Yuichi Yatsuyanagi, Tadatsugu Hatori
Mechanism of self-organization in unbounded, double-species, two-dimensional (2D) point vortex system is discussed. A kinetic equation is obtained using the Klimontovich formalism. No axisymmetric flow is assumed. The obtained collision term consists of a diffusion and a drift term similar to the Fokker-Planck type collision term. It is revealed that a mechanism for the 2D inverse cascade is mainly provided by the drift term, as the sign of the drift term for the negative vortices is opposite from the one for the positive vortices. When the system reaches a quasi-stationary state near the thermal equilibrium with negative absolute temperature, $d \omega / d \psi$ is expected to be positive, where $\omega$ is the vorticity and $\psi$ the stream function. In this case, the diffusion term dissipate the mean field energy, while the drift term produces the mean field energy. As a whole, the mean field energy is conserved. Similarly, the diffusion term increases the entropy, while the drift term decreases the entropy. As a whole, the entropy production is positive (H theorem). It ensures that the system relaxes to the global thermal equilibrium state.
View original:
http://arxiv.org/abs/1304.7306
No comments:
Post a Comment