Structure and Energetics of Non-geostrophic Non-hydrostatic Baroclinic Instability Wave with and without Convective Heating

Abstract

Non-geostrophic non-hydrostatic baroclinic instability with and without convective heating is reexamined with an emphasis on the structure and energy budget of growing modes. When the convective heating is absent, only a baroclinic instability mode has a positive growth rate for Ri = 2, where Ri is the Richardson number. The growth rate for a mode with meridional wavenumber l (l > 0) is proved to be exactly equal to that with -l. However, the energy budgets for the modes with ±l are found to be quite different: the mode with l (&> 0) gains its eddy kinetic energy (EKE) from both eddy available potential energy (EAPE) and mean kinetic energy (MKE), while the mode with -l gains EKE from EAPE, but loses it to MKE. When the convective heating is included, at least two different growing modes are found to exist for Ri = 2: One is a baroclinic instability mode (B-mode), modified by the convective heating, and the other a symmetric instability mode (S-mode) destabilized by the convective heating. The convective heating increases the growth rates of B-mode with l (> 0) more remarkably than that with -l. Energy budget analysis shows that the energy conversion between MKE and EKE is little affected by the convective heating, but that from EAPE to EKE increases more for the mode with l than for that with -l, resulting in a larger growth rate for the mode with l. For the most unstable wavenumber, B-mode has an eastward tilt of the trough with increasing height in the lower layer and a cold air to the east of the surface trough. The thermodynamic analysis shows that this cold air is caused by adiabatic cooling at the low-levels due to the updraft driven by the convective heating at the mid- and upper-levels. The present results give a useful basis for understanding the dynamics of meso-a-scale disturbances along the Baiu front and polar lows.