_{ij} = \frac{1}{2}\left ( \partial_i u_j + \partial_j u_i \right )
- \frac{1}{3}\theta\delta_{ij}

\theta = \nabla . u
Parameters:
Returns:

sigma_pid – Time series of the error on Pi-D.

Return type:

xarray.DataArray

References

[1]

Roberts, O. W., Vörös, Z., Torkar, K., Stawarz, J., Bandyopadhyay, R., Gershman, D. J., et al. (2023). Estimation of the error in the calculation of the pressure-strain term: Application in the terrestrial magnetosphere. Journal of Geophysical Research: Space Physics, 128, e2023JA031565. https://doi.org/10.1029/2023JA031565