  While conventional interior models for Jupiter and Saturn are based on the
simplistic assumption of a solid core surrounded by a homogeneous gaseous
envelope, we derive new models with an inhomogeneous distribution of heavy
elements, i.e. a gradient of composition, within these planets. Such a
compositional stratification hampers large scale convection which turns into
double-diffusive convection, yielding an inner thermal profile which departs
from the traditionally assumed adiabatic interior, affecting these planet heat
content and cooling history.
  To address this problem, we develop an analytical approach of layered
double-diffusive convection and apply this formalism to Solar System gaseous
giant planet interiors. These models satisfy all observational constraints and
yield a metal enrichment for our gaseous giants up to 30 to 60% larger than
previously thought. The models also constrain the size of the convective layers
within the planets. As the heavy elements tend to be redistributed within the
gaseous envelope, the models predict smaller than usual central cores inside
Saturn and Jupiter, with possibly no core for this latter.
  These models open a new window and raise new challenges on our understanding
of the internal structure of giant (solar and extrasolar) planets, in
particular on the determination of their heavy material content, a key
diagnostic for planet formation theories.
