A moving boundary model motivated by electric breakdown: II. Initial value problem

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Kao, C. -Y.²  Brau, F.^1,3  Ebert, U.^1,4  Schaefer, L.⁵  Tanveer, S.² 

[1] CWI, NL-1090 GB Amsterdam, Netherlands

[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[3] Univ Mons, Acad Univ Wallonie Bruxelles, Grp Phys Nucl Theor, B-7000 Mons, Belgium

[4] Eindhoven Univ Technol, Dept Phys, NL-5600 MB Eindhoven, Netherlands

[5] Univ Duisburg Essen, Fachbereich Phys, D-47048 Duisburg, Germany

关键词: Moving boundary;    Kinetic undercooling regularization;    Initial value problem;    Laplacian instability;    Electric breakdown;   

DOI  :  10.1016/j.physd.2010.03.011

来源: Elsevier

【 摘 要 】

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for t -> infinity, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free