Middle-Scale Structure of Point Vortex Clouds

Ryuji Takaki¹ and Masaki Utsumi²

¹Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan
²Fuchu Works, Toshiba Corporation, Fuchu, Tokyo 183, Japan

(Received September 30, 1990; Accepted August 31, 1991)

Keywords: Point vortex, Fractal, Energy Spectrum, Configuration temperature

Abstract. Behavior of a vortex cloud composed of 1000 point vortices in a 2D inviscid fluid is studied numerically on the basis of Biot-Savart law. Quantities characterizing its structure smaller than the size of the whole cloud are calculated, such as an exponent -a of energy spectrum, a quantity Q characterizing vortex concentration, a fractal dimension D and a configuration temperature q defined by Novikov. Initial condition is a random distribution of point vortices in a circle or a square region. If circulations of vortices are equal, a and D were seen to approach to constant values of about 3.7 and 1.7, respectively, and q remained constant, while if circulations of both signs are mixed, a~1, D decreased to a value less than 1.3 and q continued to increase. In both cases the quantity Q decreased.