CLC number: O357.5; TV131.21
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2008-12-29
Cited: 0
Clicked: 6057
Zhao-cun LIU. Scaling properties of Navier-Stokes turbulence[J]. Journal of Zhejiang University Science A, 2009, 10(3): 392-397.
@article{title="Scaling properties of Navier-Stokes turbulence",
author="Zhao-cun LIU",
journal="Journal of Zhejiang University Science A",
volume="10",
number="3",
pages="392-397",
year="2009",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0820215"
}
%0 Journal Article
%T Scaling properties of Navier-Stokes turbulence
%A Zhao-cun LIU
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 3
%P 392-397
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820215
TY - JOUR
T1 - Scaling properties of Navier-Stokes turbulence
A1 - Zhao-cun LIU
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 3
SP - 392
EP - 397
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820215
Abstract: The property of the velocity field and the cascade process of the fluid flow are key problems in turbulence research. This study presents the scaling property of the turbulent velocity field and a mathematical description of the cascade process, using the following methods: (1) a discussion of the general self-similarity and scaling invariance of fluid flow from the viewpoint of the physical mechanism of turbulent flow; (2) the development of the relationship between the scaling indices and the key parameters of the She and Leveque (SL) model in the inertial range; (3) an investigation of the basis of the fractal model and the multi-fractal model of turbulence; (4) a demonstration of the physical meaning of the flowing field scaling that is related to the real flowing vortex. The results illustrate that the SL model could be regarded as an approximate mathematical solution of Navier-Stokes (N-S) equations, and that the phenomena of normal scaling and anomalous scaling is the result of the mutual interactions among the physical factors of nonlinearity, dissipation, and dispersion. Finally, a simple turbulent movement conceptional description model is developed to show the local properties and the instantaneous properties of turbulence.
[1] Chiueh, Z., 1998. Dynamical quantum chaos as fluid turbulence. Physical Review E, 57(4):4150-4155.
[2] Dubrulle, B., 1994. Intermittency in fully developed turbulence: log-Poisson statistics and generalized scale covariance. Physical Review Letters, 73(7):959-962.
[3] Falkovich, G., Gawedzki, K., Vergassola, M., 2001. Particles and fields in fluid turbulence. Reviews of Modern Physics, 73(4):913-974.
[4] Frisch, U., 1995. Turbulence: the Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge.
[5] Frisch, U., Sulem, P., Nelkin, M., 1978. A simple dynamical model of intermittent fully developed turbulence. Journal of Fluid Mechanics, 87(4):719-736.
[6] Hunt, C.R., 2001. Developments in turbulence research: a review based on the 1999 programme of the Isaac Newton Institute Cambridge. Journal of Fluid Mechanics, 436:353-391.
[7] Lee, C.B., Lee, R., 2001. On the dynamics in a transitional boundary layer. Communications in Nonlinear Science & Numerical Simulation, 6(3):111-171.
[8] Liu, S.D., Liu, S.K., 1993. Soliton Wave and Turbulence. Shanghai Science and Technology Education Publishing House, Shanghai (in Chinese).
[9] Liu, S.D., Liu, S.K., 1997. General self-similarity and scaling invariance of fluid flow. KeXue TongBao, 42(2):180-182 (in Chinese).
[10] Liu, S.D., Liu, S.K., 1998. The fourth effect of turbulence-dispersion. Progress in Natural Science, 8(5):631-633 (in Chinese).
[11] Liu, S.D., Liu, S.K., 2002. Some problems in non-linear dynamics study. Progress in Natural Science, 12(1):1-7 (in Chinese).
[12] Marmanis, H., 1998. Analogy between the Navier-Stokes equations and Maxwell’s equations: application to turbulence. Physics of Fluids, 10(6):1428-1437.
[13] Mazzino, A., Muratore-Ginanneschi, P., Musacchio, S., 2007. Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation. Physical Review Letters, 99(5):144502.
[14] Mitra, D., Pandit, R., 2004. Varieties of dynamic multi-scaling in fluid turbulence. Physical Review Letters, 93(2):024501.
[15] Nelkin, M., 1995. Inertial range scaling of intense events in turbulence. Physical Review E, 52(5):R4610-R4611.
[16] Qian, J., 2001. On the normal and anomalous scaling in turbulence. Advance in Mechanics, 31(3):405-416 (in Chinese).
[17] She, Z.S., Su, W.D., 1999. Hierarchical structure and scaling in turbulence. Advance in Mechanics, 29(3):289-303 (in Chinese).
[18] Wu, J.Z., Ma, H.Y., Zhou, M.D., 2006. Vorticity and Vortex Dynamics. Springer, Berlin.
[19] Zou, W.N., 2003. Objectivity requirement for fluid dynamics. Applied Mathematics and Mechanics (English Edition), 24(12):1243-1248.
Open peer comments: Debate/Discuss/Question/Opinion
<1>