# Identification of standing fronts in steady state fluid flows: exact and approximate solutions for propagating MHD modes

## Abstract

The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960’s) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.

## Keywords

Magnetohydrodynamics (MHD) Waves Planets and satellites: magnetic fields Methods: analytical## Notes

### Acknowledgements

The work of Léa Griton was supported by the Centre National d’Études Spatiales (CNES) and the Observatoire de Paris (contract ref. 5100016058). Part of the presented work has been completed by Laura Munteanu during a one month internship at LESIA in June 2015.

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