Citation
O'Gorman, Paul Ambrose (2004) Theory and simulation of passive scalar mixing in the presence of a mean scalar gradient. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05272004150652
Abstract
The turbulent mixing of a passive scalar in the presence of a mean scalar gradient was investigated using theory and simulation. The velocityscalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shellsummed energy and scalar spectra. At high Schmidt number this bound limits the possible contribution of the subKolmogorov scales to the scalar flux. At low Schmidt number we use an argument of Batchelor, Howells, and Townsend (1959) to derive a new asymptotic result for the cospectrum in the inertialdiffusive range, with a 11/3 power law wavenumber dependence. A comparison is made with results from largeeddy simulation at low Schmidt number.
The sparse directinteraction perturbation (SDIP) was used to calculate the cospectrum for a range of Schmidt numbers. The Kolmogorov type scaling result is recovered in the inertialconvective range, and the constant of proportionality was calculated. At high Schmidt numbers, the cospectrum is found to decay exponentially in the viscousconvective range, and at low Schmidt numbers the 11/3 power law is observed in the inertialdiffusive range. The stretchedspiral vortex model was used to calculate the cospectrum, and asymptotic expressions were found for the contribution to the cospectrum from the axial velocity in the vortex structures. Results are reported for the cospectrum from a direct numerical simulation at a Taylor Reynolds number of 265, and a comparison is made of results for the cospectrum from the SDIP, the stretchedspiral vortex model, simulation, and experiment.
The stretchedspiral vortex model was also used to derive expressions for the modal time correlation functions of the velocity and scalar fields. These expressions were evaluated numerically and asymptotically. Winding by the vortex core is shown to lead to an inertial timescale, and movement of the vortex structures by the large scale flow leads to a sweeping timescale. The velocity and scalar modal time correlation functions were calculated in the direct numerical simulation. They coincide for large enough wavenumber, and are found to collapse to universal forms when a sweeping timescale is used.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  closure theory; Lagrangian directinteraction approximation 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  14 May 2004 
Record Number:  CaltechETD:etd05272004150652 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05272004150652 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2136 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  28 May 2004 
Last Modified:  26 Dec 2012 02:47 
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