Anisotropic Lagrangian Dispersion in Rotating Flows with a β Effect

Abstract

detailed analysis of Lagrangian tracer dispersion is performed on datasets obtained from laboratory experiments that simulate rotating turbulence in the presence of a ? effect. Compatible with the limitations of the experimental apparatus, a relatively wide range of the zonostrophy index R?, a parameter used to characterize flow regimes in ?-plane turbulence, is explored. The considered range spans from values ~O(10?1), for which the flow is nearly isotropic, to values ~O(1), corresponding to the so-called transitional range in which the flow gradually leaves the friction-dominated regime to enter the full zonostrophic regime. The degree of anistropy and the characteristic scales of the flow have been estimated by means of a Lagrangian approach based on the reconstruction of tracer trajectories and on the measure of the finite-scale Lyapunov exponents (FSLE). The FSLE analysis allows one to identify the regimes of two-particle dispersion and to relate them to the physical parameters of the system. Moreover, a Lagrangian anisotropy index (LAI) is introduced and defined in terms of the FSLE zonal and radial components, in order to describe the onset of anisotropy and to check if it is consistent with the theoretical predictions. It is remarkable that the finite-scale dispersion rates are very sensitive to the degree of anistropy of turbulence, more so than other indicators defined in terms of Eulerian quantities. Furthermore, they offer an effective diagnostic tool of the degree of anisotropy that can be used even prior to attaining a fully developed regime of zonostrophic turbulence.