[1] CHEVILLARD L,MENEVEAU C.Lagrangian dynamics and statistical geometric structure of turbulence[J].Physical Review Letters,2006,97(17):174501.
[2] OOI A,SORIA J,CHONG M S,et al.A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence[J].Journal of Fluid Mechanics,1999,381(1):141-174.
[3] ATKINSON C,CHUMAKOV S,BRRMEJO-MORENO I,et al.Lagrangian evolution of the invariant of the velocity gradient tensor in a turbulent boundary layer[J].Physics of Fluids,2012,24(10):677-686.
[4] MENEVEAU C.Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows[J].Annual Review of Fluid Mechanics,2011,43(1):219-245.
[5] KERR R M.Histograms of helicity and strain in numerical turbulence[J].Physical Review Letters,1987,59(7):783-786.
[6] ASHURST W T,KERSTEIN A R,KERR R M,et al.Alignment of vorticity and scalar gradient with the strain rate in simulated Navier-Stokes turbulence[J].Physics of Fluids,1987,30(8):2343-2353.
[7] SREENIVASAN K R,ANTONIA R A.The phenomenology of small-scale turbulence[J].Annual Review of Fluid Mechanics,1997,29(1):435-472.
[8] GIRIMAJI S S,POPE S B.A diffusion model for velocity gradients in turbulence[J].Physics of Fluids A:Fluid Dynamics,1990,2(2):242-256.
[9] MARTIN J,DOPAZO C,VALION L.Dynamics of velocity gradient invariants in turbulence:Restricted Euler and linear diffusion models[J].Physics of Fluids,1998,10(8):2012-2025.
[10] JEONG E,GIRIMAJI S S.Velocity-gradient dynamics in turbulence:Effect of viscosity and forcing[J].Theoretical and Computational Fluid Dynamics,2003,16(6):421-432.
[11] FANG L,BOS W J T,JIN G D.Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence[J].Physics of Fluids,2015,27(12):457-472.
[12] FANG L,ZHANG Y J,FANG J,et al.Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence[J].Physical Review E,2016,94(2):023114.
[13] YU H,MENEVEAU C.Lagrangian refined Kolmogorov similarity hypothesis for gradient time-evolution in turbulence flows[J].Physical Review Letters,2010,104(8):084502.
[14] TENNEKES H,LUMLEY J.湍流初级教程[M].施红辉,林培锋,金浩哲,译.北京:科学出版社,2015:14-15.TENNEKES H,LUMLEY J.A first course in turbulence[M].SHI H H,LIN P F,JIN H Z,translated.Beijing:Science Press,2015:14-15(in Chinese).
[15] 张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京:清华大学出版社,2005:11.ZHANG Z S,CUI G X,XU C X.Theory and modeling of turbulence[M].Beijing:Tsinghua University Press,2005:11(in Chinese).
[16] STOLOVITZKY G,KAILASNATH P,SREENIVASAN K R.Kolmogorov's refined similarity hypothesis[J].Physical Review Letters,1992,69(8):1178-1181.
[17] 张兆顺,崔桂香,许春晓.湍流大涡模拟的理论与应用[M].北京:清华大学出版社,2008:101-104.ZHANG Z S,CUI G X,XU C X.Theory and application of large eddy simulation of turbulence[M].Beijing:Tsinghua University Press,2008:101-104(in Chinese).
[18] 周海兵.标量湍流的数值研究[D].北京:清华大学,2003:39-45.ZHOU H B.Numerical research of scalar turbulence[D].Beijing:Tsinghua University,2003:39-45(in Chinese).
[19] XU C X,ZHANG Z S,TOONDER J M J,et al.Origin of high kurtosis levels in the viscous sublayer.Direct numerical simulation and experiment[J].Physics of Fluids,1996,8(7):1938-1944.
[20] FANG L,SHAO L,BERTOGLIO J P,et al.The rapid-slow decomposition of the subgrid flux in inhomogeneous scalar turbulence[J].Journal of Turbulence,2011,12(8):1-23. |