Nonlinear instability of baroclinic atmosphere with reference to planetary scale disturbances

Abstract. 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.