Forma, Vol. 7 (No. 2), pp. 107-120, 1992
Original Paper

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.