Eigenvalue problem for Lagrangian systems. VIII. Eigenvalue bounds with application to fluid and plasma flows

Circle theorems are obtained which furnish bounds for the complex eigenvalues arising from the linear stability analysis of states of steady motion of conservative dynamical systems. These results generalize the well-known circle theorems of Howard, Eckart, and others for fluid flows to arbitrary gyroscopic Lagrangian systems. Explicit bounds are obtained for the plane parallel flows of an inviscid fluid and a multicomponent plasma. YAG