Skip to main content
    • Aa
    • Aa

Lagrangian stochastic models for turbulent relative dispersion based on particle pair rotation


The physical picture of a fluid particle pair as a couple of material points rotating around their centre of mass is proposed to model turbulent relative dispersion in the inertial range. This scheme is used to constrain the non-uniqueness problem associated to the Lagrangian models in the well-mixed class and the properties of the stochastic process derived are analysed with respect to some turbulent velocity characteristics. A simple illustrative Markov model is developed in stationary homogeneous isotropic turbulence and the particle separation statistics are compared with direct numerical simulation data. In spite of the simplicity of the model, a consistent comparison is observed in the inertial range, supporting the formulation proposed.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

D. Anfossi , G. Degrazia , E. Ferrero , S. E. Gryning , M. G. Morselli & S. Trini Castelli 2000 Estimation of the Lagrangian structure function constant C0 from surface-layer wind data. Boundary-Layer Met. 95, 249270.

F. Anselmet , R. A. Antonia & L. Danaila 2001 Turbulent flows and intermittency in laboratory experiments. Planet. Space Sci. 49, 11771191.

R. A. Antonia , M. Ould-Rouis , Y. Zhu & F. Anselmet 1997 Fourth-order moments of longitudinal- and transverse-velocity structure functions. Europhys. Lett. 37, 8590.

R. A. Antonia , B. R. Satyaprakash & A. J. Chambers 1982 Reynolds number dependence of velocity structure functions in turbulent shear flows. Phys. Fluids 25, 2937.

G. K. Batchelor 1950 The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Met. Soc. 76, 133146.

L. Biferale , G. Boffetta , A. Celani , B. J. Devenish , A. Lanotte & F. Toschi 2005 Lagrangian statistics of particle pairs in homogeneous isotropic turbulence. Phys. Fluids 17 (11), 115101–1/9.

G. Boffetta & I. M. Sokolov 2002 Relative dispersion in fully developed turbulence: the Richardson's law and intermittency corrections. Phys. Rev. Lett. 88 (9), 094501–1/4.

M. S. Borgas & P. K. Yeung 1998 Conditional fluid–particle accelerations in turbulence. Theoret. Comput. Fluid Dyn. 11, 6993.

S. Du , J. D. Wilson & E. Yee 1994 On the moments approximation method for constructing a Lagrangian stochastic model. Boundary-Layer Met. 70, 273292.

T. K. Flesch & J. D. Wilson 1992 A two-dimensional trajectory-simulation model for non-Gaussian, inhomogeneous turbulence within plant canopies. Boundary-Layer Met. 61, 349374.

P. Franzese & M. S. Borgas 2002 A simple relative dispersion model for concentration fluctuations in contaminant clouds. J. Appl. Met. 41, 11011111.

R. J. Hill & O. N. Boratav 2001 Next-order structure–function equations. Phys. Fluids 13, 276283.

R. J. Hill & J. M. Wilczak 2001 Fourth-order velocity statistics. Fluid Dyn. Res. 28, 122.

T. Ishihara & Y. Kaneda 2002 Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence. Phys. Fluids 14, L69L72.

H. Kaplan & N. Dinar 1993 A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence. Boundary-Layer Met. 62, 217245.

O. A. Kurbanmuradov 1997 Stochastic Lagrangian models for two-particle relative dispersion in high-Reynolds number turbulence. Monte Carlo Meth. Applic. 3, 3752.

O. A. Kurbanmuradov & K. K. Sabelfeld 1995 Stochastic Lagrangian models of relative dispersion of a pair of fluid particles in turbulent flows. Monte Carlo Meth. Applic. 1, 101136.

O. A. Kurbanmuradov , S. A. Orszag , K. K. Sabelfeld & P. K. Yeung 2001 Analysis of relative dispersion of two particles by Lagrangian stochastic models and DNS methods. Monte Carlo Meth. Applic. 7, 245264.

Y. Li & C. Meneveau 2005 Origin of non-Gaussian statistics in hydrodynamic turbulence. Phys. Rev. Lett. 95, 164502–1/4.

A. Maurizi , G. Pagnini & F. Tampieri 2006 Turbulence scale dependece of the Richardson constant in Lagrangian stochastic models. Boundary-Layer Met. 118, 5568.

P. Monti & G. Leuzzi 1996 A closure to derive a three-dimensional well-mixed trajectory-model for non-Gaussian, inhomogeneous turbulence. Boundary-Layer Met. 80, 311331.

M. Nelkin & S. Chen 1998 The scaling of pressure in isotropic turbulence. Phys. Fluids 10, 21192121.

E. A. Novikov 1986 The Lagrangian–Eulerian probability relations and the random force method for nonhomogeneous turbulence. Phys. Fluids 29 (12), 39073909.

E. A. Novikov 1989 Two-particle description of turbulence, Markov property, and intermittency. Phys. Fluids A 1 2, 326330.

E. A. Novikov 1992 Probability distribution for three-dimensional vectors of velocity increments in turbulent flows. Phys. Rev. A 46, R6147R6149.

M. Ould-Rouis , R. A. Antonia , Y. Zhu & F. Anselmet 1996 Turbulent pressure structure function. Phys. Rev. Lett. 77, 22222224.

G. Pedrizzetti 1999 Quadratic Markov modeling for intermittent turbulence. Phys. Fluids 11 (6), 16941696.

S. Pope 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119192.

A. Praskovsky & S. Oncley 1994 Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers. Phys. Fluids 6, 28862888.

A. M. Reynolds 1999 aOn the non-uniqueness of Lagrangian stochastic models. Fluid Dyn. Res. 25, 217229.

A. M. Reynolds 1999 bThe relative dispersion of particle pairs in stationary homogeneous turbulence. J. Appl. Met. 38, 13841390.

A. M. Reynolds 2002 On the dynamical content of Lagrangian stochastic models in the well-mixed class. Boundary-Layer Met. 103, 143162.

L. F. Richardson 1926 Atmospheric diffusion shown on a distance-neighbor graph. Proc. R. Soc. Lond. A 110, 709737.

H. Risken 1989 The Fokker–Planck Equation. Methods of Solution and Applications, 2nd edn.Springer.

K. K. Sabelfeld & O. A. Kurbanmuradov 1997 Stochastic Lagrangian models for two-particle motion in turbulent flows. Monte Carlo Meth. Applic. 3, 5372.

K. K. Sabelfeld & O. A. Kurbanmuradov 1998 Two-particle stochastic Eulerian–Lagrangian models of turbulent dispersion. Math. Comput. Simulation 47, 429440.

B. L. Sawford 1999 Rotation of trajectories in Lagrangian stochastic models of turbulent dispersion. Boundary-Layer Met. 93, 411424.

B. L. Sawford 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289317.

B. L. Sawford 2006 A study of the connection between exit-time statistics and relative dispersion using a simple Lagrangian stochastic model. J. Turbulence 7 (13), 110.

B. L. Sawford & P. K. Yeung 2000 Eulerian acceleration statistics as a discriminator between Lagrangian stochastic models in uniform shear flow. Phys. Fluids 12 (8), 2033–424.

B. L. Sawford & P. K. Yeung 2001 Lagrangian statistics in uniform shear flow: direct numerical simulation and Lagrangian stochastic models. Phys. Fluids 13 (9), 26272634.

B. L. Sawford , P. K. Yeung & M. S. Borgas 2005 Comparison of backwards and forwards relative dispersion in turbulence. Phys. Fluids 17 (9), 095109–1/9.

B. L. Sawford , P. K. Yeung & J. F. Hackl 2008 Reynolds number dependence of relative dispersion statistics in isotropic turbulence. Phys. Fluids 20 (6), 065111–1/13.

K. R. Sreenivasan 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 27782784.

K. R. Sreenivasan & P. Kailasnath 1993 An update on the intermittency exponent in turbulence. Phys. Fluids A 5, 512514.

J. D. Wilson & T. K. Flesch 1997 Trajectory curvature as a selection criterion for valid Lagrangian stochastic models. Boundary-Layer Met. 84, 411425.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 16 *
Loading metrics...

Abstract views

Total abstract views: 41 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st September 2017. This data will be updated every 24 hours.