Some Properties of Generalized Age-Distribution Equations in Fluid Dynamics

The concept of age in fluid dynamics is analyzed in the case of a tracer advection-diffusion equation. From the general solution in a uniform velocity field, it is shown that unexpected symmetry properties arise for the age field. In particular, for a point release, the age field is isotropic, regardless of the direction of the ow and the value of the diffusion coefficient. The analysis is then extended to situations with time-varying currents, where the symmetry can be broken under some circumstances. Finally, we show a method by which a time-dependent problem can be used to assess a stationary concentration distribution function, providing details about the propagation of younger and older material at a given location.

[1]  J. Salomon,et al.  A 2D long term advection-dispersion model for the Channel and Southern North Sea Part A: Validation through comparison with artificial radionuclides , 1995 .

[2]  Eric Delhez,et al.  Macroscale ecohydrodynamic modeling on the Northwest European Continental Shelf , 1998 .

[3]  Eric Deleersnijder,et al.  A simple model of the tracer flux from the Mururoa lagoon to the Pacific , 1997 .

[4]  Wolfgang Roether,et al.  Temporal evolution of CFC 11 and CFC 12 concentrations in the ocean interior , 1996 .

[5]  Jorge L. Sarmiento,et al.  Tracer dating and ocean ventilation , 1990 .

[6]  Eric Deleersnijder,et al.  The concept of age in marine modelling I. Theory and preliminary model results , 2001 .

[7]  William J. Jenkins,et al.  Studying subtropical thermocline ventilation and circulation using tritium and 3He , 1998 .

[8]  W. J. Jenkins,et al.  The distribution of 3He in the western Atlantic ocean , 1976 .

[9]  Wallace S. Broecker,et al.  Radiocarbon age of waters in the deep Atlantic revisited , 1991 .

[10]  Johannes Karstensen,et al.  Age determination of mixed water masses using CFC and oxygen data , 1998 .

[11]  Göran Björk,et al.  Residence times in the upper Arctic Ocean , 1996 .

[12]  Anthony C. Hirst,et al.  Determination of water component age in ocean models: application to the fate of North Atlantic Deep Water , 1999 .

[13]  J. Zimmerman,et al.  Mixing and flushing of tidal embayments in the western Dutch Wadden Sea part I: Distribution of salinity and calculation of mixing time scales , 1976 .

[14]  Eric Deleersnijder,et al.  Toward a general theory of the age in ocean modelling , 1999 .

[15]  Matthew H. England,et al.  The Age of Water and Ventilation Timescales in a Global Ocean Model , 1995 .

[16]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[17]  William J. Jenkins,et al.  A comparison of ocean tracer dating techniques on a meridional section in the eastern North Atlantic , 1997 .

[18]  Thierry Fichefet,et al.  Problems with using radiocarbon to infer ocean ventilation rates for past and present climates , 1999 .

[19]  Karl K. Turekian,et al.  Transfer rates of dissolved tracers through estuaries based on 228Ra: A study of Long Island Sound , 1996 .

[20]  Bernd Kromer,et al.  Mid-1980s distribution of tritium, 3He, 14C and 39Ar in the Greenland/Norwegian Seas and the Nansen Basin of the Arctic Ocean , 1995 .

[21]  H. Takeoka.  Fundamental concepts of exchange and transport time scales in a coastal sea , 1984 .

[22]  P. Guegueniat,et al.  A 2D long term advection—dispersion model for the Channel and southern North Sea Part B: Transit time and transfer function from Cap de La Hague , 1995 .

[23]  Nelson G. Hogg,et al.  Determining the Strength of the Deep Western Boundary Current Using the Chlorofluoromethane Ratio , 1989 .

[24]  Peter Schlosser,et al.  Halocarbon and tritium 3He dating of the water masses of the Nansen Basin, Arctic Ocean , 1992 .

[25]  Eric Delhez,et al.  Integrated Modelling of the Belgian Coastal Zone , 2001 .

[26]  D. Prandle,et al.  A modelling study of the mixing of 137Cs in the seas of the European Continental Shelf , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[27]  Göte Östlund,et al.  Isotope tracing of siberian river water in the Arctic Ocean , 1994 .

[28]  M. Stuiver,et al.  Abyssal Water Carbon-14 Distribution and the Age of the World Oceans , 1983, Science.