×

zbMATH — the first resource for mathematics

Angular momentum of forced 2D turbulence in a square no-slip domain. (English) Zbl 1098.76546
Summary: Self-organization of forced two-dimensional (2D) turbulence in a square no-slip domain may drive the global angular momentum to sudden peak values. This ‘spin-up’ process was observed in several direct numerical simulations (DNS) for intermediate integral-scale Reynolds numbers. The development of viscous boundary layers at the no-slip walls destabilizes the spin-up state, causing it to break-down in semi-regular intervals. After each break-down a new event of self-organization takes place, possibly with a different of rotation.
If certain a priori bounds are satisfied, the evolution of the kinetic energy and the absolute angular momentum may be nearly similar in the spin-up state. Such a similarity defines a large-scale energy saturation time, which is shown to exhibit a lower bound scaling behaviour with respect to the usual turbulent time \(\tau\), based upon the averaged enstrophy dissipation \(\eta\).

MSC:
76F02 Fundamentals of turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76F40 Turbulent boundary layers
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Basdevant, C.; Philipovitch, T., On the validity of the “weiss criterion” in the two-dimensional turbulence, Physica D, 73, 17-30, (1994) · Zbl 0814.76050
[2] Chavanis, P.H.; Sommeria, J., Classification of self-organized vortices in two-dimensional turbulence: the case of a bounded domain, J. fluid mech., 314, 267-297, (1996) · Zbl 0864.76037
[3] Clercx, H.J.H., A spectral solver for the navier – stokes equations in velocity-vorticity formulation for flows with two nonperiodic directions, J. comp. phys., 137, 186-211, (1997) · Zbl 0904.76058
[4] Clercx, H.J.H.; Maassen, S.R.; van Heijst, G.J.F., Spontaneous spin-up during the decay of 2D turbulence in a square container with rigid boundaries, Phys. rev. lett., 80, 5129-5132, (1998)
[5] Clercx, H.J.H.; Nielsen, A.H.; Torres, D.J.; Coutsias, E.A., Two-dimensional turbulence in square and circular domains with no-slip walls, Eur. J. mech. B-fluids, 20, 557-576, (2001) · Zbl 1011.76039
[6] Courant, R.; Hilbert, D., Methoden der mathematischen physik, (1967), Springer-Verlag New Rochelle · JFM 63.0449.05
[7] Danilov, S.; Gurarie, D., Forced two-dimensional turbulence in spectral and physical space, 061208, 63, 1-12, (1993)
[8] Eyink, G.L., Exact results on stationary turbulence in 2D: consequences of vorticity conservation, Physica D, 91, 97-142, (1996) · Zbl 0896.76027
[9] Foias, C.; Manley, O.P.; Teman, R.; Treve, Y.M., Asymptotic analysis of the navier – stokes equations, Physica D, 9, 157-188, (1983) · Zbl 0584.35007
[10] Foias, C.; Manley, O.P.; Temam, R., Bounds for the Mean dissipation of 2D enstrophy and 3D energy in turbulent flows, Phys. lett. A, 174, 210-215, (1993)
[11] Foias, C., What do the navier – stokes equations tell us about turbulence?, Cont. math., 208, 151-180, (1997) · Zbl 0890.76030
[12] Galdi, G.P., An introduction to the mathematical theory of the navier – stokes equations, (1994), Springer-Verlag New York · Zbl 0949.35005
[13] Hossain, M.; Matthaeus, W.H.; Montgomery, D., Long-time state of inverse cascades in the presence of a maximum length scale, J. plasma phys., 30, 479-493, (1983)
[14] Kraichnan, R.H., Inertial ranges in two-dimensional turbulence, Phys. fluids, 10, 1417-1423, (1967)
[15] Li, S.; Montgomery, D.; Jones, W.B., Inverse cascades of angular momentum, J. plasma phys., 56, 615-639, (1996)
[16] Lilly, D., Numerical simulation of two-dimensional turbulence, Phys. fluids II, 240-249, (1969) · Zbl 0263.76046
[17] Maassen, S.R.; Clercx, H.J.H.; van Heijst, G.J.F., Self-organization of quasi-two-dimensional turbulence in stratified fluids in square and circular containers, Phys. fluids, 14, 2150-2169, (2002) · Zbl 1185.76235
[18] Malturd, M.E.; Vallis, G.K., Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence, J. fluid mech., 228, 321-342, (1991)
[19] Niemela, J.J.; Skrbek, L.; Sreenivasan, K.R.; Donnelly, R.J., The wind in thermal convection, J. fluid mech., 449, 169-178, (2001) · Zbl 0988.76502
[20] Ohkitani, K., Wave number space dynamics of enstrophy cascade in a forced tow-dimensional turbulence, Phys. fluids A, 3, 1598-1611, (1991) · Zbl 0732.76049
[21] Paret, J.; Tabeling, P., Intermittency in the two-dimensional inverse cascade of energy: experimental observations, Phys. fluids, 10, 3126-3136, (1998)
[22] Pointin, Y.B.; Lundgren, T.S., Statistical mechanics of two-dimensional vortices in a bounded container, Phys. fluids, 19, 1459-1470, (1976) · Zbl 0339.76013
[23] Saffman, P.G., Vortex dynamics, (1992), Cambridge University Press Cambridge, England · Zbl 0777.76004
[24] Smith, L.M.; Yakhot, V., Bose condensation and small-scale structure generation in a random force driven 2D turbulence, Phys. rev. lett., 71, 352-355, (1993)
[25] Smith, L.M.; Yakhot, V., Finite-size effects in forced two-dimensional turbulence, J. fluid mech., 274, 115-138, (1994) · Zbl 0825.76356
[26] Sommeria, J., Experimental study of the two-dimensional inverse energy cascade in a square box, J. fluid mech., 170, 139-168, (1986)
[27] Weiss, J., The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D, 48, 273-294, (1991) · Zbl 0716.76025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.