  The internal structure of gas giant planets may be more complex than the
commonly assumed core-envelope structure with an adiabatic temperature profile.
Different primordial internal structures as well as various physical processes
can lead to non-homogenous compositional distributions. A non-homogenous
internal structure has a significant impact on the thermal evolution and final
structure of the planets. In this paper, we present alternative structure and
evolution models for Jupiter and Saturn allowing for non-adiabatic primordial
structures and the mixing of heavy elements by convection as these planets
evolve. We present the evolution of the planets accounting for various initial
composition gradients, and in the case of Saturn, include the formation of a
helium-rich region as a result of helium rain. We investigate the stability of
regions with composition gradients against convection, and find that the helium
shell in Saturn remains stable and does not mix with the rest of the envelope.
In other cases, convection mixes the planetary interior despite the existence
of compositional gradients, leading to the enrichment of the envelope with
heavy elements. We show that non-adiabatic structures (and cooling histories)
for both Jupiter and Saturn are feasible. The interior temperatures in that
case are much higher that for standard adiabatic models. We conclude that the
internal structure is directly linked to the formation and evolution history of
the planet. These alternative internal structures of Jupiter and Saturn should
be considered when interpreting the upcoming Juno and Cassini data.
