Convection and Turbulence

Abstract

In this section, we establish the relationship between the classical Zeldovich and Kolmogorov results of turbulent transport of scalar particles and the theory of turbulent convection. Let us consider the simplified balance of energy in a convective flow. In the steady case, the rate of kinetic energy generation,

$$ {E_{( + )}} = {\alpha_\rho }\rho g\int_0^{{L_0}} {\left\langle {{V_{\rm{Z}}}T\prime} \right\rangle } {\rm{d}}z, $$

(17.1.1)

must be equal to the rate of energy dissipation of convective motions due to the viscous effects:

$$ {E_{( - )}} = - \rho {\nu_{\rm{F}}}\int_0^{{L_0}} {\left\langle {\vec{V}\Delta \vec{V}} \right\rangle } {\rm{d}}z. $$

(17.1.2)

Further Reading

1.1 Convective Turbulence

• G.I. Barenblatt, Scaling Phenomena in Fluid Mechanics (Cambridge University Press, Cambridge, 1994)

• G.K. Batchelor, H.K. Moffat, M.G. Worster, Perspectives in Fluid Dynamics (Cambridge University Press, Cambridge, 2000)

• S.B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000)

• A. Tsinober, An informal Introduction to Turbulence (Kluwer Academic Publishers, The Netherlands, 2004)

• J.S. Turner, Buoyancy Effects in Fluid (Cambridge University Press, Cambridge, 1973)

1.2 Environmental Convection

• F.T.M. Nieuwstadt, H. Van Dop (eds.), Atmospheric Turbulence and Air Pollution Modeling (D. Reidel Publishing Company, Dordrecth, 1981)

• R.S. Scorer, Environmental Aerodynamics (Wiley, New Jersey, 1978)

• G. Schubert, D.L. Turcotte, P. Olson, Mantle Convection in the Earth and Planets (Cambridge University Press, Cambridge, 2008)

1.3 Pattern Formation

• Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984)

• P. Manneville, Instabilities, Chaos and Turbulence. An Introduction to Nonlinear Dynamics and Complex Systems (Imperial College Press, London, 2004)

• A. Mikhailov, Introduction to Synergetics, Part 2 (Springer, Berlin, 1995)

• L. M. Pismen, Patterns and Interfaces in Dissipative Dynamics (Springer, Berlin, 2006)