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Review of non-local mixing in turbulent atmospheres: Transilient turbulence theory

  • Part I: Basic Studies and Novel Methods in Modeling Atmospheric Flows
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Abstract

Some of the larger eddies in a turbulent region can be coherent structures that turbulently advect air parcels across large vertical distances before smaller eddies mix the parcels with the environment. Such a process is nonlocal rather than diffusive. Transilient turbulence theory, named after a Latin word maaning “jump over”, provides a framework for considering the ensemble-averaged effect of many eddies of different sizes on the net nonlocal mixing in the vertical. Nonlocal turbulence statistics can then be examinated, and nonlocal first-order closure can be formulated.

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References

  • Berkowicz, R., 1980:On the spectral turbulent diffusivity theory for homogeneous turbulence. J. Fluid Mech.,100, 433–448.

    Google Scholar 

  • Berkowicz, R., 1984: Spectral methods for atmospheric diffusion modeling. Bound.-Layer Meteor.,30, 201–220.

    Google Scholar 

  • Berkowicz, R. and L.P. Prahm, 1979:Generalization of K-theory for turbulent diffusion. Part I: Spectral turbulent diffusivity concept. J. Appl. Meteor.,18, 266–272.

    Google Scholar 

  • Berkowicz, R. and L.P. Prahm, 1980:On the spectral turbulent diffusivity theory for homogeneous turbulence. J. Fluid Mech.,100, 433–448.

    Google Scholar 

  • Berkowicz, R. and L.P. Prahm, 1984:Spectral representation of the vertical structure of turbulence in the convective boundary layer. Quart. J. Roy. Meteor. Soc.,110, 13–34.

    Google Scholar 

  • Blackadar, A.K., 1979:Modeling pollutant transfer during daytime convection. Preprints, 4th Symp. on Turbulence, Diffusion and Air Pollution, Reno, Amer. Meteor. Soc., 443–447.

  • Boudreau, B.P. and D.M. Imboden, 1987:Mathematics of tracer mixing in sediments: III. The theory of nonlocal mixing within sediments. Amer. J. of Science287, 693–719.

    Google Scholar 

  • Chatfield, R.B. and R.A. Brost, 1987:A two-stream model of the vertical transport of trace species in the convective boundary layer. J. Geophys. Res.,92, 13,263–13,276.

    Google Scholar 

  • Chollet, J.-P. and M. Lesieur, 1981:Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci.,38, 2747–2757.

    Google Scholar 

  • Chrobok, G., 1988:Zur numerischen Simulation konvektiver Grenzschichten mit Integralen SchlieBungsansätzen. Diplomarbeit im Fach Meteorology, November 1988, Inst. für Meteorologie und Klimatologie der Universität Hannover. 92pp.

  • Deardorff, J.W., 1985:Comments on ‘Transilient turbulence theory, Part I.’ J. Atmos. Sci.,42, 2069.

    Google Scholar 

  • Eberhard, W.L., W.R. Moninger and G.A. Briggs, 1988:Plume dispersion in the convective boundary layer. Part. I. CONDORS field experiment and example measurements. J. Appl. Meteor.,27, 599–616.

    Google Scholar 

  • Ebert, E.E., U. Schumann and R.B. Stull, 1989:Nonlocal turbulent mixing in the convective boundary layer evaluated from large-eddy simulation. J. Atmos. Sci.,46, 2178–2207.

    Google Scholar 

  • Eringen, A.C., 1972:On nonlocal fluid mechanics. Int. J. Engng. Sci.,10, 561–575.

    Google Scholar 

  • Estoque, M.A., 1968:Vertical mixing due to penetrative convection. J. Atmos. Sci.,25, 1046–1051.

    Google Scholar 

  • Fiedler, B.H., 1984:An integral closure model for the vertical turbulent flux of a scalar in a mixed layer. J. Atmos. Sci.,41, 674–680.

    Google Scholar 

  • Fiedler, B.H. and C.-H. Moeng, 1985:A practical integral closure model for mean transport of a scalar in a convective boundary layer. J. Atmos. Sci.,42, 359–363.

    Google Scholar 

  • Fortak, H.G.:Non-Markovian turbulent dispersion in the atmosphere. Preprints of the 16th International Tech Meeting on Air Pollution Modelling and its Applications, 6–10 April, Lindau, F.R. Germany.

  • Gaspar, P., Y. Gregoris, R.B. Stull and C. Boissier, 1988:Long-term simulations of upper ocean vertical mixing using models of different types. Small-scale Turbulence and Mixing in the Ocean, Proceedings of the 18th Leige Colloquium on Ocean Hydrodynamics. J.C.J.Nihoul and B.M. Jamart (Ed.), Elsevier Oceanography Series,46, 542pp.

  • Hinze, J.O., 1975:Turbulence, 2nd Ed., McGraw-Hill. pp790.

  • Hostetler, C.J. and B.E. Opitz, 1982:Simulation of solute transport: A Markov model. Report from Pacific Northwest Lab, P.O. Box 999, Richland, WA 99352. pp14.

  • Imboden, D.M., 1981:Tracers and Mixing in the Aquatic Environment: A critical discussion of diffusion models and an introduction into concepts of non-Fickian transport. Habilitation Thesis. Swiss Federal Institute of Technology (ETH), Zurich, pp137.

    Google Scholar 

  • Jenkins, A.D., 1985:Simulation of turbulent dispersion using a simple random model of the flow field. Appl. Math Modelling,9, 239–245.

    Google Scholar 

  • Jochum, A.M., 1988:Turbulent transport in the convective boundary layer over complex terrain. Preprints from the Eighth Symposium on Turbulence and Diffusion, April 25–29, 1988, San Diego. Amer. Meteor. Soc. 417–420.

  • Klemp, J.B. and D.K. Lilly, 1978:Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci.,35, 78–107.

    Google Scholar 

  • Kraichnan, R.H., 1959:The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech.,5, 497–543.

    Google Scholar 

  • Kraichnan, R.H., 1966:Isotropic turbulence and inertial-range structure. Phys. Fluids,9, 1728–1752.

    Google Scholar 

  • Kraichnan, R.H., 1971a:An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech.,47, 513–524.

    Google Scholar 

  • Kraichnan, R.H., 1971b:Inertial range transfer in two and three-dimensional turbulence. J. Fluid Mech.,47, 525–535.

    Google Scholar 

  • Kraichnan, R.H., 1976:Eddy-viscosity in two and three dimensions. J. Atmos., Sci.,33, 1521–1536.

    Google Scholar 

  • Leonard, A., 1974:Energy cascade in large-eddy simulations of turbulent flows. Adv. Geophys.,18A, 237–248.

    Google Scholar 

  • Leslie, D.C., 1973:Developments in the Theory of Turbulence. Clarendon Press. pp 368.

  • Lumley, J.L. and H.A. Panofsky, 1964:The Structure of Atmospheric Turbulence. Interscience. Wiley. pp239.

  • Monin, A.S. and A.M. Yaglom, 1971:Statistical Fluid Mechanics: Mechanics of Turbulence. The MIT Press. (Originally published in Russian in 1965). pp769.

  • Morse, P.M. and H. Feshbach, 1953:Chapt. 7. Greens functions. Methods of Theoretical Physics, McGraw-Hill. 997pp.

  • Narasimhan, M.N.L. and E.A. Saibel, 1989:Turbulence in journal bearings from a nonlocal point of view. Int. J. Engng. Sci.,27, 219–236.

    Google Scholar 

  • Pasquill, F., 1974:Atmospheric Diffusion: The Dispersion of Windborne Material from Industrial and other Sources. 2nd Ed. Wiley. pp429.

  • Prahm, L.P. and R. Berkowicz, 1980:Reply (to Troen, et al. 1980a). J. Appl. Meteor.,19, 118.

    Google Scholar 

  • Prahm, L.P., R. Berkowicz and O. Christensen, 1979:Generalization of K-theory for turbulent diffusion. Part II: Spectral diffusivity model for plume dispersion. J. Appl. Meteor.,18, 273–282.

    Google Scholar 

  • Prandtl, L., 1925:Bericht über Untersuchungen zur ausgebildeten Turbulenz. Ztschr. f. angew. Math. und Mech.,5, 136–139.

    Google Scholar 

  • Raymond, W.H. and R.B. Stull, 1990:Application of transilient turbulence theory to mesoscale numerical weather forecasting. Mon. Wea. Rev.,118, 2471–2499.

    Google Scholar 

  • Roberts, P.H., 1961:Analytical theory for turbulent diffusion. J. Fluid Mech.,11, 257–283.

    Google Scholar 

  • Romanof, N., 1982:Application of Wiener-Hermite expansions to the turbulent diffusion. Meteor. and Hydrology,2, 25–31.

    Google Scholar 

  • Romanof, N., 1987:A nonlocal model for the diffusion of pollutants released by instantaneous sources. Preprints of the 16th International Tech Meeting on Air Pollution Modelling and its Applications, 6–10 April, Lindau, F.R. Germany, 10 pp.

  • Romanof, N., 1989:Nonlocal models in turbulent diffusion. Z. Meteorol.,39, 89–93.

    Google Scholar 

  • Saffman, P.G., 1969:Application of the Wiener-Hermite expansions to the diffusion of a passive scalar in homogeneous turbulent flow. Phys. Fluids,12, 1786–1798.

    Google Scholar 

  • Sawford, B.L., 1988:Comments on ‘Transilient turbulence theory. Parts I and III’ J. Atmos. Sci.,45, 2092–2093.

    Google Scholar 

  • Schumann, U., R.B. Stull and E.E. Ebert, 1989:Nonlocal turbulent mixing in boundary layers evaluated from large-eddy simulations. Preprints from the Seventh Symposium on Turbulent Shear Flows, Stanford Univ., August 21–23, 1989. 29.1.1–29.1.6.

  • Speziale, C.G. and A.C. Eringen, 1981:Nonlocal fluid mechanics description of wall turbulence. Computers & Math. with Applic.,7, 27–41.

    Google Scholar 

  • Stanišić, M.M., 1985:The Mathematical Theory of Turbulence. Universitext. Springer-Verlag. pp429.

  • Stull, R.B., 1984:Transilient turbulence theory. Part I: The concept of eddy-mixing across finite distances. J. Atmos. Sci.,41, 3351–3367.

    Google Scholar 

  • Stull, R.B., 1985:Reply to Deardorff's “Comments on “Transilient turbulence theory, Part I” J. Atmos. Sci.,42, 2070–2072.

    Google Scholar 

  • Stull, R.B., 1986:Transilient turbulence theory, Part III: Bulk dispersion rate and numerical stability. J. Atmos. Sci.,43, 50–57.

    Google Scholar 

  • Stull, R.B., 1987:Transilient turbulence algorithms to model mixing across finite distances. Environ. Software,2, 4–12.

    Google Scholar 

  • Stull, R.B., 1988a:An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht. 666pp.

    Google Scholar 

  • Stull, R.B., 1988b:A reevaluation of two dispersion theories. J. Atmos. Sci.,45, 2082–2091.

    Google Scholar 

  • Stull, R.B., 1990:Nonlocal turbulent mixing: measurement and parameterization of transilient matrices. Preprints of the Ninth Symposium of Turbulence and Diffusion. April 30 – May 3, 1990. Roskilde, Denmark. Amer. Meteor. Soc., 348–351.

    Google Scholar 

  • Stull, R.B., 1991a:A comparison of parameterized vs. measured transilient mixing coefficients for a convective mixed layer. Bound.-Layer Meteor.,55, 67–90.

    Google Scholar 

  • Stull, R.B., 1991b:Static stability — an update. Bull. Amer. Meteor. Soc.,72, 1521–1529.

    Google Scholar 

  • Stull, R.B. and A.G.M. Driedonks, 1987:Applications of the transilient turbulence parameterization to atmospheric boundary layer simulations. Bound.-Layer Meteor.,40, 209–239.

    Google Scholar 

  • Stull, R.B., E.E. Ebert, S.Jascourt, and J. Purser, 1992:Convective structure memory. (manuscript in preparation, to be submitted to J. Atmos. Sci.)

  • Stull, R.B. and T. Hasagawa, 1984:Transilient turbulence theory. Part II: Turbulent adjustment. J. Atmos. Sci.,41, 3368–3379.

    Google Scholar 

  • Stull, R.B., and E.B. Kraus, 1987:The transilient model of the upper ocean. J. Geophys. Res. — Oceans,92, 10745–10755.

    Google Scholar 

  • Tennekes, H. and J.L. Lumley, 1972:A First Course in Turbulence. The MET Press. pp300.

  • Troen, I., T. Mikkelsen and S.E. Larson, 1980a:Comments on ‘Generalization of K-theory for turbulent diffusion. Part II’. J. Appl. Meteor.,19, 117–118.

    Google Scholar 

  • Troen, I., T. Mikkelsen and S.E. Larson, 1980b:Note on spectral diffusivity theory. J. Appl. Meteor.,19, 609–615.

    Google Scholar 

  • Wang, S. and B.A. Albrecht, 1990:A mean-gradient model of the dry convective boundary layer. J. Atmos. Sci.,47, 126–138.

    Google Scholar 

  • Weast, R.C., 1968:CRC Handbook of Chemistry and Physics, 49th edition. The Chemical Rubber Co., 2106 pp.

  • Weil, J.C., 1990:A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model. J. Atmos. Sci.,47, 501–515.

    Google Scholar 

  • Willis, G.E., and J.W. Deardord, 1976:A laboratory model of diffusion into the convective planetary boundary layer. Quart. J. Roy. Meteor. Soc.,102, 427–445.

    Google Scholar 

  • Willis, G.E. and J.W. Deardorff, 1978:A laboratory study of dispersion from an elevated source within a modeled convective planetary boundary layer. Atmos. Environ.,12, 1305–1311.

    Google Scholar 

  • Willis, G.E. and J.W. Deardorff, 1981:A laboratory study of dispersion from a source in the middle of the convective boundary layer. Atmos. Environ.15, 109–117.

    Google Scholar 

  • Wyngaard, J.C., 1987:A physical mechanism for the asymmetry in top-down and botton-up diffusion. J. Atmos. Sci.,44, 1083–1087.

    Google Scholar 

  • Wyngaard, J.C. and R.A. Brost, 1984:Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci.,41, 102–112.

    Google Scholar 

  • Zhang, D. and R.A. Anthes, 1982:A high-resolution model of the planetary boundary layer — sensitivity tests and comparisons with SESAME-79 data. J. Appl. Meteor.,21, 1594–1609.

    Google Scholar 

  • Zhang, Q., 1990:Test of Transilient Turbulence Theory Against a Field Experiment. Masters Thesis. Dept. of Meteorology, University of Wisconsin-Madison, pp88.

  • Zhang, Q. and R.B. Stull, 1992:Alternative nonlocal descriptions of boundary layer evolution. (Submitted to J. Atmos. Sci.)

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Stull, R.B. Review of non-local mixing in turbulent atmospheres: Transilient turbulence theory. Boundary-Layer Meteorol 62, 21–96 (1993). https://doi.org/10.1007/BF00705546

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