Dimensional Transitions in Turbulence: The Effects of Rotation and Stratification

The transition from two-dimensional to three-dimensional turbulence is a fascinating problem which finds applications in the study of geophysical flows. This paper briefly reviews the research in this field with emphasis on the role of rotation and stratification, two important ingredients of geophysical flows at large scales. By means of direct numerical simulations of the Navier-Stokes equations, the conditions for the emergence of a split cascade, with a simultaneous cascade of energy to both the large and the small scales, are discussed.