| description abstract | A two-layer analytical model of cold- and warm-core rings has been constructed to explore steady interactions of isolated eddies with horizontally sheared flows around and below the eddies. Steady inviscid solutions to the quasi-geostrophic equations are found by assuming that the environmental sheer is weak compared to the ring's shear. It is found that such interactions lead to elliptical rings in contrast to our expectations, the eccentricity of the rings is caused solely by the lower layer shear and is independent of the surrounding upper shear. Namely, when there is no shear in the lower layer, the ring's shape is circular, even though there may exist a surrounding upper shear. When the flow inside the ring rotates in the same direction as the lower shear, the elliptical ring in aligned along the lower layer flow. On the other hand, when the flow inside the ring rotates in the opposite direction to that of the lower shear, the elliptical ring is aligned across the lower-layer flow. Surprisingly, when the surrounding upper flow shear rotates in the opposite direction to that of the flow below the ring, a chain of weak vortices is generated outside the ring in the upper layer. This chain of vortices is a result of trapped planetary waves. When the surrounding upper flow and the lower layer flow rotate in the same sense, there are no such ambient vortices. Instead, U-turned flows on both sides of the ring are established. Possible applications of this theory to both warm- and cold-core rings are mentioned. | |
