Skip to main content

Full text of "DTIC ADA335117: Scalings in Homogeneous and Inhomogeneous Turbulence"

See other formats


OFFICE OF NAVAL RESEARCH 
FINAL REPORT 

PUBLICATIONS/PATENTS/PRESENTATIONS/HONORS/STUDENTS REPORT 


for 


GRANT: N00014-9510444 
PR Number 96PR03405 

Scalings in Homogeneous and Inhomogeneous Turbulence 

Zhen-Su She, Principal Investigator 

Department of Mathematics, UCLA 
Los Angeles, CA 90095 

December 20, 1997 

Reproduction in whole, or in part, is permitted for any prupose of the 

United States Government 

This documents has been approved for public release and sale, its 

distribution is unlimited 


1 


19980122 137 



OFFICE OF NAVAL RESEARCH 

PUBLICATIONS/PATENTS/PRESENTATIONS/HONORS/ REPORT 


PR Number: 


96PR03405 


Grant Number: 


N00014-9510444 


Grant Title: 


Scalings in Homogeneous 
and Inhomogenous Turbulence 


Principal Investigator: Zhen-Su She 


Mailing Address: 


Department of Mathematics, 
UCLA, Los Angeles, CA 90095 


Phone Number: 
Fax Number: 
E-mail Address: 
http address: 


(310) 8258576 
(310) 2962679 
she@math. ucla. edu 
None 


2 



OFFICE OF NAVAL RESEARCH 

PUBLICATIONS/PATENTS/PRESENTATIONS/HONORS/ REPORT 


a. Number of papers submitted to referred journals, but not yet 
published: _3_ 

• She, Z.-S. &; Leveque, E., Invariance Principle and Hierar¬ 
chical Structures in Turbulence Phys. Rev. Lett., submitted 
(1997). 

• Liu, Li & She, Z.-S. Scaling Laws in High Reynolds Number 
Liquid Helium Turbulence Phys. Fluid, submitted (1997). 

• Yoon, J.-M. k She, Z.-S. Hierarchical Structures in Spatio- 
temporal Chaos Phys. Rev. E., submitted (1997). 

b. Number of papers published in referred journal: 3 

Published Papers in Referred Journals 

• Leveque, E. k She, Z.-S., Viscous Effects on Inertial Range 
Scalings in a Dynamical Model of Turbulence , Phys. Rev. Lett., 
75, 2690 (1995). 

• Cao, N., Chen, S. k She, Z.-S., Scaling and Relative Scaling 
in Navier-Stokes Turbulence , Phys. Rev. Lett. 76, 3711 (1996). 

• Leveque, E. k She, Z.-S., Cascade Structures and Scaling Ex¬ 
ponents in a Dynamical Model of Turbulence: Measurements 
and Comparison, Phys. Rev. E., 55 (3), 2789 (1997). 

c. Number of books or chapters submitted, but not yet pub¬ 
lished: _1_ 

• She, Z.-S., Non-equilibrium Dynamics of Turbulent Fluctu- 


3 



ations, Proceeding of 12th Nishinomiya Symposium on “Dy¬ 
namic Organizations”, will appear in Prog. Mod. Phys. (Japan) 
(1998). 

d. Number of books or chapters published: _JL 

• She, Z.-S., Scaling Laws and Hierarchical Structures in Tur¬ 
bulence, Lecture Notes in Physics, Springer-Verlag (1997). 

e. Number of printed technical reports/non-referred papers: _0_ 

f. Number of patent filed: _0_ 

g. Number of patent granted: _0_ 


4 



OFFICE OF NAVAL RESEARCH 

PUBLICATIONS/PATENTS/PRESENTATIONS/HONORS/REPORT 


• h. Number of invited presentations: 16 

Invited Presentations 

o Z.-S. She, “Hierarchical Structures and Scalings in Turbu¬ 
lence”, Gordon Conference on “Fractals”, NH, June 1996. 
o Z.-S. She, “A Simple Scaling Model of Turbulence”, at the 
International Workshop on “Turbulence in Ultrahigh Reynolds 
Number Flows”, NY, June 1996. 

o Z.-S. She, “On a Scaling Theory of Turbulence”, at the ’96 
Symposium on Computational Physics, China, June 1996. 
o Z.-S. She, “Analysis of Statistical Errors for Numerical PDE”, 
at the ’96 Symposium on “Numeircal PDE”, China, July 1996. 
o Z.-S. She, “Geometrical Structures and Statistics of Turbu¬ 
lence” , at the workshop on “Vortex Dynamics and Turbulence”, 
China, July 1996. 

o Z.-S. She, “Structures and Scalings in Turbulence”, at the 
workshop on “Turbulence Modeling and Vortex Dynamics, Turkey, 
September 1996. 

o Z.-S. She, “Simplicity in Turbulence”, at the workshop on 
“Turbulence Modeling and Vortex Dynamics, Turkey, Septem¬ 
ber 1996. 

o Z.-S. She, “A New Symmetry in Turbulence”, at the Interna¬ 
tional Workshop on “Dynamical Models of Turbulence”, Obser- 
vatoire de Nice (France), December 1996. 
o Z.-S. She, “A New Scaling Theory of Turbulence”, Special 
Invited Lecture at the National Turbulence Workshop (China), 


5 


Wuhan (China), May 1997. 

o Z.-S. She, “Inertial Range Dynamics of Turbulence”, A series 
of four lectures at the Summer School on “Turbulence”, Beijing 
University (China), June 1997. 

o Z.-S. She, “Hierarchical Symmtry in Turbulence”, Invited talk 
at the IMS/ASA Annual Meeting, Anaheim, California, August 
1997. 

o Z.-S. She, “Invariance Principle and Hierarchical Structures in 
Turbulence”, Invited talk at the 12th Nishinomiya Symposium 
on the “Dynamics Orgonization” (Japan), November 1997. 
o Z.-S. She, “Nonlinear Fluctuation Dynamics of Turbulence”, 
Invited talk at the workshop “Nonlinear Phenomenology”, Ky¬ 
oto University (Japan), November 1997. 

o Z.-S. She, “A New Scaling Model of Turbulence”, at the Col- 
loqium at UC San Diego, Mech. Eng. Dept., Oct. 1995. 
o Z.-S. She, “Structures and Scalings in Turbulence”, at the 
Colloqiumat UC Los Angeles, Atmosph. Sci. Dept., Nov. 1995. 
o Z.-S. She, “On the Development of Scaling Theory of Turbu¬ 
lence”, at the Colloqium at Univ. Arizona, Physics Dept., Nov. 
1995. 


6 



OFFICE OF NAVAL RESEARCH 

PUBLICATIONS/PATENTS/PRESENTATIONS/HONORS/ REPORT 


• i. Number of submitted presentations: _0_ 

• j. Honors/Awards/Prizes for contract/grant employees: _0_ 

• k. Total number of Full-time equivalent Graduate Students 
and Post-Doctoral associates supported during this period, un¬ 
der this R&T; project number: _2_ 

• Graduate Students: _ 2 _ 

• Post-Doctoral Associates: 0.2 

• including the number of 

• Female Graduate Students; JL 

• Asian Graduate Students: _L 

• 1. Other funding: 

Sloan Foundation Research Fellowship, $8,000. Total of $30,000 
over three years. This fund mostly supports international travels 
to scientific meetings. 


7 




OFFICE OF NAVAL RESEARCH 
FINAL REPORT 
(PART II) 


a. P. I.: Zhen-Su She 

b. Phone Number: (310) 8258576 

c. Program Officer: Michael F. Shlesinger 

d. Program Objective: 

Understand the fundamental processes which leads 
to the generation of small-scale fluctuations. Describe 
the scaling properties of turbulence based on features 
of fluid structures. Develop theories of turbulence 
for universal scaling laws and for applications 


e. Significant Results: 

• Using direct numerical simulations, we show clear 
evidence for the scaling deviation from Kolmogorov 
law for all structure functions in the Navier-Stokes flow 

• We show that the She-Leveque model give accurate 
prdictions about the scaling exponents for the NS flow 
as well as for other dynamical system of energy cascade. 

• We show that the high Reynolds number liquid Helium 
turbulent flows are also characterized by a hierarchy 

of structures (S-L model), but with slightly different 


8 



leading singularity from homogeneous open turbulent flows 

• We show that spatially extended chaotic system is 
also characterized by a hierarchy of structures predicted 
by the She-Leveque model 

• We develop a “special relativity” theory for the 
study of the multiscaling field of turbulence. This theory 
postulates the existence of an invariance property for 
any generic scaling field with finite fluctuation range, and 
explain therefore the success of the She-Leveque model for 
a large variety of systems 


9