http://arxiv.org/abs/1910.04638
The helicity-effect problem for a single compressible flow is transformed to the pure-background-field-effect one, reducing to the pure (compressible-version) Taylor-Proudman effect (TPE) and/or its magnetic analogue. A chiral base flow/field (CBF) is used to mostly clearly and simply materialize the screw-and-knot scenario for the `tightening-up’ notion, raised from the statistical result of helicity-reducing-turbulence-compressibility effect found earlier for the neutral-gas case. In the CBF, the existence of helicity nontrivially indicates a kind of mean rotation, naturally invoking the compressible version of the TPE, with horizontal-compressibility reduction but without direct constraint on the vertical velocity, which serves as the genuine mechanism, \textit{i.e.}, the underlying element of the statistical effect. The statistical fluctuations in the compressibility reduction effect may be due to that of the variation of the vertical derivative of the vertical velocity. A minimal working model with disorders in the CBFs bridges the single-flow and statistical arguments, completing the story. I further argue \textit{a posteriori} that recent data, of the superfluid and Bose-Einstein condensate model, also agree the result from my previous \textit{a priori} analysis. Statistical mechanical analyses, of compressible magnetohydrodynamics (MHD) and extended MHD for the ionized gas flows, show that helicities may reduce compressive and density modes relevant to the compressibility, i.e., tightening up the ionized-gas turbulence, implying the \textit{universality} of the notion. And, a \textit{unified} view is offered, with substantial extensions of the CBF and the analogue of the compressible TPE for a strong background magnetic field encapsulating the geometry of the Alfv\’en theorem for the (magnetised) plasma.
J. Zhu
Fri, 11 Oct 19
54/76
Comments: 2 figures