科研之友
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摘要
The theory of inhomogeneous superfluid turbulence is developed on the basis of kinetics of merging and splitting vortex loops. Vortex loops composing the vortex tangle can move as a whole with some drift velocity depending on their structure and length. The flux of length, energy, momentum, etc., executed by the moving vortex loops takes place. The situation here is exactly the same as in usual classical kinetic theory, with the difference being that the "carriers" of various physical quantities are not the point particles but extended objects (vortex loops), which possess an infinite number of degrees of freedom, with highly involved dynamics. We suggest to complete our investigation, based on the supposition that vortex loops have a Brownian structure, with the only degree of freedom being, lengths of loops l. This concept allows us to study the dynamics of the vortex tangle on the basis of the kinetic equation for the distribution function n(l, t)-the density of a loop in the space of their lengths. Imposing the coordinate dependence on the distribution function n(l, r, t) and modifying the "kinetic" equation with regard to an inhomogeneous situation, we are able to investigate various problems on the transport processes in superfluid turbulence. In this paper, we evaluate the flux of the vortex line density L(x, t) due to the gradient of this quantity. The corresponding evolution of quantity L(x, t) obeys the diffusion type equation, as it can be expected from dimensional analysis. The diffusion coefficient is arrived at from calculation of the (size-dependent) free path and drift velocity of the vortex loops, and takes the value 2.2 kappa, which exceeds approximately 20-fold the value obtained in early numerical simulation. We discuss the probable reason for this large discrepancy. We use the diffusion equation to describe the decay of the vortex tangle at a very low temperature. Comparison with recent experiments on decay of the superfluid turbulence is presented.
- 出版日期2010-2
