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Lagrangian evolution of velocity increments in rotating turbulence: the effects of rotation on non-Gaussian statistics. (English) Zbl 1211.37095

The effects of rotation on the evolution of non-Gaussian statistics of velocity increments in rotating turbulence are studied in this paper. Following the Lagrangian evolution of the velocity increments over a fixed distance on an evolving material element, we derive a set of equations for the increments which provides a closed representation for the nonlinear interaction between the increments and the Coriolis force. Applying a restricted-Euler-type closure to the system, we obtain a system of ordinary differential equations which retains the effects of nonlinear interaction between the velocity increments and the Coriolis force. A priori tests using direct numerical simulation data show that the system captures the important dynamics of rotating turbulence. The system is integrated numerically starting from Gaussian initial data. It is shown that the system qualitatively reproduces a number of observations in rotating turbulence. The statistics of the velocity increments tend to Gaussian when strong rotation is imposed. The negative skewness in the longitudinal velocity increments is weakened by rotation. The model also predicts that the transverse velocity increment in the plane perpendicular to the rotation axis will have positive skewness, and that the skewness will depend on the Rossby number in a non-monotonic way. Based on the system, we identify the dynamical mechanisms leading to the observations.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76F55 Statistical turbulence modeling
76U05 General theory of rotating fluids
76F65 Direct numerical and large eddy simulation of turbulence
76B65 Rossby waves (MSC2010)
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References:

[1] Greenspan, H. P., The Theory of Rotating Fluids (1968), Cambridge University Press · Zbl 0182.28103
[2] Sagaut, P.; Cambon, C., Homogeneous Turbulence Dynamics (2008), Cambridge University Press · Zbl 1154.76003
[3] Mansour, N. N.; Shih, T.-H.; Reynolds, W. C., The effects of rotation on initially anisotropic homogeneous flows, Phys. Fluids A, 3, 2421 (1991) · Zbl 0746.76089
[4] Cambon, C.; Mansour, N. N.; Godeferd, F. S., Energy transfer in rotating turbulence, J. Fluid Mech., 337, 303-332 (1997) · Zbl 0891.76044
[5] Yeung, P. K.; Zhou, Y., Numerical study of rotating turbulence with external forcing, Phys. Fluids, 10, 2895 (1998)
[6] Smith, L. M.; Waleffe, F., Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence, Phys. Fluids, 11, 1608 (1999) · Zbl 1147.76500
[7] Yang, X.; Domaradzki, J. A., Large eddy simulations of decaying rotating turbulence, Phys. Fluids, 16, 11, 4088-4104 (2004) · Zbl 1187.76576
[8] Chen, Q.; Chen, S.; Eyink, G. L.; Holm, D. D., Resonant interactions in rotating homogeneous three-dimensional turbulence, J. Fluid Mech., 542, 139-164 (2005) · Zbl 1097.76033
[9] Morize, C.; Moisy, F.; Rabaud, M., Decaying grid-generated turbulence in a rotating tank, Phys. Fluids, 17, 095105 (2005) · Zbl 1187.76367
[10] Zhou, Y., A phenomenological treatment of rotating turbulence, Phys. Fluids, 7, 2092 (1995) · Zbl 1039.76516
[11] Bellet, F.; Godeferd, F. S.; Scott, J. F.; Cambon, C., Wave turbulence in rapidly rotating flows, J. Fluid Mech., 562, 83-121 (2006) · Zbl 1157.76338
[12] Hossain, M., Reduction in the dimensionality of turbulence due to a strong rotation, Phys. Fluids, 6, 1077-1080 (1994) · Zbl 0925.76240
[13] Bartello, P.; Mètais, O.; Lesieur, M., Coherent structures in rotating three-dimensional turbulence, J. Fluid Mech., 273, 1-29 (1994)
[14] Smith, L. M.; Lee, Y., On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number, J. Fluid Mech., 535, 111-142 (2005) · Zbl 1072.76067
[15] Bourouiba, L.; Bartello, P., The intermediate Rossby number range and two-dimensional-three-dimensional transfers in rotating decaying turbulence, J. Fluid Mech., 587, 139-161 (2007) · Zbl 1141.76396
[16] Davidson, P. A.; Staplehurst, P. J.; Dalziel, S. B., On the evolution of eddies in a rapidly rotating system, J. Fluid Mech., 557, 135-144 (2006) · Zbl 1147.76623
[17] Staplehurst, P. J.; Davidson, P. A.; Dalziel, S. B., Structure formation in homogeneous freely decaying rotating turbulence, J. Fluid Mech., 598, 81-105 (2008) · Zbl 1151.76494
[18] Frisch, U., Turbulence: The Legacy of A.N. Kolmogorov (1995), Cambridge University Press: Cambridge University Press Cambridge
[19] P.K. Yeung, J. Xu, K.R. Sreenivasan, Scaling properties in rotating homogeneous turbulence, in: Proceeding of FEDSM’03, 2003 4th ASME/JSME Joint Fluids Engineering Conference, 2003.; P.K. Yeung, J. Xu, K.R. Sreenivasan, Scaling properties in rotating homogeneous turbulence, in: Proceeding of FEDSM’03, 2003 4th ASME/JSME Joint Fluids Engineering Conference, 2003.
[20] van Bokhoven, L. J.A.; Cambon, C.; Liechtenstein, L.; Godeferd, F. S.; Clercx, H. J.H., Refined vorticity statistics of decaying rotating three-dimensional turbulence, J. Turbul., 9 (2008) · Zbl 1273.76176
[21] Gence, J.-N.; Frick, C., Birth of the triple correlations of vorticity in an homogeneous turbulence submitted to a solid body rotation, C. R. Acad. Sci., Paris, 329, 351-356 (2001) · Zbl 1012.76033
[22] Baroud, C. N.; Plapp, B. B.; Swinney, H. L.; She, Z.-S., Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows, Phys. Fluids, 15, 2091 (2003) · Zbl 1186.76043
[23] Műller, W.-C.; Thiele, M., Scaling and energy transfer in rotating turbulence, Europhys. Lett., 77, 34003 (2007)
[24] Seiwert, J.; Morize, C.; Moisy, F., On the decrease of intermittency in decaying rotating turbulence, Phys. Fluids, 20, 071702 (2008) · Zbl 1182.76676
[25] Thiele, M.; Muller, W. C., Struture and decay of rotating homogeneous turbulence, J. Fluid Mech., 637, 425-442 (2009) · Zbl 1183.76750
[26] Vieillefosse, P., Local interaction between vorticity and shear in a perfect incompressible fluid, J. Phys., 43, 837-842 (1982)
[27] Cantwell, B. J., Exact solution of a restricted Euler equation for the velocity gradient tensor, Phys. Fluids A, 4, 782-793 (1992) · Zbl 0754.76004
[28] Ashurst, W. T.; Kerstein, A. R.; Kerr, R. M.; Gibson, C. H., Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence, Phys. Fluids, 30, 2343-2353 (1987)
[29] Tsinober, A.; Kit, E.; Dracos, T., Experimental investigation of the field of velocity-gradients in turbulent flows, J. Fluid Mech., 242, 169-192 (1992)
[30] Chertkov, M.; Pumir, A.; Shraiman, B. I., Lagrangian tetrad dynamics and the phenomenology of turbulence, Phys. Fluids, 11, 2394-2410 (1999) · Zbl 1147.76360
[31] Jeong, E.; Girimaji, S. S., Velocity-gradient dynamics in turbulence: effect of viscosity and forcing, Theor. Comput. Fluid Dyn., 16, 421-432 (2003) · Zbl 1068.76522
[32] Naso, A.; Pumir, A., Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence, Phys. Rev. E, 72, 056318 (2005)
[33] Chevillard, L.; Meneveau, C., Lagrangian dynamics and statistical geometric structure of turbulence, Phys. Rev. Lett., 97, 174501 (2006)
[34] Suman, S.; Girimaji, S. S., Homogenized Euler equation: a model for compressible velocity gradient dynamics, J. Fluid Mech., 620, 177-194 (2009) · Zbl 1156.76435
[35] Li, Y.; Meneveau, C., Origin of non-Gaussian statistics in hydrodynamic turbulence, Phys. Rev. Lett., 95, 164502 (2005)
[36] Li, Y.; Meneveau, C., Intermittency trends and Lagrangian evolution of non-Gaussian statistics in turbulent flow and scalar transport, J. Fluid Mech., 558, 133-142 (2006) · Zbl 1156.76404
[37] Kraichnan, R. H., Model of intermittency in hydrodynamic turbulence, Phys. Rev. Lett., 65, 575-578 (1990) · Zbl 1050.76546
[38] Sreenivasan, K. R.; Antonia, R. A., The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech., 29, 435-472 (1997)
[39] Li, Y.; Chevillard, L.; Eyink, G.; Meneveau, C., Matrix exponential-based closures for the turbulent subgrid-scale stress tensor, Phys. Rev. E, 79, 016305 (2009)
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