Citation
BermejoMoreno, Ivan (2008) On the nonlocal geometry of turbulence. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05092008173614
Abstract
A multiscale methodology for the study of the nonlocal geometry of eddy structures in turbulence is developed. Starting from a given threedimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multiscale decomposition based on the curvelet transform is applied to the full threedimensional field, resulting in a finite set of component fields, one per scale. Second, by isocontouring each component field at one or more isocontour levels, a set of closed isosurfaces is obtained that represents the structures at that scale. For periodic domains, those structures intersecting boundaries are reconnected with their continuation in the opposite boundaries. The characterization stage is based on the joint probability density function (jpdf), in terms of area coverage on each individual isosurface, of two differentialgeometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the isosurface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the jpdf of each structure, that specify its location as a point in a multidimensional 'feature space'. At each scale the set of points in feature space represents all structures at that scale, for the specified isocontour value. This allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 512^3 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Re_{lambda}=265). These show transition, with decreasing scale, from bloblike structures in the larger scales to blob and tubelike structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheetlike structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behavior of passive scalar stirring and mixing by turbulence are discussed. We apply the same methodology to the enstrophy and kinetic energy dissipation rate instantaneous fields of a second numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256^3, 512^3 and 1024^3 grid points, with k_{max}bar{eta} approximately 1, 2, and 4, respectively, the same initial conditions and Re_{lambda}approx 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from bloblike and moderately stretched tubelike shapes at the large scales to highly stretched sheetlike structures at the small scales. The intermediate scales show a predominance of tubelike structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency toward structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256^3 grid resolution case (k_{max}bar{eta}approx 1) was unable to detect the predominance of highly stretched sheetlike structures at the smaller scales. The same methodology, but without the multiscale decomposition, is then applied to two scalar fields used by existing local criteria for the eduction of tube and sheetlike structures in turbulence, Q and [A_{ij}]_+ respectively, obtained from invariants of the velocity gradient tensor and alike in the 1024^3 case. This adds the nonlocal geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally we introduce a new methodology for the study of proximity issues among different sets of structures, based also on geometrical and nonlocal analyses. We apply it to four of the fields previously studied. Tubelike structures of Q are mainly surrounded by sheets of [A_{ij}]_+, which appear at close distances. For the enstrophy, tubelike structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  geometry; multiscale; nonlocal; turbulence 
Degree Grantor:  California Institute of Technology 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  18 April 2008 
Author Email:  ivan.bermejo.moreno (AT) gmail.com 
Additional Information:  2008 William F. Ballhaus Prize for outstanding doctoral dissertation in aeronautics 
Record Number:  CaltechETD:etd05092008173614 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05092008173614 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1713 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  30 May 2008 
Last Modified:  05 Mar 2013 21:58 
Thesis Files

PDF (00_preamble.pdf)
 Final Version
See Usage Policy. 300Kb  

PDF (01_chapter1.pdf)
 Final Version
See Usage Policy. 187Kb  

PDF (02_chapter2.pdf)
 Final Version
See Usage Policy. 1623Kb  

PDF (03_chapter3.pdf)
 Final Version
See Usage Policy. 926Kb  

PDF (04_chapter4.pdf)
 Final Version
See Usage Policy. 14Mb  

PDF (05_chapter5.pdf)
 Final Version
See Usage Policy. 20Mb  

PDF (06_chapter6.pdf)
 Final Version
See Usage Policy. 9Mb  

PDF (07_chapter7.pdf)
 Final Version
See Usage Policy. 4Mb  

PDF (08_chapter8.pdf)
 Final Version
See Usage Policy. 123Kb  

PDF (09_appendixA.pdf)
 Final Version
See Usage Policy. 165Kb  

PDF (10_appendixB.pdf)
 Final Version
See Usage Policy. 903Kb  

PDF (11_appendixC.pdf)
 Final Version
See Usage Policy. 375Kb  

PDF (12_appendixD.pdf)
 Final Version
See Usage Policy. 311Kb  

PDF (13_appendixE.pdf)
 Final Version
See Usage Policy. 142Kb  

PDF (14_appendixF.pdf)
 Final Version
See Usage Policy. 148Kb  

PDF (15_appendixG.pdf)
 Final Version
See Usage Policy. 146Kb  

PDF (16_appendixH.pdf)
 Final Version
See Usage Policy. 82Kb  

PDF (17_bibliography.pdf)
 Final Version
See Usage Policy. 101Kb  

PDF (18_subjectIndex.pdf)
 Final Version
See Usage Policy. 130Kb  

PDF (abstract.pdf)
 Final Version
See Usage Policy. 91Kb  

PDF (acknowledgments.pdf)
 Final Version
See Usage Policy. 41Kb  

PDF (listOfFigures.pdf)
 Final Version
See Usage Policy. 193Kb  

PDF (listofTables.pdf)
 Final Version
See Usage Policy. 88Kb  

PDF (nomenclature.pdf)
 Final Version
See Usage Policy. 132Kb  

PDF (tableOfContents.pdf)
 Final Version
See Usage Policy. 123Kb  

PDF (thesisBermejoMoreno.pdf)
 Final Version
See Usage Policy. 47Mb 
Repository Staff Only: item control page