Advances in Geosciences www.adv-geosci.net 1680-7340 1680-7359 15 Topics in modern geophysical fluid dynamics 2009 10.5194/adgeo-15-57-2009 http://www.adv-geosci.net/15/57/2009/ http://www.adv-geosci.net/15/57/2009/adgeo-15-57-2009.html http://www.adv-geosci.net/15/57/2009/adgeo-15-57-2009.pdf 57 63 2009-02-23 Model of oscillatory instability in vertically-homogeneous atmosphere P. B. Rutkevich peter@d902.iki.rssi.ru P P. Rutkevych Space Research Institute (IKI), Moscow, Russia Institute of high performance computing, Singapore Existence and repeatability of tornadoes could be straightforwardly explained if there existed instability, responsible for their formation. However, it is well known that convection is the only instability in initially stable air, and the usual convective instability is not applicable for these phenomena. In the present paper we describe an instability in the atmosphere, which can be responsible for intense vortices. This instability appears in a fluid with Coriolis force and dissipation and has oscillatory behaviour, where the amplitude growth is accompanied by oscillations with frequency comparable to the growth rate of the instability. In the paper, both analytical analysis of the linear phase of the instability and nonlinear simulation of the developed stage of the air motion are addressed. This work was supported by the RFBR grant no. 09-05-00374-a. Arnold, V. I., Gusein-Zade, S. M., and Varchenko, A. N.: Singularities of differentiable maps, Vol 1, Birkhauser Boston Inc., 1988. Bengtsson, L. and Lighthill, J. (Eds.): Intense atmospheric vortices, Springer-Verlag, 1982. Doswell III, C. A. and Burgess, D. W.: Tornadoes and tornadic storms: A review of conceptual models, in: The Tornado: Its Structure, Dynamics, Prediction and Hazards, edited by: Church, C., Burgess, D., Doswell, C., Davies-Jones, R., Geophys. Monogr. 79, Amer. Geophys. Union, 161–172, 1993. Landau, L. D. and Lifshitz, E. M.: Fluid mechanics, 2nd Ed., Butterworth-Heinemann, 1987. Lupyan, E. A., Mazurov, A. A., Rurkevich, P. B., and Tur, A. V.: Generation of large-scale nortices through the action of spiral turbulence of a covectine nature, Sov. Phys. JETP, 75, 833–838, 1992. Monin, A. S. and Yaglom, A. M.: Statisticheskaya Gidromekhanika, Parts 1, 2 (Statistical Fluid Mechanics), Moscow, Nauka, 1965, 1967 (Translated into English, Cambridge, Mass., MIT Press, 1971, 1975.). Morgulis, A. B. and Yudovich, V. I.: Doklady Physics, 46(10), 736–739, 2001 (Translated from Doklady Akademii Nauk, 380(5), 623–626, 2001.). Rasmussen, E. N., Straka, J. M., Davies-Jones, R., Doswell III, C. A., Carr, F. H., Eilts, M. D., and MacGorman, D. R.: Bulletin of American Meteorological Society, 75(6), 995–1006, 1994. % %Rutkevich P.B. and Rutkevich P.P., On horizontal modes interaction in tornado %structure, Singapore Journal of Physics, \bf 19(1), p. 99-111, (2002). % %Rutkevich P.B., Rutkevich P.P., and L.S. Rozumenko, %On Tne Tornado funnel origin, %Moscow, IKI RAS, Pr-2074, 14~p. (2002). Wurman, J.: Weather and forecasting, 17, 473–505, 2002. Zavolzhenskii, M. V.: Model for the hydrodynamic structure of a steady-state tornado, Izvestiya, Atmospheric and Oceanic Physics, 38(1), p 48, 2002.