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A turbulence velocity scale for curved shear flows

Published online by Cambridge University Press:  29 March 2006

Ronald M. C. So
Ronald M. C. So
Affiliation:
Geophysical Fluid Dynamics Program, Rutgers University, New Brunswick, New Jersey 08903
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Abstract

Assuming the turbulence length scale to be unaffected by streamline curvature, a turbulence velocity scale for curved shear flows is derived from the Reynolds-stress equations. Closure of the equations is obtained by using the scheme of Mellor & Herring (1973), and the Reynolds-stress equations are simplified by invoking the two-dimensional boundary-layer approximations and assuming that production of turbulent energy balances viscous dissipation. The resulting formula for the velocity scale has one free parameter, but this can be determined from data for non-rotating unstratified plane flows. Consequently there is no free constant in the derived expression. A single value of the constant is found to give good agreement between calculated and measured values of the velocity scale for a wide variety of curved shear flows.

The result is also applied to test the validity and extent of the analogy between the effects of buoyancy and streamline curvature. This is done by comparing the present result with that obtained by Mellor (1973). Excellent agreement is obtained for the range −0·21 [les ] Rif [les ] 0·21. Therefore the present result provides direct evidence in support of the use of a Monin–Oboukhov (1954) formula for curved shear flows as proposed by Bradshaw (1969).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 1 , 15 July 1975 , pp. 37 - 57
Copyright
© 1975 Cambridge University Press

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References

Arya, S. P. S. 1972 Quart. J. Roy. Met. Soc. 98, 264–273.
Bradshaw, P. 1969 J. Fluid Mech. 36, 177–191.
Bradshaw, P. 1973 AGARDograph, no. 169.
Businger, J. A. 1966 Proc. Symp. Arctic Heat Budget & Atmos. Circulation, Rand Corp., Santa Monica, Calif., pp. 305–322.
Businger, J. A., Wyngaard, J. C., Izumi, Y. & Bradley, E. 1971 J. Atmos. Sci. 28, 181–189.
Dean, R. C. 1968 A.S.M.E. Special Publ. H-38.
Ellis, L. B. & Joubert, P. N. 1974 J. Fluid Mech. 62, 65–84.
Eskinazi, S. & Yeh, H. 1956 J. Aero. Sci. 23, 23–24.
Giles, J. A., Hays, A. P. & Sawyer, R. A. 1966 Aero. Quart. 14, 201–215.
Görtler, H. 1959 Ing. Arch. 28, 71–78.
Halleen, R. M. & Johnston, J. P. 1967 Thermosci. Div., Mech. Engng Dept., Stanford University, Rep. MD-18.
Johnson, D. S. 1959 J. Appl. Mech. 26, 325–336.
Johnston, J. P. 1971 AGARD Current Paper, no. 93.
Klebanoff, P. S. 1955 N.A.C.A. Rep. no. 1247.
Kolmogorov, A. N. 1941 C. R. Akad. Nauk. S.S.S.R. 30, 301–305. (Trans. Turbulence, Classic Papers on Statistical Theory (ed. S. K. Friedlander & L. Topper). Interscience, 1961.)
Laufer, J. 1954 N.A.C.A. Rep. no. 1174.
Lezius, D. K. & Johnston, J. P. 1971 Thermosci. Div., Mech. Engng Dept., Stanford University, Rep MD-29.
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Mellor, G. L. 1973 J. Atmos. Sci. 30, 1061–1069.
Mellor, G. L. & Herring, H J. 1973 A.I.A.A. J. 11, 590–599.
Mellor, G. L. & Yamada, T. 1974 J. Atmos. Sci. 31, 1791–1806.
Monin, A. S. & Oboukhov, A. M. 1954 Trudy Geofiz. Inst. AN S.S.S.R. 24, 163–187.
Moore, J. 1967 M.I.T. Gas Turbine Lab. Rep. no. 89.
Pandolfo, J. P. 1966 J. Atmos. Sci. 23, 495–502.
Parr, O. 1963 Ing. Arch. 32, 393–413.
Patel, V. C. 1969 Aero. Res. Counc. R. & M. no. 3599.
Prandtl, L. 1929 Sonderdruck aus Vortrage aus dem Gebiete der Aerodynamik und verwandter Gebiete. Aachen. (Trans. N.A.C.A. Tech. Memo. no. 625.)
Rastogi, A. K. & Whitelaw, J. H. 1971 A.S.M.E. Paper, no. 71-WA/FE-37.
Richardson, L. F. 1920 Proc. Roy. Soc. A 97, 354–373.
Rotta, J. C. 1951a Z. Phys. 129, 547–572.
Rotta, J. C. 1951b Z. Phys. 131, 51–77.
Schmidbauer, H. 1936 Luftfahrtforsch. 13, 160. (Trans. N.A.S.A. Tech. Memo. no. 791.)
Schubauer, G. B. & Klebanoff, P. S. 1951 N.A.C.A. Rep. no. 1030.
So, R. M. C. 1975 Trans. A.S.M.E., J. Fluids Engng (to appear).
So, R. M. C. & Mellor, G. L. 1972 N.A.S.A. Contractor Rep. no. 1940.
So, R. M. C. & Mellor, G. L. 1973 J. Fluid Mech. 60, 43–62.
So, R. M. C. & Mellor, G. L. 1975 Aero. Quart. 26, 25–40.
Townsend, A. A. 1958 J. Fluid Mech. 3, 361–372.
Wattendorf, F. L. 1935 Proc. Roy. Soc. A 148, 565–598.
Wyngaard, J. C. & Coté, O. R. 1971 J. Atmos. Sci. 28, 190–201.