Abstract
In this paper, we review recent progress on several problems of transition and turbulence. First, we explore the role of secondary instabilities in transition to turbulence in both wall bounded and free shear flows. It is shown how the competition between secondary instabilities and classical inviscid inflectional instabilities is important in determining the evolution of free shear flows. An outline of a general theory of inviscid instability is given. Then, we explore recent ideas on the force-free nature of coherent flow structures in turbulence. The role of viscosity in generating small-scale features of turbulence is discussed for both the Taylor-Green vortex and for two-dimensional turbulence. Finally, we survey recent ideas on the application of renormalization group methods to turbulence transport models. These methods yield fundamental relationships between various types of turbulent flow quantities and should be useful for the development of transport models in complex geometries with complicated physics, like chemical reactions and buoyant heat transfer.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Drazin, P. G., Reid, W. H. Hvdrodvnamic stabili tv. Cambridge University Press, Cambridge 1981.
Details and other references are given in Orszag, S. A., Patera, A. T., J. Fluid Mech., 128 (1983), 347.
Goldhirsch, I., Orszag, S. A. An efficient method for computing the leading eigenvalues and eigenvectors of large asymmetric matrices, to be published (1986).
Kleiser, L., Schumann, U. Laminar-turbulent transition process in plane Poiseuille flow, in Proceedings of the Symposium in Spectral Methods ( Philadelphia, PA, 1984 ), 141.
Nishioka, M., Iida, S., Kanbayashi, S. An experimental investigation of the subcritical instability in plane Poiseuille flow, in Proceedings of the 10th Turbulence Symposium (Tokyo, 1978 ), 55.
Bayly, B. J. Kinematic and dynamical properties of complex three-dimensional flows, Ph. D. thesis, Princeton University (1986).
Patnaik, P. C., Sherman, F. S., Corcos, G. M., J. Fluid Mech., 73 (1982), 215.
Metcalfe, R., Orszag, S. A., Brächet, M. E., Menon, S., Riley, J. Secondary Instability of Free Shear Flows, submitted to J. Fluid Mech..
Pierrehumbert, R. T., Widnall, S. E., J. Fluid Mech., 1H (1982), 59.
Brächet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H., Frisch, U., J. Fluid Mech., 130 (1982), 411–452.
Pelz, R. B., Yakhot, V., Orszag, S. A., Shtilman, L., Levich, E. Velocity-Vorticity Patterns in Turbulent Flow, Phys. Rev. Lett., 51 (1985), 2505.
Levich, E., Tsinober, A. On the role of helical structures in three-dimensional turbulent flow, Phys. Lett., 22A (1983), 293–297.
Tsinober, A., Levich, E. On the helical nature of three-dimensional coherent structures in turbulent flows, Phys. Lett., 22A (1983), 321–324.
Shtilman, L., Levich, E., Orszag, S. A., Pelz, R. B., Tsinober, A. On the role of helicity in complex fluid flows, Phys. Lett., 113A (1985) 32–37.
Arnold, V. I. The asymptotic Hopf invariant and its application, in Proceedings of Summer School in Differential Equations. Erevan Armenian SSR Academy of Sciences, (1974).
Moffatt, H. K. Magnetostatic equilibria in viscous, perfectly conducting fluid and analogous Euler flows of an incompressible fluid: I. Fundamentals, J. Fluid Mech., 159 (1985) 359–478.
Batchelor, G. K. Phys. Fluids 12 (1969), 233.
Kraichnan, R. H. Phys. Fluids 10 (1967), 1417.
Saffman, P. G. Studies in Applied Math., 50 (1971), 377.
Brächet, M. E., Sulem, P. L. Free decay of high Reynolds number, two-dimensional turbulence, in Ninth International Conference on Numerical Methods in Fluid Mechanics, Lecture Notes in Physics, 218 Springer (1985), 103.
Orszag, S. A. in Fifth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, 59, Springer (1977), 32.
Yakhot, V., Orszag, S. A. Renormalization group analysis of turbulence I. Basic theory, J. Sci. Comp., 1 (1986) 1.
Kraichnan, R. H., J. Fluid Mech., 5. (1959), 497.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin, Heidelberg
About this paper
Cite this paper
Orszag, S.A., Pelz, R.B., Bayly, B.J. (1986). Secondary Instabilities, Coherent Structures and Turbulence. In: Kuwahara, K., Mendez, R., Orszag, S.A. (eds) Supercomputers and Fluid Dynamics. Lecture Notes in Engineering, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82908-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-82908-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17051-8
Online ISBN: 978-3-642-82908-6
eBook Packages: Springer Book Archive