Residence and exposure times: when diffusion does not matter
In: Ocean Dynamics. SpringerVerlag: Berlin; Heidelberg; New York. ISSN 16167341; eISSN 16167228, more
 
Author keywords 
Advectiondiffusion; Residence time; Exposure time; CART 
Authors   Top 
 Delhez, E.J.M., more
 Deleersnijder, E., more



Abstract 
Under constant hydrodynamic conditions and assuming horizontal homogeneity, negatively buoyant particles released at the surface of the water column have a mean residence time in the surface mixed layer of h/w, where h is the thickness of the latter and w ( > 0) is the sinking velocity Deleersnijder (Environ Fluid Mech 6(6):541547, 2006a). The residence time does not depend on the diffusivity and equals the settling timescale. We show that this behavior is a result of the particular boundary conditions of the problem and that it is related to a similar property of the exposure time in a onedimensional infinite domain. In 1D advectiondiffusion problem with a constant and uniform velocity, the exposure timewhich is a generalization of the residence time measuring the total time spent by a particle in a control domain allowing the particle to leave and reenter the control domainis also equal to the advection timescale at the upstream boundary of the control domain. To explain this result, the concept of point exposure is introduced; the point exposure is the time integral of the concentration at a given location. It measures the integrated influence of a point release at a given location and is related to the concept of number of visits of the theory of random walks. We show that the point exposure takes a constant value downstream the point of release, even when the diffusivity varies in space. The analysis of this result reveals also that the integrated downstream transport of a passive tracer is only effected by advection. While the diffusion flux differs from zero at all times, its integrated value is strictly zero. 
