TOPOLOGICALLY RELATED QUANTITIES IN TURBULENT FLOWS.
Item
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Title
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TOPOLOGICALLY RELATED QUANTITIES IN TURBULENT FLOWS.
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Identifier
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AAI8801687
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identifier
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8801687
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Creator
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CASSIDY, WILLIAM ALFRED.
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Contributor
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Benjamin G. Levich | Evgeny V. Levich
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Date
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1987
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Fluid and Plasma
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Abstract
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The purpose of this work is to study the role of changes in the topology of the vortex field in the development of turbulence. Analytical work on helicity and representability in terms of Clebsch variables is presented relating both to the instantaneous topology of the vortex field and to the dynamics of the time development of the fields in the case of incompressible, Newtonian flows. It is found that, at a given point, the topological changes relating to helicity and Clebsch representability are due to only one component of the viscosity term in the Navier-Stokes, that component which is parallel to the vorticity at the point. When this component of the viscosity term is subtracted a modified Navier-Stokes equation results which conserves helicity and Clebsch representability. Some analytical properties of the resulting equation are discussed.;The simulation of the resulting equation is discussed and the results are presented. The usual statistics of the resulting flow fields are presented as well as some more novel ones. Comparing the simulation results of the usual and modified Navier-Stokes equations, the most remarkable differences that emerge are related to the nonlinearity of the modified viscosity term rather than the conservation of helicity and Clebsch representability. The growth of helicity spectral density is observed for the lowest wave-number modes, and appears insensitive to the preservation of Clebsch representability and conservation of total helicity as well. It is concluded that conservation in time of total helicity and preservation of Clebsch representability do not prevent the development of turbulence. Suggestions of the implications of this to possible further research are given.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Engineering
