Epi-Two-Dimensional Fluid Flow: A New Topological Paradigm for Dimensionality

Journal Article · Mon Dec 11 00:00:00 EST 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.119.244501· OSTI ID:1541257

Yoshida, Z. ^[1]; Morrison, P.  J. ^[2]

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1. Univ. of Tokyo, Kashiwa (Japan). Dept. of Advanced Energy
2. Univ. of Texas, Austin, TX (United States). Dept. of Physics

While a variety of fundamental differences are known to separate two-dimensional (2D) and three-dimensional (3D) fluid flows, it is not well understood how they are related. Conventionally, dimensional reduction is justified by an a priori geometrical framework; i.e., 2D flows occur under some geometrical constraint such as shallowness. However, deeper inquiry into 3D flow often finds the presence of local 2D-like structures without such a constraint, where 2D-like behavior may be identified by the integrability of vortex lines or vanishing local helicity. Here we propose a new paradigm of flow structure by introducing an intermediate class, termed epi-two-dimensional flow, and thereby build a topological bridge between 2D and 3D flows. The epi-2D property is local and is preserved in fluid elements obeying ideal (inviscid and barotropic) mechanics; a local epi-2D flow may be regarded as a “particle” carrying a generalized enstrophy as its charge. A finite viscosity may cause “fusion” of two epi-2D particles, generating helicity from their charges giving rise to 3D flow.

• Research Organization: Univ. of Texas, Austin, TX (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Fusion Energy Sciences (FES)
• Grant/Contract Number: FG02-04ER54742; 15K13532; 17H01177; FG02-04ER-54742
• OSTI ID: 1541257
• Alternate ID(s): OSTI ID: 1412630
• Journal Information: Physical Review Letters, Vol. 119, Issue 24; ISSN 0031-9007
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English