×

zbMATH — the first resource for mathematics

Exact solutions for near-wall turbulence theory. (English) Zbl 0966.76035
Summary: Using the two-dimensional case as a simple example, we outline an analytical approach to the near wall turbulence outside of the viscous sublayer. Our theory combines the Reynolds-averaged mean-flow equation nonlinearly coupled to the rapid distortion theory equations for turbulence with a weak small-scale forcing. Such an external forcing models the dilute vortex debris propagating away from the wall as a result of intermittent bursts accompanying the breakdown of coherent vortices in viscous sublayer. We show that the log law of the wall exists as an exact analytical solution in our model if the starting turbulent vorticity is statistically homogeneous in space and shortly correlated in time.

MSC:
76F40 Turbulent boundary layers
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Th. von Karman, Mechanische Aehnlichkeit und Turbulenz, Nach. Ges. Wiss. Göttingen Math-Phys. Klasse, 1932, pp. 58-76.
[2] L. Prandtl, Zur turbulenten Stroemung in Rohren und laengs Platten, Ergeb. Aerodyn. Versuch., Series 4, Göttingen, 1932.
[3] Barenblatt, G.I., J. fluid mech., 248, 513, (1993)
[4] Barenblatt, G.I.; Chorin, A.J., Proc. nat. acad. sci. USA, 93, 6749, (1996)
[5] Barenblatt, G.I.; Chorin, A.J.; Prostokishin, V.M., Proc. nat. acad. sci. USA, 94, 773, (1997)
[6] W. George, L. Castillo, M. Wosnik, TAM Report No 872, UILU-ENG-97-6033, University of Illinois at Urbana-Champain, November 1997.
[7] J. Nikuradze, Forsch. Arb. Ing.-Wes. No 356 (1932).
[8] Zagarola, M.V.; Smits, A.J., Phys. rev. lett., 78, 239, (1997)
[9] Zagarola, M.V.; Perry, A.E.; Smits, A.J., Phys. fluids, 9, 2094, (1997)
[10] Kim, J.; Moser, R., J. fluid mech., 177, 133, (1987)
[11] H.K. Moffatt, The interaction of turbulence with a strong wind shear, in: A.M. Yaglom, V.I. Tatarsky (Eds.), Proc. URSI-IUGG International Colloquim on Atmospheric turbulence and radio wave propagation, Moscow, June 1965 Nauka Moscow, 1967.
[12] S. Nazarenko, N.K.-R. Kevlahan, B. Dubrulle, Nonlinear RDT theory of near-wall turbulence, to appear in Physica D (1999). · Zbl 0965.76032
[13] B. Dubrulle, J.-P. Laval, S. Nazarenko, N.K.-R. Kevlahan, Derivation of equilibrium profiles in plane parallel flows using a dynamic subgrid-scale model, submitted to Phys. Fluids (1999).
[14] Dyachenko, A.I.; Nazarenko, S.V.; Zakharov, V.E., Phys. lett. A, 165, 330, (1992)
[15] Dubrulle, B.; Nazarenko, S., Physica D, 110, 123, (1997)
[16] Nazarenko, S.V.; Kevlahan, N.; Dubrulle, B., J. fluid mech., 390, 325, (1999)
[17] Perry, A.E.; Henbest, S.; Chong, M.S., J. fluid mech., 165, 163, (1986)
[18] Savill, A.M., Ann. rev. fluid mech., 19, 537, (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.