G ridG eneratedTurbulence : from R λ of 5 0 to 5 0 0 0 andBeyond .

1. Early studies.

2. The era of Corrsin, Townsend and company

3. Active grids

4. Review of advances and outstanding problems

Zellman Warhaft, Cornell University

“Finally, if we are to list the reasons for studying homogeneous turbulence, we should add that it is a profoundly

interesting physical phenomenon which still defies satisfactory mathematical analysis; this is, of course, the most

compelling reason” G.K. Batchelor, The Theory of Homogeneous Turbulence, 1953.

“ Why on earth are you studying grid turbulence?” Statement of a turbulence researcher to ZW, conference on “Structure and Mechanisms of turbulence.” Berlin, 1976.

Wind tunnels

Eiffel

Prandtl 1904

Wright Brothers 1901

Hopkins….. MPI

“The only future use for wind tunnels will be to store computer output” Statement of a turbulence researcher to ZW, mid 1980’s.

Early work (G.I. Taylor, Proc. Roy. Soc. Lon. A. 151, 1935)

Note Taylor takes: which is incorrect.

See also L.F.G. Simmons and C. Salter. 1934

Proc. Roy. Soc. Ser. A, Vol. 145, No. 854, 00. 212-234

Dryden (Taylor 1935)

Proc. Roy. Soc. 1949

Batchelor and Townsend 1949

Batchelor and Townsend 1949

Corrsin and Townsend

“Corrsin carried on a correspondence with Townsend for several years regarding the

isotropy of grid turbulence. Corrsin’s measurements indicated that turbulence in

Baltimore was not quite isotropic, while Townsend continued to refer to his turbulence

as isotropic. At one point, Corrsin wrapped up one of his grids and sent

it to Townsend. There was no reply. Ultimately, the difference was traced to

X- wire calibration and the hot-wire length correction. In fact, as Corrsin has claimed,

the grid turbulence was not quite isotropic (see below) ”.

From “A Century of Turbulence” by J.L. Lumley and A.M. Yaglom. Flow, Turbulence and Combustion, 66: 241-286, 2001

Comte-Bellot & Corrsin 1966, (also 1972)

Square grid rods

Comte-Bellot & Corrsin 1966

Partial list of other passive grid turbulence experiments

Diffusion from line sources:

Uberoi, M.S. & Corrsin, S. 1953 NACA Rep. 1142

Townsend, A.A. 1954 Proc. Roy. Soc.Lon. A, 224

Stapuntsis, Hunt et al. JFM 1986, W. 1984 JFM

Axisymmetric strain:

Uberoi, M.S. 1956, J. Aero. Sc. 23.

Mills, R. R. & Corrsin, S. 1959 NASA memo 5-5-59

W. 1980. JFM 99

Heated grids & homogeneous scalars:

Yeh, T.T. & van Atta, C.W. 1973 J. Fluid Mech. 58

Mills, R. R. & Corrsin, S. 1959 NASA memo 5-5-59 W

Lumley, J.L. & W. J. Fluid Mech. 1978

Sreeninvasan, K.R., Tavoularis, S. Henry, R. & Corrsin, S. J. 1980 Fluid Mech. 100

Lagrangian: Snyder, W.H. & Lumley, 1971, J. Fluid Mech. 48., Qureshi, Bourgoin

PRL 2007.

Homogeneous Shear: S. Corrsin and Co-workers

Turbulence mixing layer: Gilbert, Veeravalli & W.

..,....................

Active Grids

Gad-El-Hak, M. Corrisin, S. J. Fluid Mech. (1974) [jets, co-& counter flow]

H.Makita, K. Sassa,. I Iwasaki & A. Iidu (1987), Trans. Japan Soc. Mech. Engng 1987

H.Makita (1991) Fluid Dynamics Research (Japan)

Mydlarski & W* (1996), J. Fluid Mech.

Poorte R.E.G. & Biesheuvel (2002) J. Fluid Mech .[ gas bubbles]

Kang, H.S.Chester, S. Meneveau, C. (2003) J. Fluid Mech. [decaying turbulence and LES]

Kang, H.S. Meneveau, C. (2008) Phys. Fluids [shearless mixing layer]

Mordant, N (2008) American J. Physics [teaching tool]

Savelsber R & Van de Water, w. (2009) J. Fluid Mech. [ free surface turbulence]

*Z.W and Mydlarski, L, Shen, X, Ayyalasomayajula S, Gylfason,A, Gerashchenko, S. Sharpe, N.Neuscaman S, [Passive scalars, homogeneous shear, inertial particles, boundary layer, axisymmetric strain]

Turbulence intensity ~ drag coeff. ~ solidity. Solidity > 0.4, unstable

Active vs. passive grids

The issue of isotropy and integral scale

Active vs. passive grids

Active vs. passive grids

Large and Small Scales

Passive grid experiments, particularly those of Corrsin and Townsend, were focused on seeking large scale isotropy to test kinematics and theories of isotropic turbulence.

Active grid experiments are focused on achieving high Reynolds numbers at the expense of large scale isotropy, and of having the largest eddies significantly smaller than that of the tunnel.

There is more and more reason to suggest that the large and small scales are (directly) related.

Other new ways of generating “isotropic” turbulence

Meng et al. Digital holographic imaging

Bodenschatz et al.Stereoscopic 3D tracking

Eaton et al. laser sheet Cornell (Makita) et al. Sled/laser sheet Bodenschatz et al.

Pinton et al. Doppler sonar

Prefactors and exponents

Perhaps! We still do not know the values of important constants well (von Karman constant, a_0 etc. ). Reynolds number dependencies, pre-factors are not well documented.But, as we have seen at this meeting, a great deal IS understood. And soon much

more with the PMI-SF6 tunnel.