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

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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