Axially Symmetric Meridional Motions in the Baroclinic Circular Vortex: a Numerical Experiment

[摘要] The time evolution of symmetric meridional motions in various unstable baroclinic circular vortices in an incompressible and inviscid fluid is studied by numerical integration of the hydrodynamic equations as an initial value problem. The fluid is bounded in a rectangular domain. Several types of the initial balanced state are considered. All the types belong to Ooyama's (1966) Class (C) vortices, i. e., there exist negative eigenvaues of the stability tensor somewhere in the domain.The results of the numerical experments demonstrate the sufficiency of the above condition for an unlimited growth of the meridional motion from certain types of initial disturbances. The growth rate of the meridional motion primarily depends on the smallest eigenvalue of the stability tensor, but it also depends on the ratio of the smallest to the largest eigenvalue in the domain. When the ratio is small, the growth of the meridional motion becomes very sensitive to the choice of initial perturbations. The preferred orientation of the meridional motion coincides with that expected from the linear theory which assumes no boundaries. When only a part of the domain is unstable, the development of the meridional motion is confined within the unstable subdomain. The direction of energy transformations between the meridional kinetic energy and the zonal kinetic energy and between the meridional kinetic energy and the potential energy is discussed.

[学科分类] 大气科学