Abstract
A subset of complex physical systems are those for which the basic equations describing the system are known. An example are the Navier-Stokes equations describing turbulent flows in arbitrary geometrical configurations. Based on energy type balances, bounds on transport quantities can be derived rigorously. In many cases of turbulent fluid flow the extremalizing vector fields show surprising similarities with the observed turbulent velocity fields.
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Busse, F.H. (1969): Bounds on the transport of mass and momentum by turbulent flow between parallel plates. J. Applied Math. Phys. (ZAMP) 20, 1–14
Busse, F.H. (1970): Bounds for turbulent shear flow. J. Fluid Mech. 41, 219–240
Busse, F.H. (1972a): The bounding theory of turbulence and it physical significance in the case of turbulent Couette flow. Springer Lecture Notes in Physics, vol. 12, 103–126
Busse, F.H. (1972b): A property of the energy stability limit for plane parallel shear flow. Arch. Rat. Mech. Anal. 47, 28–35
Busse, F.H. (1978): The Optimum Theory of Turbulence. Adv. Appl. Mech. 20, 77–121
Doering, C.R., Constantin, P. (1992): Energy dissipation in shear driven turbulence. Phys. Rev. Lett. 69, 1648–1651
Doering, C.R., Constantin, P. (1994): Variational bounds on energy dissipation in incompressible flows: shear flow. Phys. Rev. E 49, 4087–4099
Gebhardt, T., Grossmann, S., Holthaus, M., Löhden, M. (1995): Rigorous bound on the plane-shear-flow dissipation rate. Phys. Rev. E 51, 360–365
Hopf, E. (1941): Ein allgemeiner Endlichkeitssatz der Hydrodynamik. Math. Annalen 117, 764–775
Lathrop, D.P., Fineberg, J., Swinney, H.L. (1992): Transition to shear-driven turbulence in Couette-Taylor flow. Phys. Rev. A 46, 6390–6405
Reichardt, H. (1959): Gesetzmäßigkeiten der geradlinigen turbulenten Couetteströmung. Mitt. Max-Planck-Institut für Strömungsforschung, Göttingen, Nr. 22
Smith, G.P., Townsend, A.A. (1982): Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123, 187–217
Soward, A.M., Kerswell, R.R. (1996): Upper bounds for turbulent Couette flow incorporating the poloidal constraint. J. Fluid Mech., in press
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© 1996 Springer-Verlag
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Busse, F.H. (1996). Bounds for properties of complex systems. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105424
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DOI: https://doi.org/10.1007/BFb0105424
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