On the kinetic energy of the divergent and nondivergent flow in the atmosphere

Abstract

The kinetic energy of horizontal flow in a hydrostatic atmosphere is divided into the kinetic energies of its divergent and nondivergent components. The law of conversion between these two energies for large-scale flows in the atmosphere is derived and discussed using balanced and unbalanced models of circulations in the atmosphere. It is shown that the total potential energy is converted into the kinetic energy of the divergent flow which, in turn, is converted into the kinetic energy of the nondivergent flow. These energy conversions are equal in a so-called balanced model, but may differ in a model based on the primitive equations. The analysis shows that the kinetic energy reservoir of the divergent part of the flow may play a quasi-catalytic role in the energy conversion between the total potential energy and the kinetic energy of the nondivergent flow. Two sets of data, the history data generated by the NCAR GCM of a January simulation, and the NMC wind data and FNWC height field of August 1 to 15 of 1970, were used to evaluate the energies and energy conversions. The computations confirm the direction of energy conversions in the theoretical argument and the quasi-catalytic nature of the kinetic energy of the divergent part of the flow. The energy conversions between the total potential energy and the kinetic energy of the divergent flow occurs mainly in the lower layers of the atmosphere at middle latitudes where the baroclinic eddy activities are dominant. The energy conversion between the kinetic energies of the divergent and the nondivergent flows is mostly carried out by the Coriolis effect. In other words, the quasi-geostrophic model explains most of this energy conversion. The introduction of a more sophisticated model gives small improvement as far as the magnitude of energy is concerned.