# 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. More precisely, the balance equations that can be solved are the following:

$\partial_t u_i = -\partial_j (u_i u_j)-\partial_i p+\nu \nabla^2u_i+f_i+f^{Lorentz}_i$

$\partial_t b_i = -\partial_j (b_i u_j-u_i b_j)+\eta \nabla^2 b_i$

$\partial_t c_\alpha = -\partial_j (c_\alpha u_j)+\kappa_\alpha \nabla^2 c_\alpha +\sigma_\alpha(\{c_\beta\})$

where $u$ is the velocity field, $b$ is the magnetic field, $c$ are passive scalar(s), each of which is characterized by a diffusion coefficient κ. Summation is assumed over repeated Latin style indices, but not over Greek style indices which correspond to passive scalar species. The kinematic viscosity is $\nu$ and the magnetic diffusivity is $\eta$. There is the possibility to include source or sink terms or even chemistry terms in the scalar equations through the function $\sigma(c)$.

TURBO can be downloaded and freely used. 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.

The source code of TURBO 2.05, including documentation, can be downloaded here.

Some help for Mac OS X (Lion) users willing to use TURBO on their machines. Download here.