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 densi
ties with the fluctuations in the electrostatic potential. The well kn
own Rayleigh-Taylor instability is recovered by linear stability analy
sis based on a local approach in the long-wave limit. This mode is uns
table when the pressure profile is more peaked than the profile of the
square of the magnetic field. Using a quasi-linear approach it is rev
ealed that the turbulent fluctuations driven by this instability may g
ive rise to up-gradient transport, a 'pinch flux', of either heat or p
articles.