  The Kepler mission is dramatically increasing the number of planets known in
multi-planetary systems. Many adjacent planets have orbital period ratios near
resonant values, with a tendency to be larger than required for exact
first-order mean-motion resonances. This intriguing feature has been shown to
be a natural outcome of orbital circularization of resonant planetary pairs due
to star-planet tidal interactions. However, this feature holds in
multi-planetary systems with periods longer than ten days, for which tidal
circularization is unlikely to provide efficient divergent evolution of the
planets orbits. Gravitational interactions between planets and their parent
protoplanetary disk may instead provide efficient divergent evolution. For a
planet pair embedded in a disk, we show that interactions between a planet and
the wake of its companion can reverse convergent migration, and significantly
increase the period ratio from a near-resonant value. Divergent evolution due
to wake-planet interactions is particularly efficient when at least one of the
planets opens a partial gap around its orbit. This mechanism could help account
for the diversity of period ratios in Kepler's multiple systems comprising
super-Earth to sub-jovian planets with periods greater than about ten days.
Diversity is also expected for planet pairs massive enough to merge their gap.
The efficiency of wake-planet interactions is then much reduced, but convergent
migration may stall with a variety of period ratios depending on the density
structure in the common gap. This is illustrated for the Kepler-46 system, for
which we reproduce the period ratio of Kepler-46b and c.
