Residence and exposure times: when diffusion does not matter
Delhez, E.J.M.; Deleersnijder, E. (2012). Residence and exposure times: when diffusion does not matter. Ocean Dynamics 62(10-12): 1399-1407. dx.doi.org/10.1007/s10236-012-0568-y
In: Ocean Dynamics. Springer-Verlag: Berlin; Heidelberg; New York. ISSN 1616-7341; e-ISSN 1616-7228, more
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):541-547, 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 one-dimensional infinite domain. In 1-D advection-diffusion problem with a constant and uniform velocity, the exposure time-which 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 domain-is 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.
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