A two-dimensional model describing the nonlinear evolution of pressure driven flute modes in an inhomogeneous magnetic field is derived. The model couples fluctuations in ion and electron temperatures and densities with the fluctuations in the electrostatic potential. The well known Rayleigh - Taylor instability is recovered by linear stability analysis based on a local approach in the long-wave limit. This mode is unstable when the pressure profile is more peaked than the profile of the square of the magnetic field. Using a quasi-linear approach it is revealed that the turbulent fluctuations driven by this instability may give rise to up-gradient transport, a `pinch flux', of either heat or particles.
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