Large-scale bottleneck effect in two-dimensional turbulence

Abstract

The bottleneck phenomenon in three-dimensional turbulence is generally associated with the dissipation range of the energy spectrum. In the present work, it is shown by using a two-point closure theory, that in two-dimensional turbulence it is possible to observe a bottleneck at the large scales, due to the effect of friction on the inverse energy cascade. This large-scale bottleneck is directly related to the process of energy condensation, the pile-up of energy at wavenumbers corresponding to the domain size. The link between the use of friction and the creation of space-filling structures is discussed and it is concluded that the careless use of hypofriction might reduce the inertial range of the energy spectrum.

Keywords:

• homogeneous turbulence
• isotropic turbulence
• two-dimensional turbulence

Acknowledgements

We acknowledge interaction and discussion with Claude Cambon, Uriel Frisch, Fabien Godeferd, Walter Pauls, Samriddhi Sankar Ray, Jian-Zhou Zhu, and two anonymous referees.