The eddy-to-mean energy transfer in turbulent flows is discussed. The discussion proceeds from the theory of rotationally anisotropic turbulence (RAT theory). It is shown that the rotational viscosity introduced in the RAT theory to quantify the interaction between the orientated (large-scale) turbulence constituent and the average flow can explain the eddy-to-mean energy transfer. The theoretical predictions are particularized for a jet stream model in a geophysical situation and compared with the data measured in the Gulf Stream transverse sections along 26°N (Florida Straits) and along 35°N (off Onslow Bay). The suggested model agrees with the measured data and points to a substantial difference in the data interpretation within the suggested model and within the conventional turbulence mechanics.
1. Starr, V. P. Physics of Negative Viscosity Phenomena. McGraw-Hill, New York, 1968.
2. Morimoto, H. and Maekawa, T. Negative viscosity induced in a ferromagnetic colloidal system subjected to both external shear flow and ac magnetic fields. Int. J. Modern Phys. B, 2002, 16, 2610–2615.
https://doi.org/10.1142/S0217979202012736
3. Bacri, J.-C., Perzynski, R., Shliomis, M. I. and Burde, G. I. “Negative-viscosity” effect in a magnetic fluid. Phys. Rev. Lett., 1995, 75, 2128–2131.
https://doi.org/10.1103/PhysRevLett.75.2128
4. Smoljakov, A. I., Diamond, P. H. and Malkov, M. Coherent structure phenomena in drift wave-zonal flow turbulence. Phys. Rev. Lett., 2000, 80, 491–494.
https://doi.org/10.1103/PhysRevLett.84.491
5. Heinloo, J. Phenomenological Mechanics of Turbulence. Valgus, Tallinn, 1984 (in Russian).
6. Heinloo, J. Turbulence Mechanics. Introduction to General Theory of Turbulence. Estonian Academy of Sciences, Tallinn, 1999 (in Russian).
7. Heinloo, J. The formulation of turbulence mechanics. Phys. Rev. E, 2004, 69, 056317.
https://doi.org/10.1103/PhysRevE.69.056317
8. Webster, T. F. The effects of meanders on the kinetic energy balance of the Gulf Stream. Tellus, 1961, 13, 392–401.
https://doi.org/10.3402/tellusa.v13i3.9515
9. Lin, G. and Atkinson, J. A mechanism for offshore transport across the Gulf Stream. J. Phys. Oceanogr., 2000, 30, 225–232.
https://doi.org/10.1175/1520-0485(2000)030<0225:AMFOTA>2.0.CO;2
10. Toompuu, A., Heinloo, J. and Soomere, T. Modelling of the Gibraltar Salinity Anomaly. Oceanology, 1989, 29, 698–702 (English translation).
11. Heinloo, J. and Võsumaa, Ü. Rotationally anisotropic turbulence in the sea. Ann. Geophys., 1992, 10, 708–715.
12. Võsumaa, Ü. and Heinloo, J. Evolution model of the vertical structure of the active layer of the sea. J. Geophys. Res., 1996, 101, 25635–25646.
https://doi.org/10.1029/96JC01988
13. Heinloo, J. and Toompuu, A. Antarctic Circumpolar Current as a density-driven flow. Proc. Estonian Acad. Sci. Phys. Math., 2004, 53, 252–265.
https://doi.org/10.3176/phys.math.2004.4.05
14. Heinloo, J. Eddy-driven flows over varying bottom topography in natural water bodies. Proc. Estonian Acad. Sci. Phys. Math., 2006, 55, 235–245.
15. Heinloo, J. and Toompuu, A. Modelling a turbulence effect in formation of the Antarctic Circumpolar Current. Ann. Geophys., 2006, 24, 3191–3196.
https://doi.org/10.5194/angeo-24-3191-2006
16. Truesdell, C. A. The Elements of Continuum Mechanics. Springer, New York, 1966.
17. Sedov, L. I. A Course in Continuum Mechanics. Kluwer, 1987.
18. Eringen, A. C. and Chang, T. S. Micropolar description of hydrodynamic turbulence. Recent Adv. Engng. Sci., 1970, 5, 1–8.
19. Peddieson, J. An application of the micropolar fluid model to the calculation of turbulent shear flow. Int. J. Eng. Sci., 1992, 10, 23–32.
https://doi.org/10.1016/0020-7225(72)90072-9
20. Eringen, A. C. Micromorphic description of turbulent channel flow. J. Math. Anal. Appl., 1972, 39, 253–256.
https://doi.org/10.1016/0022-247X(72)90239-9
21. Nikolaevskiy, V. N. Angular Momentum in Geophysical Turbulence: Continuum Spatial Averaging Method. Kluwer, 2003.
https://doi.org/10.1007/978-94-017-0199-0
22. Dahler, J. S. and Scriven, L. F. Angular momentum of continua. Nature, 1961, 192, 36–37.
https://doi.org/10.1038/192036a0
23. Dahler, J. S. Transport phenomena in a fluid composed of diatomic molecules. J. Chem. Phys., 1959, 30, 1447–1475.
https://doi.org/10.1063/1.1730220
24. Eringen, A. C. Theory of micropolar fluids. Math. and Mech., 1966, 16, 1–18.
https://doi.org/10.1512/iumj.1967.16.16001
25. Ariman, T., Turk, M. A. and Silvester, D. O. Microcontinuum fluid mechanics – review. Int. J. Eng. Sci., 1973, 11, 905–930.
https://doi.org/10.1016/0020-7225(73)90038-4
26. Richardson, O. Weather Prediction by Numerical Process. Cambridge University Press, 1922.
27. Kolmogoroff, A. N. The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers. C. R. Acad. Sci. URSS, 1941, 30, 376–387.
28. Sagaut, P. Large Eddy Simulation for Incompressible Flows. Springer-Verlag, 2006.
29. Lesieur, M., Métais, O. and Comte, P. Large-Eddy Simulations of Turbulence. Cambridge University Press, Cambridge, 2005.
https://doi.org/10.1017/CBO9780511755507
30. Volker, S., Venugopal, P. and Moser, R. D. Optimal large eddy simulation of turbulent channel flow based on a direct numerical simulation statistical data. Phys. Fluids, 2002, 14, 3675–3692.
https://doi.org/10.1063/1.1503803
31. O’Dwyer, J., Williams, R. G., Lacasce, J. H. and Speer, K. G. Does the potential vorticity distribution constrain the spreading of floats in the North Atlantic? J. Phys. Oceanogr., 2000, 30, 721–732.
https://doi.org/10.1175/1520-0485(2000)030<0721:DTPVDC>2.0.CO;2
32. Pedlosky, J. Geophysical Fluid Dynamics. Springer-Verlag, 1982.
https://doi.org/10.1007/978-3-662-25730-2
