Nonlinear instability of baroclinic atmosphere with reference to planetary scale disturbances

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 (Zmax, polytropic atmospheric height). The dependence of height Zmax on values of the vertical gradient of the zonal wind and the zonal temperature distribution is calculated.

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

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.

Instabilities in a Polytropic Atmosphere

The density in the outer layers of stars varies by several orders of magnitude and it is desirable to include the full effects of compressibility in any study of instabilities arising in stellar convection zones. In an unstable compressible fluid-layer that is thermally conducting both the oscillatory and non-oscillatory motions can simultaneously arise. The conditions under which the oscillatory acoustic modes can be overstabilized in a polytropic atmosphere are examined. It is argued that the linearized perturbation theory breaks down when applied to an inviscid complete polytrope which has vanishing density and temperature at the top for both optically-thin and optically-thick approximations. However, the linearized theory is demonstrated to be self-consistent when viscosity and thermal conductivity are included in the study of complete polytropes.