Abstract:
We calculate the topological noise characterizing the direction of line vortices in superfluid and classical turbulence by finding the intersection of line vortices with square surfaces of edge length $l_s$ positioned normal to three orthogonal axes. In the case of homogeneous superfluid turbulence in thermal counterflow, we find that the noise scales like $l_s$ along the two directions normal to the counterflow and like $l_s^{3/2}$ along the direction parallel to it. In homogeneous isotropic superfluid turbulence at $T\rightarrow 0\,$K, the noise scales like $l_s^{7/4}$. In homogeneous isotropic classical turbulence the scaling is $l_s^{2}$. We offer possible interpretations of the computed scalings, as well as, justification for their differences.
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