problem requires greater computer resolution or. alternatiwly, an exact or
reliable approximate analytical description of the smaller scale motion of the
turbulence. This conclusion can be translated to practical situations, that is,
fairly coarse mesh descriptions can provide adequate information on singlepoint diffusion but attempts to use the same mesh sizes to study relative
two-point diffusion can lead to serious errors.
Finally, it must be noted that while one can get extensive information
about the relation between the Eulerian and Lagrangian field quite easily
from a numerical simulation, in a sense, numerical simulations provide
almost too much information. Little is known about the EulerianLagrangian relation problem and the mere fact that a good deal of output
information is available from a numerical simulation cannot add appreciably to the understanding of this problem unless the information is
properly used. That is, numerical simulation, of and by itself, is of little help
in solving the Eulerian-Lagrangian problem unless more theoretical background is obtained so that the correct questions can be asked. Essentially.
the numerical simulation is a means of providing the data we need to study
the Eulerian-Lagrangian problem, but stronger theoretical understanding of
this problem is essential.
ACKNOWLEDGMENTS
The author wishes to acknowledge Dr. Douglas Lilly, NCAR' for his aid and discussion of
the twodimensional diflusion problem. Valuable discussions were also held with Dr. Janies
Dccrdorff. NCAR. on both the two- and the threedimensional diffusion study. Twodimensional diNuunion work was done while the author was in rcsidencc at NCAR at that time
holding a Rutgers University Research Council Faculty Fellowship. Dr. E. J. Kau. Aero-Chem
Research Laboratories. contributed greatly to the study of the threedimensional diffusion
prohkm. Portions or this work were sponsored by the National Science Foundation. Division
or Engineering, Grant No. CK-317RHX. and Atmospheric Sciences Section. Grant No.
GA-3342 I.
REFERENCES
Hatchelor, G , K. (1969). Phys. Fluids It, Suppl. II. 233-239.
Carlson, C. R. (1973). Turhulcnt gas-solid How measurements utilizing a laserdoppler velocCharney, J. G. (1971). J . A i m s . Sci. 2& 287-295.
C'omtc-Bellot. G. (1965). "Ecoulemeni turbulent entre deux parois parallbles." Publ. Sci. Tech.
Corrsin. S. (1959). Adnm. Cuopfiys. 6, 161.
imcter. Ph.D. Thesis. RutBers Univ, New Brunswick. New Jersey.
Ministhre de L'Air, Paris.
' The National Center for Atmospheric Research is sponsored by the National Science
Foundation.
reliable approximate analytical description of the smaller scale motion of the
turbulence. This conclusion can be translated to practical situations, that is,
fairly coarse mesh descriptions can provide adequate information on singlepoint diffusion but attempts to use the same mesh sizes to study relative
two-point diffusion can lead to serious errors.
Finally, it must be noted that while one can get extensive information
about the relation between the Eulerian and Lagrangian field quite easily
from a numerical simulation, in a sense, numerical simulations provide
almost too much information. Little is known about the EulerianLagrangian relation problem and the mere fact that a good deal of output
information is available from a numerical simulation cannot add appreciably to the understanding of this problem unless the information is
properly used. That is, numerical simulation, of and by itself, is of little help
in solving the Eulerian-Lagrangian problem unless more theoretical background is obtained so that the correct questions can be asked. Essentially.
the numerical simulation is a means of providing the data we need to study
the Eulerian-Lagrangian problem, but stronger theoretical understanding of
this problem is essential.
ACKNOWLEDGMENTS
The author wishes to acknowledge Dr. Douglas Lilly, NCAR' for his aid and discussion of
the twodimensional diflusion problem. Valuable discussions were also held with Dr. Janies
Dccrdorff. NCAR. on both the two- and the threedimensional diffusion study. Twodimensional diNuunion work was done while the author was in rcsidencc at NCAR at that time
holding a Rutgers University Research Council Faculty Fellowship. Dr. E. J. Kau. Aero-Chem
Research Laboratories. contributed greatly to the study of the threedimensional diffusion
prohkm. Portions or this work were sponsored by the National Science Foundation. Division
or Engineering, Grant No. CK-317RHX. and Atmospheric Sciences Section. Grant No.
GA-3342 I.
REFERENCES
Hatchelor, G , K. (1969). Phys. Fluids It, Suppl. II. 233-239.
Carlson, C. R. (1973). Turhulcnt gas-solid How measurements utilizing a laserdoppler velocCharney, J. G. (1971). J . A i m s . Sci. 2& 287-295.
C'omtc-Bellot. G. (1965). "Ecoulemeni turbulent entre deux parois parallbles." Publ. Sci. Tech.
Corrsin. S. (1959). Adnm. Cuopfiys. 6, 161.
imcter. Ph.D. Thesis. RutBers Univ, New Brunswick. New Jersey.
Ministhre de L'Air, Paris.
' The National Center for Atmospheric Research is sponsored by the National Science
Foundation.