Abstract
It is shown that Newton’s shear law for laminar flow and the Difference-Quotient Turbulence Model (DQTM) for turbulent flow are the analog constitutive laws describing the relations between shear strain rate and shear stress. Whereas the laminar case is fully linear and local, the turbulent counterpart is nonlinear and nonlocal. In this brief article the capacity of the new model is outlined by quoting references and related articles which contain results of convincing simplicity and accuracy and a presentation and discussion of the resulting analytical solutions of plane turbulent Couette flow. Newton’s linear velocity profile between sheared plates for laminar flow is embedded in this solution as a special case. The solution of the corresponding nonlinear differential equation also reveals a cooperative phenomenon.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Taylor, G.I.: Eddy motion in the atmosphere. Phil. Trans. R. Soc. Lond. 215, 523–537 (1915)
Prandtl, L.: Bemerkungen zur Theorie der freien Turbulenz. ZAMM 5(22), 241–243 (1942)
Boussinesq, J.: Mém. Prés. Div. Savant Acad. Sci. 23, 46 (1872)
Pope, S.B.: A more general effective-viscosity hypothesis. J. Fluid Mech. 72(2), 331–340 (1975)
Bernard, P.S., Handler, R.A.: Reynolds stress and the physics of turbulent momentum transport. J. Fluid Mech. 220, 90–124 (1990)
Huang, Y.-N.: On modeling the Reynolds stress in the context of continuum mechanics, communications in nonlinear. Sci. Num. Sim. 9, 543–559 (2004)
Hamba, F.: Nonlocal analysis of the Reynolds stress in turbulent shear flow. Phys. Fluids 17, 115102 (2005)
Egolf, P.W.: A new model on turbulent shear flows. Helv. Phys. Acta 64, 944–945 (1991)
Egolf, P.W.: Difference-quotient turbulence model: a generalization of Prandtl’s mixing-length theory. Phys. Rev. E 49(2), 1260–1268 (1994)
Egolf, P.W., Weiss, D.A.: Model for turbulent plane Couette flow. Phys. Rev. Lett. 75(16), 2956–2959 (1995)
Egolf, P.W.: Difference-quotient turbulence model: the axi-symmetric isothermal jet. Phys. Rev. E 58(1), 459–470 (1998)
Egolf P.W., Weiss D.A.: Difference-quotient turbulence model: Analytical solutions for the core region of plane Poiseuille flow, Phys. Rev E 62/1-A, 553–563 (2000)
Egolf, P.W.: Lévy statistics and beta model: a new solution of “wall” turbulence with a critical phenomenon. Int. J. Refrig. 32, 1815–1836 (2009)
Reif, F.: Fundamentals of Statistical and Thermal Physics. MacGraw Hill Company, New York (1965)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Egolf, P.W., Hutter, K. (2016). Turbulent Shear Flows Described by the Algebraic Difference-Quotient Turbulence Model. In: Peinke, J., Kampers, G., Oberlack, M., Wacławczyk, M., Talamelli, A. (eds) Progress in Turbulence VI. Springer Proceedings in Physics, vol 165. Springer, Cham. https://doi.org/10.1007/978-3-319-29130-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-29130-7_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29129-1
Online ISBN: 978-3-319-29130-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)