Kinematics of age mixing in advection-dispersion models

Abstract

This paper investigates age mixing processes arising in advection-dispersion models, where large-scale travel and residence time distributions can be explicitly calculated based on the underlying velocity field. In particular, we analyze spatially integrated age mixing dynamics by comparing the age distributions of the storage and of the outflow(s). The relevance of the work lies in the impact of age mixing dynamics on the shape of travel time distributions (TTDs), which ultimately control the long-term memory of catchment transport processes. We set up a theoretical framework that bridges previous Lagrangian and Eulerian water age theories in heterogeneous media. The framework allows for the analysis of the dynamical connection between water age distributions in large-scale volume and flux samples. Theoretical advances are then illustrated through the application to a finite one-dimensional domain with constant advection and dispersion coefficient. Therein, we analyze the type of mixing emerging for different Peclet numbers and diverse spatiotemporal patterns of solute input. We find that in spite of the enhanced nonstationarity of TTDs, the type of mixing is markedly invariant. Moreover, for relatively low Peclet numbers the different ages available in the control volume are systematically removed from the domain at a rate nearly proportional to their relative abundance (random sampling). Emerging large-scale patterns of age mixing yield theoretical and practical implications for watershed hydrology, where TTDs can be used to infer general patterns of catchment response across scales.