Shear layer instability in a highly diffusive stably stratified atmosphere

The linear stability of a shear layer in a highly diffusive stably stratified atmosphere has been investigated. This study completes and extends previous works by Dudis (1974) and Jones (1977). We show that: (i) an asymptotic regime is reached in the limit of large thermal diffusivity, (ii) there exists two different types of unstable modes. The slowest growing modes correspond to predominantly horizontal motions and the fast growing ones to isotropic motions, (iii) the physical interpretation of the stability properties in this asymptotic regime is simple. Applications to the dynamics of stellar radiative zone are discussed.