Local instability of an elliptical flow subjected to a Coriolis force :

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Abstract

We make the local stability analysis of a rotating flow with circular or elliptically strained streamlines, subjected to a Coriolis force, based on the WKB method. For the case of slow precession, without strain, the growth rate takes the same value as that of Kerswell (1993) though the basic flow is different. In the absence of strain, the growth rate approaches the angular velocity of the basic flow as the precessional angular velocity is increased. The cooperative action of the weak Coriolis force and the elliptical straining field is investigated both numerically and analytically. An analysis of using the Mathieu method reveals that the elliptical instability is weakened by the precession, while that the precessional instability is either enhanced or weakened depending on the orientation of the strain.

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