BIFURCATION AT KIRCHHOFF ELLIPTIC VORTEX WITH ECCENTRICITY 2-ROOT-2 3/

Consider vortex motion of an incompressible inviscid flow in the plane . Love showed that for the series of Kirchhoff elliptic vortices, vort ices become unstable if and only if their eccentricities have values > 2 root 2/3. In this paper, we show that: there exists a family of non -elliptic rotating vortex patches which bifurcates from an elliptic vo rtex with eccentricity 2 root 2/3. These non-elliptic rotating vortex patches are unstable. This result confirms that the Kirchhoff vortex i s manifestly unstable at the bifurcation. We use the momentum-energy m ethod for this bifurcation problem. The relevant third- and fourth-ord er coefficients of the argumented energy function are calculated symbo lically by Maple V and evaluated numerically by Matlab.