# TURBO

**TURBO = Solver for TURbulent flows with periodic BOundary conditions.**

The TURBO code is designed to solve numerically the equations for an incompressible fluid in a three dimensional geometry with periodic boundary conditions in the three directions. The fluid can also be electrically conductive, in which case the magnetohydrodynamic equations are being solved. The trajectories of test particles or field lines can also be tracked in time.

TURBO was developed at Universite Libre de Bruxelles and can be downloaded and freely used from **here**.

The only restriction is that if you use it for any kind of publications, the following reference, where TURBO is described, should be quoted:

* • B. Teaca, M.K. Verma, B. Knaepen, and D. Carati, Energy transfer in anisotropic magnetohydrodynamic turbulence, Phys. Rev. E 79, 46312, 2009. *

If you are a researcher in the field of fluid or plasma turbulence and are interested in newer versions of the code that are not released to the public, please contact Dr. Teaca directly.

# ALLIANCE^{4D}

**ALLIANCE = spectrAL soLver for kInetic plAsma turbuleNCE.**

The ALLIANCE code is a spectral solver for turbulence in four-dimensional phase space (three spatial directions and one velocity) that evolves in time a set of equations appropriate for magnetized plasma in the drift kinetic approximation. The code makes use of a Fourier Hermite representation and is designed to study fundamental aspects of kinetic turbulence.

See relevant publications:

* • E.A. Gorbunov and B. Teaca, Four-dimensional equations for the study of electromagnetic plasma turbulence in a drift kinetic limit Journal of Plasma Physics 88, 905880117, 2022. *

* • E.A. Gorbunov and B. Teaca, ALLIANCE: Spectral solver for kinetic plasma turbulence, Journal of Computational Physics 495, 112550, 2023. *

The code is not available currently to the public. Contact Evgeny Gorbunov or Bogdan Teaca directly to express interest in using the code.