Spontaneous Singularity Formation in the Shape of Vortex Sheet in Three-Dimensional Flow

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概要

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• The three-dimensional motion of a flat uniform vortex sheet slightly perturbed initially in both streamwise and spanwise directions is studied on the basis of a Lagrangian representation of the motion. The vortex sheet at time t is represented as R(λ_1, λ_2, t)=(λ_1, λ_2, 0)+Σ_<n, m>A_<n, m>(t) exp i(nλ_1+mδλ_2), where λ_1 and λ_2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. The behaviour of A n, 0 and A_<n, 1> is studied by an asymptotic analysis valid at large t. The analysis shows that singularity appears on the sheet at a critical time O(ln (ε^<-1>_1)), where ε_1 is the initial amplitude of the streamwise disturbance. The singularity is such that A_<n, 0> behaves like n^<-5/2> while A_<n, 1> behaves like n^<-3/2>, for large n. The latter is associated with the vortex stretching intrinsic in three-dimensional dynamics of the sheet.

• 社団法人日本物理学会の論文
• 1994-02-15

著者

• Kaneda Yukio

  Department Of Applied Physics Faculty Of Engineering Nagoya University

• Ishihara Takashi

  Department Of Applied Physics Nagoya University

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