Estimation of residence times in semi-enclosed basins with steady flows

Abstract

Abstract The dispersion processes in semi-enclosed basins with stationary flows have been studied by means of an Eulerian advection–diffusion model. Special interest has been given to quantities which characterize the macroscopic state of the system: the normalized total quantity C(t) of a tracer inside the basin, and its residence time T. The sensitivity of the results to a number of parameters, including flow structure, Peclet number, initial and boundary conditions, have been studied. In particular, the difference between unidirectional flows and flows with recirculations has been investigated. A priori estimates of the value of T are provided, valid for a wide range of parameters. For unidirectional flows, T≃Tout+τ0, where Tout is the time a substantial amount of tracer takes to reach the outflow and τ0 is the inverse of the principal eigenvalue of the advection–diffusion operator. Both parameters Tout and τ0 can be computed knowing the flow structure and the Peclet number, and they are representative, respectively, of the initial and asymptotic phase of dispersion. For flows with recirculations it is found that T≃τ0 over the whole parameter space considered. Conceptually, the difference is due to the tendency of the recirculation to trap the tracer, which enhances the importance of the asymptotic phase. For these flows, the values of T do not change significantly in the range of realistic Peclet numbers considered, suggesting that the macroscopic dispersion properties depend only weakly on the eddy diffusion coefficient. This can have obvious consequences in terms of the possibility of a priori estimates of the residence time, even without having available accurate measurements of the diffusivity.