Peter Bradshaw


Thomas V. Jones Professor of Engineering, Emeritus, and, by courtesy, Professor of Aeronautics and Astronautics

(A side view is also available - 240kB.)
Phone: (650) 725-0704 | Fax: (650) 725-4862 | E-mail:

I do not, repeat NOT, have any funds to support students at any level

Degrees, etc.

B.A. Cambridge University - Aeronautical Engineering, 1957.
Fellow, Royal Society of London, 1981.
D.Sc. (Hon.) Exeter University, 1990.
Distinguished Lecturer, American Society of Mechanical Engineers, 1992-1993.
Fluid Dynamics Award, American Institute of Aeronautics and Astronautics, 1994

Research interests

Complex turbulent flows, turbulence modeling, large-eddy simulation, experimental techniques and wind-tunnel design.
Author or co-author of over 200 papers and six books in the above areas.

These Web pages contain:-

A 10000-entry selected Bibliography on turbulence, covering the period from 1980 to 2002 with some earlier and later entries

Details of the international project on Collaborative Testing of Turbulence Models (1990-93) including links to the database assembled for this collaboration.

Hypertext document on wind-tunnel design This is the new (August 2002) version: the old version is still available but will not be updated further apart from possible correction of errors

We are clearing out our stock of the Proceedings of Computation of Turbulent Boundary Layers -- 1968 AFOSR-IFP-Stanford Conference also known as "Stanford Olympics 1".

Vol. 1 (600 pages) contains detailed presentations of the calculation methods, plus transcripts of the -- sometimes extensive -- oral discussions that followed each group of presentations. This volume is largely of historical interest, as showing the state of the art 25 years ago.

Vol. 2 (530 pages) contains data (mainly mean velocity profiles) for the boundary-layer test cases used for the meeting, with a timeless review paper "The Young Person's Guide to the Data" by Donald Coles. The data include classic experiments whose original publications would be very difficult to find today.

The two-volume set is available for $15, the cost of shipping and handling of a 6 lb. package (overseas shipping by surface mail). Individual volumes will NOT be available. Personal checks will be accepted (in most cases it will be simpler for everybody for copies for university or company use to be purchased this way: we will send a receipt that can be used to claim payment from "petty cash" funds).

Make checks payable to "Stanford University" and send to

P. Bradshaw, ME Dept., Stanford University, STANFORD CA 94305.

DO NOT send checks to University Administration!

Recent Publications (see also complete list of published papers)

P. Bradshaw and C.U. Buice, "Inclined Impinging Jets in Crossflow", AIAA-96-0204, 1996.

P. Bradshaw, B.E. Launder and J.L. Lumley, "Collaborative Testing of Turbulence Models", J. Fluids Engg 118, 243, 1996.

P. Bradshaw, "Turbulence in Compressible Flow - Physics and Modeling", J. Jap. Soc. Fluid Mech. 15, 354, 1996.

P. Bradshaw, "Turbulence Modeling with Application to Turbomachinery", Prog. Aerospace Sci. 32, 575, 1996.

P. Bradshaw, "The Understanding and Prediction of Turbulent Flow - 1996" (presented at Engineering Foundation Conference on Turbulent Heat Transfer, San Diego 1996), Int. J. Heat and Fluid Flow 18, 45, 1997.

B.J. Cantwell, J. Chacin and P. Bradshaw, "On the Dynamics of Turbulent Boundary Layers", in "Self-Sustaining Mechanisms of Wall Turbulence" (Advances in Fluid Mech. vol. 15, ed. R.L. Panton), Computational Mech. Publications, 1997, p. 365.

J.S. Chow, G.G. Zilliac and P. Bradshaw, "Mean and Turbulence Measurements in the Near Field of a Wingtip Vortex", AIAA J. 35, 1561, 1997.

F.T.M. Nieuwstadt and P. Bradshaw, "Similarities and Differences in Turbulent Boundary-Layer, Pipe and Channel Flows", Boundary-Layer Separation in Aircraft Aerodynamics (R.A.W.M. Henkes and P.G. Bakker, eds.), Delft Univ. Press, p. 15, 1997.

D.M. Bott and P. Bradshaw, "Effect of High Free-Stream Turbulence on Boundary-Layer Skin Friction and Heat Transfer", AIAA 98-0531, 1998 (more detail in Stanford Univ. M.E. Dept Rept. MD-75, 1997).

P. Bradshaw, "Highlights of Turbulence Modeling", presented at ASME International Mech. Engg Conference and Exposition, Anaheim, CA, 1998. No written paper -  transcript of slides can be viewed or downloaded in .html,   PostScript, or pdf format*. Note that, as requested by ASME, this lecture is at advanced graduate level, not state-of-the-art.....

S.G. Saddoughi, P. Koumoutsakos, P. Bradshaw and N.N. Mansour, "Investigations of `On Demand' Vortex Generators", Stanford/Ames Center for Turb. Res. CTR Ms. 171, 1998.

P. Bradshaw, "The Best Turbulence Models for Engineers", in Modeling Complex Turbulent Flows - ICASE 1997 Symposium (M.D. Salas, J.N. Hefner and L. Sakell, eds.), Kluwer, p. 9, 1999.

B.A. Younis and P. Bradshaw, "A Rational Model for the Triple Velocity Correlations", Presented at Am. Phys. Soc. DFD meeting, 1999.

F. Nicoud and P. Bradshaw, "A Velocity Transformation for Heat and Mass Transfer", Phys. Fluids 12, 237, 2000.

P. Bradshaw, "A Note on `Critical Roughness Height' and `Transitional Roughness'", Phys. Fluids 12, 1611, 2000.

P. Bradshaw, "Turbulence Modeling for High Reynolds Number Separated Flows", in NASA/CR-2001-210841, ICASE Interim Rept. 37 "Turbulence Modeling Workshop", 2001.

* pdf files can be read and printed with the Acroread utility which can be downloaded free of charge. pdf files are in binary and usually 1-1/2 to 2 times the size of .ps ASCII files, but assembly of a document from separate text and figures can be easier. PostScript (.ps) files require Ghostview/gsview or similar reader.

Collaborative Testing of Turbulence Models

This international project, "CTTM" for short, was organized by Bradshaw, with Brian Launder (UMIST, Manchester) and John Lumley(Cornell): see Bradshaw, Launder and Lumley (1996), above, for details. Most of the project documentation exists only as paper copies and is available from Bradshaw at the cost of reproduction and handling (see Price List). This Web site contains the Final Report to the sponsors, and a description of the Data Library containing selections of the data collected for the project (not all of which was used).

The data collected for the project (including the data used in the 1980-81 Stanford conference on Computation of Complex Turbulent Flows) and explanatory documents are now available in the Journal of Fluids Engineering electronic Data Bank at Virginia Polytechnic Institute and State University. The Bank includes some data sets which were not distributed to the Collaborators but were later selected by an independent research worker as potentially useful, well-documented test cases.

The URL containing the JFE Data Bank holds some other material as well. On its home page, choose "ejournals", then "current journals" then "Journal of Fluids Engineering", "Databank"and "DB96-243" (code numbers give year and JFE page of accompanying article, in this case Bradshaw, Launder and Lumley 1996). Click "Readme.txt", which gives a short explanation and then directs you to "Intro.txt".

Please report difficulties in reading/downloading to the JFE editors, and difficulties in understanding/using the data to Bradshaw.

The data are also available on 3-1/2in. (1.44MB) IBM (MS-DOS/Windows) disks from Bradshaw, again at cost (see Price List).

A Bibliography of Turbulent Flows

This is a set of plain-text files (ASCII characters only, no graphics) of over 10000 references to papers on turbulence and associated numerical and experimental techniques. The papers have been read and selected by Bradshaw, and are arranged in standard format, labeled with index categories, and accompanied by short abstracts. The main file is over 2MB long, and the same information is repeated in sorted files, one per index category. The bibliography was set up for private use and is being made available on the Web as a public service with no warranty (particularly as regards the abstracts, which are expressions of personal opinion recorded when the papers were first read).The bibliography covers the period 1980 to 2002 with some earlier and later entries, and includes reports and other publicly-available documents as well as journal papers. The files can be downloaded directly from the Bibliography Home Page.

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Last updated 29 January 2009