By Tom Mullin, R. R. Kerswell

ISBN-10: 1402040482

ISBN-13: 9781402040481

ISBN-10: 1402040490

ISBN-13: 9781402040498

An exhilarating new path in hydrodynamic balance idea and the transition to turbulence is anxious with the position of disconnected states or finite amplitude options within the evolution of disease in fluid flows. This quantity comprises refereed papers offered on the IUTAM/LMS subsidized symposium on "Non-Uniqueness of options to the Navier-Stokes equations and their reference to Laminar-Turbulent Transition" held in Bristol 2004. Theoreticians and experimentalists amassed to debate advancements in figuring out either the onset and cave in of disordered movement in shear flows resembling these present in pipes and channels. The crucial target of the symposium was once to debate the expanding quantity of experimental and numerical facts for finite amplitude suggestions to the Navier-Stokes equations and to set the paintings right into a sleek theoretical context. The individuals incorporated the various major professionals within the topic and this quantity captures a lot of the flavor of the ensuing stimulating and vigorous discussions.

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**Extra resources for IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions (Fluid Mechanics and Its Applications)**

**Example text**

And Dauchot, O. (2001). Patterning and transition to turbulence in subcritical systems: The case of plane Couette ﬂow. In Coherent Structures in Classical Systems D. L. M. Rubi (eds), Springer Verlag, Berlin, pp. 58ff. Modeling the Direct Transition to Turbulence 33 Manneville, P. and Locher, F. (2000). A model for transitional plane Couette ﬂow. R. Acad. Sc. IIb – Mécanique 328, 159–164. , Faisst, H. and Eckhardt, B. (2004). A low-dimensional model for turbulent shear ﬂows. New J. Phys. 6, pp.

Computational study of turbulent laminar patterns in Couette ﬂow. Phys. Rev. Lett. 94, 014502. R. R. (2000). New results in rotating Hagen–Poiseuille ﬂow. J. Fluid Mech. 417, 103–126. Boberg, L. and Brosa, U. (1988). Onset of turbulence in a pipe. Z. Naturforsch. 43a, 697–726. Bottin, S. and Chaté, H. (1998). Statistical analysis of the transition to turbulence in plane Couette ﬂow. Eur. Phys. J. B 6, 143–155. , Dauchot, O. and Daviaud, F. (1997). Intermittency in a locally forced plane Couette ﬂow.

A fully turbulent state is prepared with R = 100. At t = 2050, R is suddenly decreased. The observable here is the surface-averaged perturbation kinetic energy K. For R = 50 turbulence is still sustained, whereas it decays for R = 45 after a “long” turbulent transient. As R is further decreased, a direct relaxation to the laminar state is observed. are imposed at the typical size of the MFU, nontrivial behavior is observed at roughly the same R values as those for Waleffe’s model. An important difference is, however, observed: sustained chaos and chaotic transients are obtained instead of time-independent regimes and oscillatory transients, which is the consequence of an enlarged effective phase space.

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