Asymptotic analysis and renormalized perturbation theory of the non-Hermitian dynamics of an inviscid vortex.
An analysis of the non-Hermitian fluid systems described by the Rayleigh equation in an unbounded domain has been carried out in the regime of large wave numbers. The evolution of a special class of localized vorticities is also discussed. Asymptotic and perturbative approaches lead to the same final result. In the limit considered, the system is stable. The perturbation analysis reveals interesting pathologies of the non-Hermitian systems. Under specific conditions, the expansion is found to show secular growth. A discussion about the mechanism of insurgence of such singular behavior is presented. It is also shown that the divergent expansion is renormalizable by means of the renormalization group method-the renormalized results are in complete conformity with the asymptotic solutions.
Volponi
F
F
Graduate School of Engineering, The University of Tokyo, Japan. fvolponi@plasma.q.t.u-tokyo.ac.jp
Mahajan
S M
SM
Yoshida
Z
Z