Transition to geostrophic turbulence in the laboratory, and as a paradigm in atmospheres and oceans

Geostrophic turbulence has become a classical paradigm for understanding a wide variety of natural systems, including the large- and meso-scale circulation in the atmosphere and oceans of the Earth. In this paper, we review the fundamental basis of the theory of 2D and geostrophic turbulence, with reference to experimental investigations of fluid motion in the laboratory, numerical models and observational studies of the atmosphere and oceans. Attention is concentrated on the initial transitions from laminar to 'turbulent' flow via various routes to low-dimensional chaos (also known sometimes as 'weak turbulence'), as well as on statistical descriptions of the mean state of the fully developed turbulent flow. In the latter case, we also discuss the classical approach to deriving energy spectra and the potential implications of such a state for the predictability of rapidly rotating fluid systems such as the atmosphere and oceans. Finally, we also offer an outlook for the future, highlighting some potential developments of techniques which offer the possibility of combining statistical and dynamical information to predict the behaviour of quasi-stable, coherent structures in an otherwise turbulent system