Shibboleth / Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.Ĭhoose this option to get remote access when outside your institution. Typically, access is provided across an institutional network to a range of IP addresses. If you are a member of an institution with an active account, you may be able to access content in one of the following ways: Get help with access Institutional accessĪccess to content on Oxford Academic is often provided through institutional subscriptions and purchases. While conventional stability analysis does not apply to these families of steady normal-mode vortices, there is a latent algebraic instability in terms of linearly growing offspring vortices evolving from an initial state where a small initial perturbation is added to the steady normal-mode vortex. One such example is demonstrated, where the circle sector has an angle of |$63.77^\circ$|. In a circle sector with a designed angle, it is possible to add two fully 2D normal-mode vortices so that their superposed flow is steady. This eigenvalue has to be dictated by a normal-mode vortex that is fully 2D. The requirement for steady flow is that the wavenumber eigenvalues for the Helmholtz equations are identical. A way to satisfy the vorticity equation with two superposed normal-mode vortices is to let one of them have circular streamlines, trivially satisfying the kinematic boundary condition at the circle boundary. An individual normal-mode vortex satisfies the steady 2D vorticity equation. A normal-mode vortex is a continuous vortex that satisfies a Helmholtz equation for the streamfunction. This article establishes elementary families of steady two-dimensional (2D) vortices in circular enclosures filled with inviscid fluid.