To understand why the findings of Deleersnijder et al. [(2006), Environ Fluid Mech 6: 25–42]—the residence time in the mixed layer in not necessarily zero at the pycnocline—are consistent with those of Delhez and Deleersnijder [(2006), Ocean Dyn 56:139–150]—the residence time in a control domain vanishes at the open boundaries of this control domain—, it is necessary to consider a control domain that includes part of the pycnocline, in which the eddy diffusivity is assumed to be zero. Then, depending on the behaviour of the eddy diffusivity near the bottom of the mixed layer, the residence time may be seen to exhibit a discontinuity at the interface between the mixed layer and the pycnocline. If such a discontinuity exists, the residence time is non-zero in the former and zero in the latter. This is illustrated by analytical solutions obtained under the assumption that the eddy diffusivity is constant in the mixed layer.
Adjoint model Mixed mayer Pycnocline Residence time
This is a preview of subscription content, log in to check access.
Bolin B, Rodhe H (1973) A note on the concepts of age distribution and transit time in natural reservoirs. Tellus, 25:58–62CrossRefGoogle Scholar
Deleersnijder E, Beckers J.-M, Delhez EJM (2006) The residence time of settling particles in the surface mixed layer. Environ Fluid Mech, 6:25–42CrossRefGoogle Scholar
Delhez EJM, Deleersnijder E (2006) The boundary layer of the residence time field. Ocean Dyn, 56:139–150CrossRefGoogle Scholar
Delhez EJM, Heemink AW, Deleersnijder E (2004) Residence time in a semi-enclosed domain from the solution of an adjoint problem. Estuar Coast Shelf Sci, 61:691–702CrossRefGoogle Scholar
Takeoka H (1984) Fundamental concepts of exchange and transport time scales in a coastal sea. Cont Shelf Res 3:311–326CrossRefGoogle Scholar
Whitham GB (1974) Linear and nonlinear waves. Wiley, New YorkGoogle Scholar
Zimmerman JTF (1976) Mixing and flushing of tidal embayments in the Western Dutch Wadden Sea, Part I: distribution of salinity and calculation of mixing time scales. Neth J Sea Res. 10: 149–191CrossRefGoogle Scholar