On the development of baroclinic waves influenced by friction and heating

Abstract

The influence of surface skin friction and a specific type of heating on the stability of baroclinic waves in a two-level, quasi-geostrophic model is investigated. It is found that the effect of friction alone changes the neutral stability curve in such a way that a broader band of wavelengths are unstable for a given value of the vertical windshear. The neutral stability curve is independent of the intensity of friction in this case. The effect of heating is to make all waves longer than a certain critical wave length unstable, but the amplification rate is very small for large values of the wavelength. The combined effect of friction and heating will in general tend to stabilize the waves. The amplification rate is investigated in all cases. Numerical integrations of the linearized equations show that the flow in the stable case will reach a steady state characterized by vanishing dissipation and heat transport, but with a certain wave length dependent ratio between the kinetic energy of the vertical shear flow and the vertical mean flow. It is shown that this ratio can be predicted from the steady state solutions in the adiabatic, frictionless case. A comparison is made between the predictions of the energetics of the waves in the model and observational studies.