Effect of Deformation Radius on Stability of Flow

Abstract

To study effects of deformation radius on stability of flow, we perform a linear stability analysis of a parallel shear flow whose velocity profile has a single maximum in the context of the Charney--Hasegawa--Mima equation. The linear stability analysis shows that as the deformation radius decreases, both the wavenumber and growth rate of the fastest growing mode decrease. To understand these results physically, first, the concept of resonance between neutral waves is applied. The analysis based on this concept well predicts the wavenumber of the fastest growing mode. Next, we introduce a low-degree-of-freedom system which represents a qualitative picture of the linear stability of the parallel shear flow. Combining this system with the concept of wave resonance, we derive a theoretical prediction of the growth rate of the fastest growing mode as a function of deformation radius. This prediction is in good agreement with the growth rate of the fastest growing mode calculated by the linear stability analysis.