  We investigate the evolution of a system of two super-Earths with masses < 4
Earth masses embedded in a turbulent protoplanetary disk. The aim is to examine
whether or not resonant trapping can occur and be maintained in presence of
turbulence and how this depends on the amplitude of the stochastic density
fluctuations in the disk. We have performed 2D numerical simulations using a
grid-based hydrodynamical code in which turbulence is modelled as stochastic
forcing. We assume that the outermost planet is initially located just outside
the position of the 3:2 mean motion resonance (MMR) with the inner one and we
study the dependance of the resonance stability with the amplitude of the
stochastic forcing. For systems of two equal-mass planets we find that in disk
models with an effective viscous stress parameter {\alpha} 10^{-3}, damping
effects due to type I migration can counteract the effects of diffusion of the
resonant angles, in such a way that the 3:2 MMR can possibly remain stable over
the disk lifetime. For systems of super-Earths with mass ratio q=m_i/m_o < 1/2,
where m_i (m_o) is the mass of the innermost (outermost) planet, the 3:2 MMR is
broken in turbulent disks with effective viscous stresses 2x10^{-4}< {\alpha}<
10^{-3} but the planets become locked in stronger p+1:p resonances, with p
increasing as the value for {\alpha} increases. For {\alpha}> 2x10^{-3}, the
evolution can eventually involve temporary capture in a 8:7 commensurability
but no stable MMR is formed. Our results suggest that for values of the viscous
stress parameter typical to those generated by MHD turbulence, MMRs between two
super-Earths are likely to be disrupted by stochastic density fluctuations. For
lower levels of turbulence however, as is the case in presence of a dead-zone,
resonant trapping can be maintained in systems with moderate values of the
planet mass ratio.
