Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 11 3 2004 10.5194/npg-11-363-2004 http://www.nonlin-processes-geophys.net/11/363/2004/ http://www.nonlin-processes-geophys.net/11/363/2004/npg-11-363-2004.html http://www.nonlin-processes-geophys.net/11/363/2004/npg-11-363-2004.pdf 363 370 2004-08-02 Nonlinear instability of baroclinic atmosphere with reference to planetary scale disturbances I. A. Pisnichenko Center for Weather Forecasting and Climate Studies/Brazilian National Institute for Space Research, Brazil, on leave from A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia In this paper we investigate the stability of zonal flow in a baroclinic atmosphere with respect to finite-amplitude planetary-scale disturbances by applying Arnold's method. Specifically, we examine the sign of the second variation of a conserved functional for the case of a polytropic atmosphere (i.e. one with a linear lapse rate) and with a linear profile of zonal wind. Sufficient stability conditions for an infinite atmosphere (i.e. with a temperature lapse rate equal to zero) are satisfied only for an atmosphere in solid body rotation. For a polytropic atmosphere of finite extent (a lapse rate is not equal zero) the sufficient conditions of stability can be satisfied if a lid is placed below min (Z_max, polytropic atmospheric height). The dependence of height Z_max on values of the vertical gradient of the zonal wind and the zonal temperature distribution is calculated.