Optimal Excitation of Asymmetric Perturbations on an Axisymmetric Barotropic Vortex: A Linear Singular-Value Analysis

摘要: AbstractSingular vectors on a barotropic circular vortex consisting of three regions piecewise-constant vorticity are investigated under the L2 norm to reveal shape and growth rate possible perturbations that may contribute formation hierarchal structure seen in natural artificial vortices. Here, analytical form singular values forward backward derived for comparison with corresponding eigenvalues vectors. The results indicate no notable difference between growing eigenvector Michalke Timme’s profile, which is characterized by ring high vorticity. In contrast, Syōno’s incorporates negative region solidly rotating core potentially surroundings, pattern vector giving maximum specified time interval differs crucially from eigenvector: whereas radial peak streamf...