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On vortex air motions above an axisymmetric source of mass, momentum and heat

Published online by Cambridge University Press:  26 April 2006

Y. A. Berezin  and
K. Hutter
Y. A. Berezin
Affiliation:
Institute for Theoretical and Applied Mechanics, Novosibirsk 630090, Russia
K. Hutter
Affiliation:
Institute for Theoretical and Applied Mechanics, Novosibirsk 630090, Russia Institut für Mechanik, Technische Hochshule, 64289 Darmstadt, Germany
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Abstract

We study axisymmetric plume dispersion from a steady source of mass, momentum and/or heat that is subjected to either a time-dependent large-scale external vortex or small-scale turbulent axisymmetric helicity. On the basis of the turbulent boundary layer and Boussinesq assumptions and by assuming similarity profiles with Gaussian distribution in the radial direction the balance equations of mass, momentum, and energy reduce to a system of nonlinear differential equations for amplitude functions of axial velocity, pressure and density differences as well as azimuthal velocity. The system of equations is closed with Taylor's entrainment assumption.

The plume radius and the typical radius of the large-scale external vortex are also determined. For a simple density structure of the ambient atmosphere (i.e. adiabatic conditions) analytical results can be obtained, but for more complicated cases, i.e. a layered polytropic atmosphere, the governing equations are examined numerically; computations are reasonably simple and efficient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 290 , 10 May 1995 , pp. 299 - 317
Copyright
© 1995 Cambridge University Press

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References

Berezin, Y. A., Hutter, K. & Zhukov, V. P. 1991 Large-scale vortical structure supported by small-scale turbulent motions. Helicity as a cause for inverse energy cascade. Continuum Mech. Thermodyn. 3, 127–146.Google Scholar
Carrier, G. F., Fendell, F. E. & Feldman, P. S. 1985 Firestorms. Trans. ASME E: J. Heat Transfer 107, 154–189.Google Scholar
Gostintsev, Y. A., Kopylov, N. P., Ryzhov, A. M. & Khasanov, I. R. 1991 Numerical modelling of convective motions over large fires under different atmospheric conditions. Phys. Combust Explosion 27, 10–17 (in Russian).Google Scholar
Grishin, A. M., Gruzin, A. D. & Zverev, V. G. 1983 Mathematical modelling of the forest fire propagation. Soviet Dokl. 269, 822–826 (in Russian).Google Scholar
Levich, E., Shtilman, L. & Tur, A. V. 1991 The origin of coherence in hydrodynamical turbulence. Physica A 176, 241–296.Google Scholar
Long, R. R. 1967 Firestorms. Fire Res. Abstr. Rev. 9, 53–68.Google Scholar
Markatos, N. C. & Pericleous, K. A. 1984 An investigation of three-dimensional fires in enclosures. Rev. Gen. Therm. 266, 67–78.Google Scholar
Small, R. D. & Heikes, K. E. 1988 Early cloud formation by large area fires. J. Appl. Meteorol. 27, 654–663.Google Scholar
Small, R. D. & Larson, D. A. 1984 Velocity fields generated by large fires. Isr. J. Technol. 22, 173–186.Google Scholar
Smith, R. K., Morton, B. R. & Leslie, L. M. 1975 The role of dynamic pressure in generating fire wind. J. Fluid Mech. 68, 1–19.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar