553.794 Turbulence Theory II:
Turbulence & Solid Walls

Spring 2023

Top: flow with a laminar boundary layer separating before the equator.
Bottom: flow with turbulent boundary layer due to a trip wire, with delayed separation

General Information

Instructor: Greg Eyink

Department: Applied Mathematics & Statistics

Email: eyink 'at' ams.jhu.edu

Phone: (410) 516-7201

Office: Wyman Park N449, https://wse.zoom.us/j/7633492271

Office Hours: Friday 4:00-6:00pm (or by appointment)

Teaching Assistant: Lowen Peng

Department: Applied Mathematics & Statistics

Email: lpeng22 'at' jhu.edu

Office: Wyman Park ???, https://jhubluejays.zoom.us/j/????

Office Hours: ???

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Lectures: Gilman 75, https://wse.zoom.us/j/92146942075

Class Times: Mon, Wed 4:30-5:45pm

Piazza Discussion Group: https://piazza.com/jhu/spring2023/553794

Canvas: https://jhu.instructure.com/courses/37280

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 preprint account here.
We shall discuss related papers on filtering approaches from the engineering fluids literature,
such as M. Germano, "Turbulence: The Filtering Approach", published 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.
A very comprehensive discussion of fluctuating hydrodynamics with solid walls is given by the 2016
PhD Thesis of Martin Reichelsdorfer at Erlangen University, available here
A panoramic view of fluid interactions with solid walls was given by Sir M. James Lighthill in his
article "Introduction: Boundary Layer Theory" in Laminar Boundary Theory, L. Rosenhead, ed.
(Oxford University Press, Oxford, 1963), pp.46-113, which is available here . We shall discuss this
paper in detail in the course, including modern developments and refinements.
An old review of Doligalski, Smith, and Walker, "Vortex interactions with walls," Annual Review
of Fluid Mechanics 26.1 (1994): 573-616 is here . This paper discusses explosive eruption
of vorticity from solid walls, based mainly on Prandtl's laminar boundary-layer equations.
Useful works on general vortex dynamics in fluids are monographs of Saffman and Wu, Ma & Zhou
A paper reporting simulations of flow past an impulsively started cylinder is Chatzimanolakiset al. (2022)
with three nice movies at Re=25000, 50000, and 100000 here
An interesting paper by Lenaers et al. (2012) on statistics of skin friction in turbulent channel flow is here.
Three important papers on the theme of "weak-strong uniqueness" are the classical work of Kato (1984),
the work of Bardos & Titi (2013), and the very useful review paper of Wiedemann (2018).

Reading Assignments

Assignment	Date Due
Reading 1: Temam (2006)	January 30, 2023
Reading 2: Lighthill (1963), section 1; Morton (1984); Terrington et al. (2021)	February 6, 2023
Reading 3: Lighthill (1963), section 2; Cassel & Conlisk (2014); Haller (2004)	February 20, 2023
Reading 4: Lighthill (1963), section 3 & 4; Wang et al. (2022); Smith et al. (1991)	March 6, 2023
Reading 5: Huggins (1970); Kustepeli (2016); Eyink (2021)	March 20, 2023
Reading 6: Johnson (2022); Hoffman (2006); Quan & Eyink (2022)	April 10, 2023

Problem Assignments

Assignment	Date Due	Solutions
Problem Set #1	February 10, 2023	Problem Set #1
Problem Set #2	March 6, 2023	Problem Set #2
Problem Set #3	March 20, 2023	Problem Set #3
Problem Set #4	April 10, 2023	Problem Set #4
Problem Set #5	April 26, 2023	Problem Set #5

Old Course Notes

These are course notes from the previous version of this class, which I will
sometimes reference and which 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.

New Course Notes

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, 2023, and give the URL.

Supplemental Textbooks

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)

Review Papers

Scale-Invariance and Turbulence Models for Large-Eddy Simulation : 2000 Annu. Rev. Fluid Mech. article on LES
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

Some Links

http://www.efluids.com : general webpage on fluids resources

http://turbulence.pha.jhu.edu : JHU Turbulence Webpage

553.794 Turbulence Theory II: Turbulence & Solid Walls