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Macroscopic effects of Lagrangian velocity noise in turbulent flow

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Title: Macroscopic effects of Lagrangian velocity noise in turbulent flow
Author(s): Shen, Hubert Hsueh-Han
Doctoral Committee Chair(s): Wyld, H.W.
Department / Program: Physics
Discipline: Physics
Degree: Ph.D.
Genre: Dissertation
Subject(s): lagrangian velocity noise eulerian velocity field turbulent flow
Abstract: In the first part of the thesis, we discuss the implications of Lagrangian velocity noise for the Eulerian velocity field and the time evolution of the position of a fluid element. We find that the best-estimate (in the mean square sense) of the velocity field (given the velocity and deformation at a single point) in a turbulent flow is attained when the fluid particle position r obeys a generalized Langevin equation. A particular class of estimates is found to optimize an uncertainty principle. A Schrodinger analogy is noted. In the second part of the thesis, we discuss the implications of Lagrangian velocity noise for the time evolution of the volume of a fluid element. We show how mean velocity may be nonsolenoidal in a mean-incompressible flow with spatially-intermittent turbulent intensity. Arguments for a mean mass current due to inhomogeneous self-diffusion are suggested (with implications for entrainment.) Contributions of V*u to pressure and (wavevector-dependent) temperature are calculated using kinetic and linear-response arguments (with implications for jet noise and energy spectra). In the third part of the thesis, we discuss the implications of Lagrangian velocity noise for the spatial and temporal evolution of the boundaries of turbulent eddies (viewed here as regions of high enstrophy |w|2, where w is the vorticity V*w.) The evolution in space of the enstrophy gradient for a steady Beltrami flow (modelling turbulent coherent structures) is found to be approximately given by a Langevin equation with quadratic colored noise. Solving for the probability distribution, one finds a change in the character of the solution above a certain noise intensity threshold. An approach to temporal evolution is indicated.
Issue Date: 1988
Genre: Dissertation / Thesis
Type: Text
Language: English
URI: http://hdl.handle.net/2142/28684
Rights Information: 1988 Hubert Hsueh-Han Shen
Date Available in IDEALS: 2012-01-23
 

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