The criterion of dynamic stability of zonal motion including the vertical shear

Summary Many writers treated on the problem of dynamic instability of westerly flow due to the excessive horizontal shear, and the present author discusses the corresponding dynamic instability due to the vertical shear. The critical vertical shear in indifferent stratification is given by the condition — the meridional component of absolute vorticity vanishes, — and is an approximate negative valueof 10^–4sec^–1 in middle latitude. However the critical vertical shear in normal stable stratification is a fairly large negative value of 2 sec^–1. It might be emphasized that the problem of this study differs fromRichardson's criterion of turbulence, for the present author discusses the condition under which the zonal flow is dynamically stable, whileRichardson expressed the condition under which the turbulence will decrease.