Convective Jets: Volcanic Activity and Turbulent Mixing in the Boundary Layers of the Atmosphere and Ocean

  • Alexander Vulfson
  • Oleg Borodin
  • Petr Nikolaev
Conference paper
Part of the Springer Geology book series (SPRINGERGEOL)


In the article, it is considered a modification of an integral model of unsteady turbulent jet with a presence of pressure force. Stationary solutions of the presented model is compared with well-known analytical results of classical models. It is shown that the inclusion of pressure forces changes dynamic parameters of a jet by about 15%. An analytical solution of a steady forced buoyant jet that corresponds to a volcanic outburst is deduced. An analytical solution for the spontaneous jet of convective surface layer is presented. The simplest model of an ensemble of the buoyant jets of convective surface layer is built. A hydrodynamic formation mechanism of vertical profiles of the turbulent diffusivity and the turbulent statistical moments of the atmospheric surface layer related to the ascent of the jets’ system, is formulated.


Convective thermal Convective jet Forced convective jet Ensemble of convective jets Eddy diffusivity Turbulent moments 


  1. 1.
    Delichatsios, M.A.: Time similarity analysis of unsteady buoyant plumes. J. Fluids Mech. 93(2), 241–250 (1979)ADSCrossRefGoogle Scholar
  2. 2.
    Yu, H.-Z.: Transient plume influence in measurement of convective heat release rates of fast-growing fires using a large-scale fire products collector. Trans. ASME 112, 186–191 (1990)CrossRefGoogle Scholar
  3. 3.
    Vul’fson, A.N.: Convective-region top front propagation in a uniform medium under the action of point, linear, and plane heat and momentum sources. Fluid Dyn. 36(3), 418–428 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Vul’fson, A.N., Borodin, O.O.: Self-similar propagation regimes of a nonstationary high-temperature convective jet in the adiabatic atmosphere. J. Appl. Mech. Tech. Phys. 42(2), 255–261 (2001)ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    Scase, M.M., Hewitt, R.E.: Unsteady turbulent plume models. J. Fluid Mech. 697, 455–480 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Craske, J., van Reeuwijk, M.: Generalised unsteady plume theory. J. Fluid Mech. 792, 1013–1052 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Woodhouse, M.J., Phillips, J.C., Hogg, A.J.: Unsteady turbulent buoyant plumes. J. Fluid Mech. 794, 595–638 (2016)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Costa, A., Suzuki, Y.J., Cerminara, M., Devenish, B.J., Ongaro, T.E., Herzog, M., Van Eaton, A.R., Denby, L.C., Bursik, M., Vitturi, M.D.M., Engwell, S.: Results of the eruptive column model inter-comparison study. J. Volcanol. Geoth. Res. 326, 2–25 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    Vulfson, A.N., Borodin, O.O.: System of convective thermals as a generalized ensemble of Brownian particles. Phys. Usp. 59(2), 109 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    Shraiman, B.I., Siggia, E.D.: Scalar turbulence. Nature 405(8), 639–646 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    Vulfson, A.N., Nikolaev, P.V.: Integral bubble and jet models with pressure forces. Izv. Atmos. Oceanic Phys. 53(4), 419–427 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Sedov, L.I.: Mechanics of Continuous Media, 6th edn. LAN, St. Petersburg (2004)Google Scholar
  13. 13.
    Zel’dovich, B.Y.: Limiting laws of free-rising convective currents. Zh. Eksp. Teor. Fiz. 12, 1463–1465 (1937)Google Scholar
  14. 14.
    Abramovich, G.N.: Theory of Turbulent Jets. Nauka, Moscow (1984)Google Scholar
  15. 15.
    Priestly, C.H.B., Ball, F.K.: Continuous convection from an isolated source of heat. Quart. J. Roy. Meteor. Soc. 81(348), 144–157 (1955)ADSCrossRefGoogle Scholar
  16. 16.
    Priestly, C.H.B.: Turbulent Transfer in the Lover Atmosphere. University Chicago Press, Chicago (1959)Google Scholar
  17. 17.
    Kader, B.A., Yaglom, A.M.: Mean and fields and fluctuation moments in unstably stratified turbulent boundary layers. J. Fluid Mech. 212, 637–662 (1990)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Prandtl, L.: Meteorogische anwendung der stromungslehre. Beitr. Phys. fr. Atmos. 19(3), 188–202 (1932)zbMATHGoogle Scholar
  19. 19.
    Obukhov, A.M.: Turbulence in thermally inhomogeneous atmosphere. Trudy Inst. Teor. Geofiz. Akad. Nauk SSSR 1, 95–115 (1946)Google Scholar
  20. 20.
    Batchelor, G.K.: Heat convection and buoyancy effects in fluids. Quart. J. Roy. Met Soc 80(345), 339–358 (1954)ADSCrossRefGoogle Scholar
  21. 21.
    Huppert, H.E., Turner, J.S.: Double-diffusive convection. J. Fluid Mech. 106, 299–329 (1981)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Vulfson, A.N., Borodin, O.O.: An ensemble of dynamically identical thermals and vertical profiles of turbulent moments in the convective surface layer of atmosphere. Russ. Meteorol. Hydrol. 34(8), 491–500 (2009)CrossRefGoogle Scholar
  23. 23.
    Deardorff, J.W.: Convective velocity and temperature scales for the unstable planetary boundary layer and for Raylegh convection. J. Atmos. Sci. 27(8), 1211–1212 (1970)ADSCrossRefGoogle Scholar
  24. 24.
    Troen, I., Mahrt, L.: A simple model of the atmospheric boundary layer: sensitivity to surface evaporation. Bound.-Layer Meteorol. 37, 129–148 (1986)ADSCrossRefGoogle Scholar
  25. 25.
    Lenschow, D.H., Wyngaard, J.C., Pennel, W.T.: Mean field and second-moment budgets in a baroclinic, convective boundary layer. J. Atmos. Sci. 37(6), 1313–1326 (1980)ADSCrossRefGoogle Scholar
  26. 26.
    Vulfson, A.N., Volodin, I.A., Borodin, O.O.: Local similarity theory and universal profiles of turbulent characteristics in the convective boundary layer. Russ. Meteorol. Hydrol. 10, 1–10 (2004)Google Scholar
  27. 27.
    Gryanik, V.M., Hartman, J.: A turbulence closure for the convective boundary layer based on a two-scale mass-flux approach. J. Atmos. Sci. 59(18), 2729–2744 (2002)ADSCrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Oil and Gas ProblemsRussian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.National University of Science and Technology MISISMoscowRussia

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