Abstract
A generalized turbulent diffusion model has been developed which evaluates the time rate of growth of a simulated ‘cloud’ of particles released into a turbulent (i.e. diffusive) atmosphere. The general model, in the form of second-order differential equations, computes the three-dimensional size of the cloud as a function of time. Parameters which influence the cloud growth, and which are accounted for in the model equations, are: (1) length scales and velocity magnitudes of the diffusive field, (2) rate of viscous dissipation ε, (3) vertical stability as characterized by the relative adiabatic lapse rate (1/T)(g/C p +∂T/∂z), and (4) vertical shear in the mean horizontal winds\({{\partial \bar U} \mathord{\left/ {\vphantom {{\partial \bar U} {\partial z}}} \right. \kern-\nulldelimiterspace} {\partial z}}\), and\({{\partial \bar V} \mathord{\left/ {\vphantom {{\partial \bar V} {\partial z}}} \right. \kern-\nulldelimiterspace} {\partial z}}\), for a given height and of spatial extent equal to that of the diffusing cloud. Sample results for near ground level and for upper stratospheric heights are given. For the atmospheric boundary layer case, the diffusive field is microscale turbulence. In the upper stratospheric case it is considered to be a field of highly interactive and dispersive gravity waves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews, D. G. andMcIntyre, M. E. (1976),Planetary waves in horizontal and vertical shear: asymptotic theory for equatorial waves in weak shear, J. Atmos. Sci.33, 2049–2053.
Batchelor, G. K. (1950),The application of similarity theory of turbulence to atmospheric diffusion, Quart. J. Roy. Meteorol. Soc.76, 133–146.
Boyd, J. P. (1976),The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum, J. Atmos. Sci.33, 2285–2291.
Chang, J. S. (1974),Simulations, Perturbations, and Interpretations, inProc. 3rd Conf. on CIAP, DOT-TSC-OST, 74-15, 330–341.
Danielsen, E. F. (1968),Stratospheric-tropospheric exchange based on radio-activity ozone, and potential vorticity, J. Atmos. Sci.25, 502–518.
Danielsen, E. F. andDeaven, D. (1974),Methods for deriving a two-dimensional transport model, inProc. 3rd Conf. on CIAP, 83–90.
Danielsen, E. F. (1975),Transport by mean and turbulent motions, inCIAP Monograph 1, DOT-TST-75-51, 6.1 and 6.2.
Deardorff, J. W. andPeskin, R. L. (1970),Lagrangian statistics from numerically integrated turbulent shear flow, Phys. Fluids13, 584.
Ehhalt, D. H. et al. (1972),The concentration of atmospheric methane between 44 and 62 kilometers altitude, J. Geophys. Res.77, 2193–2196.
Gifford, F. A. (1961),Use of routine meteorological observations for estimating atmosphere dispersion, Nuclear Safety,2, 47–51.
Gifford, F. A. (1977),Tropospheric Relative diffusion observations, J. Appl. Meteorol.,16, 311–313.
Hicks, J. E. (1971), ‘A Numerical Simulation of Nearly Incompressible Stably Stratified Atmospheric Turbulent Diffusion’, Ph.D. Thesis, Georgia Institute of Technology.
Hines, C. O. (1970),Eddy diffusion coefficeents due to instabilities in internal gravity waves, J. Geophys. Res.75, 3937–3939.
Justus, C. G. (1973),Upper atmospheric mixing by gravity waves, in AIAA Paper No. 73-495,Proc. Conf. on the Environmental Impact of Aerospace Operations in the High Atmosphere, Denver, Co. June.
Justus, C. G. (1957)Observations of planetary and gravity waves, inVIth International Conference of the IUGG, Grenoble, France, Sept.
Justus, C. G., Roper, R. G., Woodrum, Arthur, andSmith, O. E. (1975),Global reference atmospheric model for Aerospace applications, J. Spacecraft and Rockets12, 449–450.
Justus, C. G., Roper, R. G., Woodrum, Arthur, andSmith, O. E. (1976),A global reference atmospheric model for surface to orbital altitudes, J. Appl. Meteorol.,15, 3–9.
Kao, S. K. andLee, H. N. (1977),The nonlinear interaction and maintenance of the large scale moving waves in the atmosphere, J. Atmos. Sci.34, 471–485.
Kao, S. K. et al. (1977), ‘Horizontal Eddy Diffusivities in the Northern Hemispheric Stratosphere and Lower Mesosphere’, Report on NASA Contract NAS-6-2498, June.
Lilly, D. K., Waco, D. E. andAdelfang, S. I. (1974),Stratospheric mixing estimated from high altitude turbulence measurements, J. Appl. Meteorol.13, 488–493.
Lindzen, R. S., ‘Tides and gravity waves in the upper atmosphere’, inMesospheric Models and Related Experiments (ed. G. Riocco), (Reidel Publishing Company, 1971).
Mahlman, J. D. (1975a), ‘GFDL model for transport of a chemically inert substance in the lower stratosphere’, inCIAP Monograph 3 DOT-TST-75-53, § 4.5.1.
Mahlman, J. D. (1975b), ‘The effect of transport upon the distribution of ozone’, inCIAP Monograph 1, DOT-TST-75-1, § 6.6.2.
Pasquill, F., (1961),The estimation of the dispersion of windborne material, Meteorol. Mag.90, 1063, 33–49.
Smith, F. B. (1965),The role of wind shear in horizontal diffusion of ambient particles, Quart. J. Roy. Meteorol. Soc.91, 318–329.
Taylor, G. I. (1921),Diffusion by continuous movements, Proc. London Math Soc.,2, 20, 196–202.
Wofsy, S. C. andMcElroy, M. B., (1973),On vertical mixing in the upper stratosphere and lower mesosphere J. Geophys. Res.78, 2619–2624.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Justus, C.G., Mani, K.K. A model for the simulation of turbulent and eddy diffusion processes at heights of 0–65 km. PAGEOPH 117, 513–530 (1978). https://doi.org/10.1007/BF00876631
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00876631