553.793 Turbulence Theory I

Spring 2025

Instructor: Greg Eyink

Department: Applied Mathematics & Statistics

Email: eyink 'at' ams.jhu.edu

Phone: (410) 516-7201

Office Hours: Wedn Friday, 4-6pm (or by appointment)

Teaching Assistant: Lowen Peng

Department: Applied Mathematics & Statistics

Email: lpeng22 'at' jhu.edu

Office Hours: ???? (or by appointment)

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Class Times: Mon, Wed 6:30-7:45pm

Watch this space for important announcements, course information, and supplemental materials.
We shall be discussing in detail the paper of L. Onsager, "Statistical Hydrodynamics",
Nuovo Cim. Suppl. 6 : 279-287 (1949) , elaborating upon a recent JFM Perspectives Essay here.
We shall discuss related papers on filtering approaches from the engineering fluids literature,
such as M. Germano, "Turbulence: The Filtering Approach", published here, and work on other
coarse-graining approaches, such as recent papers of P. Johnson, here and here.
We discuss also related works from the physics literature, such as the 1983 paper of G. Parisi & U. Frisch,
"On the singularity spectrum of fully developed turbulence", reproduced here as a scanned pdf,
also the 1998 paper of D. Bernard et al. "Slow modes in passive advection", published here,

A very contrary (and contrarian) point of view on turbulence is expressed here.
A neglected paper describing an experiment on the role of thermal noise in turbulent small-scales is
R. Betchov, "On the fine structure of turbulent flows." Journal of Fluid Mechanics 3, 205-216 (1957)
with a very important theoretical follow-up published in a paper for a conference collection, R. Betchov,
"Thermal agitation and turbulence," in: Rarefied Gas Dynamics , Proceedings of the 2nd International
Symposium, edited by L. Talbot , Academic Press , New York (1961), which is available here.
The often-cited (but seldom read) paper of Obukhov on entropy cascade in incompressible fluid
turbulence is A. M. Obukhov, "Structure of the Temperature Field in Turbulent Flow", published
in Izvestiia Akademii Nauk S.S.S.R., Ser. Geogr. i Geofiz., Vol. II, No. 1, (1949), pp 58-69
in Russian and with an English translation made for the U. S. Department of the Army in 1968,
which is available here.

All of the course notes from which I lecture in class will be available here.
Some of the content is original. If you wish to cite any such results, please
quote them as from G. L. Eyink, "Turbulence Theory," course notes,
The Johns Hopkins University, 2007-2008, and give the URL.

A First Course in Turbulence : Hendrik Tennekes & John L. Lumley, MIT Press (1972)
Turbulence: The Legacy of A. N. Kolmogorov : Uriel Frisch, Cambridge University Press (1995)

Scale-Invariance and Turbulence Models for Large-Eddy Simulation : 2000 Annu. Rev. Fluid Mech. article on LES
Particles and Fields in Fluid Turbulence : 2001 Rev. Mod. Phys. article on the Kraichnan passive-scalar model
Onsager and the Theory of Hydrodynamic Turbulence : 2006 Rev. Mod. Phys. article on Onsager's turbulence work
Continuous Dissipative Euler Flows and a Conjecture of Onsager: : 2012 review of Onsager's conjecture & convex integration
at the 6th European Congress of Mathematics in Krak�w, Poland