Dispersion processes and residence times in a semi-enclosed basin with recirculating gyres: An application to the Tyrrhenian Sea

In this paper we investigate the dispersion of a tracer in a semi-enclosed basin characterized by a steady flow with recirculations. In particular, we focus on the macroscopic behavior of the system, characterized by the total concentration of the tracer in the basin, C(t), and by its residence time T. As a case study, the circulation in an idealized basin mirroring some of the major characteristics of the Tyrrhenian Sea is considered, with a northward current connecting the inflow and the outflow regions of the basin, and with a main cyclonic gyre in the northern part of it. Numerical simulations are performed from several release points in the basin and for two different values of the diffusivity coefficient K. Two independent models for dispersion are used, an Eulerian and a Lagrangian one, allowing us to validate both the basic formalism and the numerical results. The experiments show that the macroscopic properties of dispersion are largely influenced by the presence of the main gyre, while they do not depend strongly on K in the considered range. Namely, after a first phase which depends on the initial conditions, the tracer tends to be concentrated in the region of the northern gyre, and this influences the trend of C(t) versus time and the value T. For almost all the simulations, the decrease of C(t) in time can be approximated by an exponential decay, indicating a constant probability of tracer escaping the basin. The e-folding timescale of the decay is the inverse of the principal eigenvalue of the advection-diffusion operator, and it can be computed a priori knowing the flow field; this allows us to compute also an a priori estimate for the residence time T. Only when the initial release is very close to the outflow, is the initial decay of C(t) distinctly different from an exponential, and a more detailed analysis is necessary. The basic results appear generalizable to a number of other similar systems with recirculations.