  The Cassini and Juno probes have revealed large coherent cyclonic vortices in
the polar regions of Saturn and Jupiter, a dramatic contrast from the east-west
banded jet structure seen at lower latitudes. Debate has centered on whether
the jets are shallow, or extend to greater depths in the planetary envelope.
Recent experiments and observations have demonstrated the relevance of deep
convection models to a successful explanation of jet structure and cyclonic
coherent vortices away from the polar regions have been simulated recently
including an additional stratified shallow layer. Here we present new
convective models able to produce long-lived polar vortices. Using simulation
parameters relevant for giant planet atmospheres we find flow regimes that are
in agreement with geostrophic turbulence (GT) theory in rotating convection for
the formation of large scale coherent structures via an upscale energy transfer
fully three-dimensional. Our simulations generate polar characteristics
qualitatively similar to those seen by Juno and Cassini: they match the
structure of cyclonic vortices seen on Jupiter; or can account for the
existence of a strong polar vortex extending downwards to lower latitudes with
a marked spiral morphology and the hexagonal pattern seen on Saturn. Our
findings indicate that these vortices can be generated deep in the planetary
interior. A transition differentiating these two polar flows regimes is
described, interpreted in terms of different force balances and compared with
previous shallow atmospheric models which characterised polar vortex dynamics
in giant planets. In addition, the heat transport properties are investigated
confirming recent scaling laws obtained in the context of reduced models of GT.
