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Spectra of local and nonlocal two-dimensional turbulence. (English) Zbl 0823.76034
Summary: We propose a family of two-dimensional incompressible fluid models indexed by a parameter \(\alpha\in [0, \infty]\), and discuss the spectral scaling properties for homogeneous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spectrally local for \(\alpha< 2\), but becomes dominated by nonlocal interactions for \(\alpha> 2\). Numerical simulation indicate that the spectral slopes are systematically steeper than those predicted by the local scaling argument.

MSC:
76F05 Isotropic turbulence; homogeneous turbulence
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[1] Rhines, P.B., Geostrophic turbulence, Ann. rev. fluid mech., 11, 401-442, (1979) · Zbl 0474.76054
[2] Kolmogorov, A.N., The local structure of turbulence in incompressible fluid at very high Reynolds number, Dokl. akad. sci. USSR, 30, 299-303, (1941)
[3] Kraichnan, R., Eddy viscosity in two and three dimensions, J. atmos. sci., 33, 1521-1536, (1976)
[4] Kraichnan, R., Inertial-range transfer in two- and three-dimensional turbulence, J. fluid mech., 47, 525-535, (1971) · Zbl 0224.76053
[5] Ottino, J., The kinematics of mixing: stretching, chaos and transport, (1989), Cambridge University Press Cambridge · Zbl 0721.76015
[6] Pierrehumbert, R.T., Chaotic mixing of tracer and vorticity by modulated travelling Rossby waves, Geophys. astrophys. fluid dynamics, 58, 285-319, (1991)
[7] Blumen, W., Uniform potential vorticity flow—part I: theory of wave interactions and two-dimensional turbulence, J. atmos. sci., 35, 774-783, (1978)
[8] Hoyer, J.-M.; Sadourny, R., J. atmos. sci., 39, 707-721, (1982)
[9] Kraichnan, R., Inertial ranges in two-dimensional turbulence, Phys. fluids, 10, 1417-1423, (1967)
[10] Batchelor, G.K., Small-scale variation of convected quantities like temperature in turbulent fluid—part 1; general discussion and the case of small conductivity, J. fluid mech., 5, 113-133, (1959) · Zbl 0085.39701
[11] Dritschel, D.G.; Haynes, P.H.; Juckes, M.N.; Shepherd, T.G., The stability of a two-dimensional vorticity filament under uniform strain, J. fluid mech., 230, 647-665, (1991) · Zbl 0728.76045
[12] Brachet, M.E.; Meneguzzi, M.; Sulem, P.L., Small-scale dynamics of high Reynolds number two-dimensional turbulence, Phys. rev. lett., 57, 683-686, (1986)
[13] Basdevant, C.; Legras, B.; Sadourny, R.; Beland, M., A study of barotropic model flows: intermittency, waves and predictability, J. atmos. sci., 38, 2305-2326, (1981)
[14] Herring, J.; Kraichnan, R., J. fluid mech., 153, 229-242, (1985)
[15] Juckes, M.N.; McIntyre, M.E., A high resolution, one-layer model of breaking planetary waves in the stratosphere, Nature lond., 328, 590-596, (1987)
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