Abstract
In this article we demonstrate that turbulent stress contributions which depend on the rotation of the frame of reference (and therefore are system dependent) give rise to the inverse energy cascade, and thus introduce an ordering in the structure of turbulence.
We first demonstrate that a non-rotating Boussinesq fluid subject to an artificial force that is not invariant under parity changes of the orthogonal group has a destabilizing effect in the B'enard problem. This destabilization is due to helicity and the stability regimes are divided into two regions: (1) If the helicitys is below a threshold values *, then long and very short wavelength disturbances at Rayleigh numbers Ra > Racrit are stable whereas those with intermediate wavelengths are unstable. (2) If the helicitys >s * then all disturbances are unstable.
For a rotating turbulent Boussinesq fluid we derive the most simple rotation dependent expression for the stress divergence and demonstrate that it leads quantitatively to a similar helicity dependent force. In the B6nard problem it gives rise to an analogous division of the stability/instability regime as obtained for non-rotating fluids subject to the artificial helicity dependent force.
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Moiseev, S. S.; Sagdeev, R. Z.; Tur, A. V.; Khomenko, G. A.; Yanovsky, V. V.: The theory of large-scale structures formation in hydrodynamical turbulence. Z. Eksp.-Teor. Fiz. 85 (1983) 1979–1987 (Russian)
Tsinober, A.; Levich, E.: On the helical nature of three-dimensional coherent structures in turbulent flows. Phys. Lett 99 A (1983) 321–324
Levich, E.; Tzvetkov, E.: Helical cyclogenesis. Phys. Lett. 100 A (1984) 53–56
Sivashinsky, G.; Yakhot, V.: Negative viscosity effect in large-scale flows. Phys. Fluids 28 (1985) 1040–1042
Yakhot, V.; Peltz, R.: Large-scale structure generation by anisotropic small-scale flows. Phys. Fluids 30 (1987) 1272–1277
Lilly, D. K.: The structure, energetics and propagation of rotating convective storms. Part II: Helicity and storm stabilization. J. Atoms. Sci. 43 (1986) 126–140
Frisch, U.; She, Z. S.; Sulem, P. L.: Large-scale flow driven by an anisotropic kinetic alpha effect. Physica D 28 (1987) 382–392
Rogers, M. M.; Moin, P.: Helicity fluctuations in incompressible turbulent flows. Phys. Fluids 30 (1987) 2662–2671
Moiseev, S. S.; Rutkevich, P. B.; Tuz, A. V.; Yanovsky, V. V.: Vortex dynamo in a convective fluid with helical turbulence. Z. Exp.-Teor. Fiz. 94 (1988) 144–153 (Russian)
Sulem, P. L.; She, Z. S.; Scholl, H.; Frisch, U.: Generation of large-scale structures in three-dimensional flow lacking partiy-invariance. J. Fluid. Mech. 205 (1989) 341–358
Berezin, Yu. A.; Sagdeev, R. Z.: On fire-hose instability of a rarefied plasma. Soviet Doklady 184 (1969) 570–574 (Russian)
Frisch, U.; Pouguet, A.; Leorat, J.; Mazure, A.: Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. J. Fluid Mech. 68 (1975) 769–778
Betchov, R.: Semi-isotropic turbulence and helicoidal flows. Phys. Fluids 4 (1961) 925–926
Gershuni, G. Z.; Zhukhovitskii, E. M.: Convective stability of incompressible fluids. Jerusalem: Keter Publishing House Jerusalem Lt. 1976
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Berezin, Y.A., Hutter, K. & Zhukov, V.P. Large-scale vortical structure, supported by small-scale turbulent motions. Helicity as a cause for inverse energy cascade. Continuum Mech. Thermodyn 3, 127–146 (1991). https://doi.org/10.1007/BF01129031
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DOI: https://doi.org/10.1007/BF01129031