# THE ORIGIN OF TURBULENCE IN WALL-BOUNDED FLOWS

## Main Article Content

## Abstract

The motion of liquids and gases can be either laminar, flowing slowly in orderly parallel and continuous layers of fluid that cannot mix, or turbulent in which motion exhibits disorder in time and space with the ability to promote mixing. Breakdown of ordered to disordered motion can follow different scenarios so that no universal mechanism can be identified even in similar flow configurations [1]. Only under very special circumstances can the mechanism associated with the appearance of turbulence be studied within the deterministic theory of hydrodynamic stability [2] or employing direct numerical simulations [3] which themselves cannot provide the necessary understanding [4]. Here we show that the representative mechanism responsible for the origin of turbulence in wall-bounded flows is associated with large variations of anisotropy in the disturbances [5]. During the breakdown process, anisotropy decays from a maximum towards its minimum value, inducing the explosive production of the dissipation which logically leads to the appearance of small-scale three-dimensional motions. By projecting the sequence of events leading to turbulence in the space which emphasizes the anisotropic nature in the disturbances [6], we explain why, demonstrate how and present what can be achieved if the process is treated analytically using statistical techniques [7]. It is shown that the statistical approach provides not only predictions of the breakdown phenomena which are in fair agreement with available data but also requirements which ensure persistence of the laminar regime up to very high Reynolds numbers.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2324>. Date accessed: 20 feb. 2018. doi: https://doi.org/10.2298/TSCI160413184J.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-14

Published 2017-03-14

## References

[2] Lin, C.C. The Theory of Hydrodynamic Stability. Cambridge University Press, Cambridge 1955

[3] Orszag, S.A. Numerical studies of transition in planar shear flows. In Laminar-Turbulent Transition (Eppler, E. and Fasel, H., editors). Springer-Verlag, Berlin 1980, pp. 153–162

[4] Holmes, P., Lumley, J.L. and Berkooz, G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge, 1998

[5] Jovanovi´c, J. and Pashtrapanska, M. On the criterion for the determination transition onset and breakdown to turbulence in wall-bounded flows. J. Fluids Eng. 126 (2004), pp. 626–633

[6] Lumley, J.L. Computational modeling of turbulent flows, Adv. Appl. Mech. 18 (1978), pp. 23–176

[7] Jovanovi´c, J. The Statistical Dynamics of Turbulence. Springer-Verlag, Berlin 2004.

[8] Emmons, H.W. The laminar-turbulent transition in a boundary layer-Part I, J. Aero. Sci. 18 (1951), pp. 490–498

[9] Gad-el-Hak, M. A visual study of the growth and entrainment of turbulent spots, In Laminar- Turbulent Transition (Eppler, E. and Fasel, H. editors). Springer-Verlag, Berlin, 1980, pp. 297–310

[10] Cantwell, B., Coles, D. and Dimotakis, P. Structure and entrainment in the plane of symmetry of a turbulent spot, J. Fluid. Mech. 87 (1978), pp. 641–672

[11] Van Dyke, M. An Album of Fluid Motion. Parabolic Press, Stanford 1988.

[12] Herbert, Th. and Morkovin, M.V. Dialog on bridging some gaps in stability and transition research. In Laminar-Turbulent Transition (Eppler, E. and Fasel, H. editors). Springer-Verlag, Berlin, 1980, pp. 47–72

[13] Kim, J., Moin, P. and Moser, R. Turbulence statistics in a fully developed channel flow at low Reynolds numbers. J. Fluid Mech. 177 (1987), pp. 133–166

[14] Antonia, R.A. Teitel, M., Kim, J. and Browne, L.W.B. Low-Reynolds number effects in a fully developed channel flow. J. Fluid Mech. 236 (1992), pp. 579–605

[15] Moser, R.D., Kim, J. and Mansour, N.N. Direct numerical simulation of turbulent channel flow up to Ret = 590. Phys. Fluids 11 (1999), pp. 943–945

[16] Kuroda, A., Kasagi, N. and Hirata, M. Direct numerical simulation of the turbulent plane Couette- Poiseulle flows: effect of mean shear on the near wall turbulence structures. Proc. 9th Symp. on Turbulent Shear Flows, Kyoto, 8.4.1-8.4.6 1993, http://www.thtlab.t.u-tokyo.ac.jp/

[17] Horiuti, K., Miyake, Y., Miyauchi, T., Nagano, Y. and Kasagi, N. Establishment of the DNS database of turbulent transport phenomena. Rep. Grants-in-Aid for Scientific Research, No. 02302043, 1992, http://www.thtlab.t.u-tokyo.ac.jp/

[18] Jovanovi´c, J. and Hillerbrand, R. On peculiar property of the velocity fluctuations in wall-bounded flows, J. Thermal Sci. 9 (2005), pp. 3–12

[19] Jovanovi´c, J. and Oti´c, I. On the constitutive relation for the Reynolds stresses and the Prandtl- Kolmogorov hypothesis of effective viscosity in axisymmetric strained turbulence, J. Fluids Eng. 122 (2000), pp. 48–50

[20] Jovanovi´c, J., Oti´c, I. and Bradshaw, P. On the anisotropy of axisymmetric strained turbulence in the dissipation range, J. Fluids Eng. 125 (2003), pp. 410–413

[21] Schlichting, H. Boundary-Layer Theory. 6th edn. McGraw-Hill, New York, 1968.

[22] Kolmogorov, A.N. On degeneration of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk SSSR 6, 538–540 (1941).

[23] Jovanovi´c, J., Ye, Q.-Y. and Durst, F. Statistical interpretation of the turbulent dissipation rate in wall-bounded flows, J. Fluid Mech. 293 (1995), pp. 321–347

[24] Spangler, J.G. and Wells, C.S. Effects of free stream disturbances on boundary-layer transition, AIAA J. 6 (1968), pp. 534–545

[25] Kachanov, Y.S., Kozlov, V.V. and Levchenko, V.Y. The Origin of Turbulence in the Boundary Layer. Nauka, Novosibirsk, 1982.

[26] Saric, W.S. and Reynolds, G.A. Experiments on the stability and nonlinear waves in a boundary layer. In Laminar-Turbulent Transition (Eppler, E. and Fasel, H. editors). Springer-Verlag, Berlin, 1980, pp. 125–134

[27] Jovanovi´c, J., Frohnapfel, B., ˇ Skalji´c, E. and Jovanovi´c, M. Persistence of the laminar regime in a flat plate boundary layer at very high Reynolds number, J. Thermal Sci. 10 (2006), pp. 63–96

[28] Bake, S. Herman-F¨ottinger Institute, Berlin, personal communication, 1999.