000013957 001__ 13957
000013957 005__ 20161115094006.0
000013957 04107 $$aeng
000013957 046__ $$k2016-08-21
000013957 100__ $$aMcLaughlin, Richard
000013957 24500 $$aGeometric Control of Asymmetries in Passive Scalars Advected in Rectangular and Elliptical Pipes

000013957 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000013957 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000013957 506__ $$arestricted
000013957 520__ $$2eng$$aWe explore the role different geometries (amongst rectangular and elliptical domains of arbitrary aspect ratios) play in controlling emerging up-stream/downstream asymmetries in the cross-sectionally averaged distribution of diffusing passive scalars advected by laminar, pressure driven shear flows. We show using a combination of rigorous analysis, asymptotic expansions, and Monte-Carlo simulations, that on short time scales relative to the shortest diffusion times, elliptical domains preserve initial uptream/downstream symmetric distributions, while rectangular ducts break this symmetry. Skinny ducts produce distributions with negative skewness, while fat ducts produce positive skewness for symmetric initial data which is uniformly distributed in the cross-section. There is a special aspect ratio of approximately 2-1 ratio for which symmetry is preserved. In turn, long-time (relative to the longest diffusion timescale) exact analysis shows that all geometries generically break symmetry before ultimately symmetrizing in infinite time.

000013957 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013957 653__ $$a

000013957 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000013957 720__ $$aMcLaughlin, Richard
000013957 8560_ $$ffischerc@itam.cas.cz
000013957 8564_ $$s31878$$uhttps://invenio.itam.cas.cz/record/13957/files/PO.FM11-1.08.68.pdf$$yOriginal version of the author's contribution as presented on CD, XMLout( page 1238, code PO.FM11-1.08.68).
000013957 962__ $$r13812
000013957 980__ $$aPAPER