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Title:  Macroscopic effects of Lagrangian velocity noise in turbulent flow 
Author(s):  Shen, Hubert HsuehHan 
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 bestestimate (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 meanincompressible flow with spatiallyintermittent turbulent intensity. Arguments for a mean mass current due to inhomogeneous selfdiffusion are suggested (with implications for entrainment.) Contributions of V*u to pressure and (wavevectordependent) temperature are calculated using kinetic and linearresponse 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 w2, 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 HsuehHan Shen 
Date Available in IDEALS:  20120123 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics
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