Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T18:32:08.107Z Has data issue: false hasContentIssue false
  • English
  • Français

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

Published online by Cambridge University Press:  26 April 2006

M. S. Borgas  and
B. L. Sawford
M. S. Borgas
Affiliation:
CSIRO Division of Atmospheric Research, FBI Mordialloc, Victoria 3195, Australia
B. L. Sawford
Affiliation:
CSIRO Division of Atmospheric Research, FBI Mordialloc, Victoria 3195, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 279 , 25 November 1994 , pp. 69 - 99
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. I. Eulerian analysis. Austral. J. Sci. Res. A 2, 437–450.Google Scholar
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Borgas, M. S. 1991 The multifractal nature of turbulent dispersion. In Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson), pp. 125–132. Springer.
Borgas, M. S. 1993 The multifractal Lagrangian nature of turbulence. Phil. Trans. R. Soc. Lond. A 342, 379–411.Google Scholar
Borgas, M. S. & Sawford, B. L. 1991 The small-scale structure of acceleration correlations and its role in the statistical theory of turbulent dispersion. J. Fluid Mech. 228, 295–320.Google Scholar
Borgas, M. S. & Sawford, B. L. 1994 Stochastic equations with multifractal increments for modelling turbulent dispersion. Phys. Fluids 6, 618–633.Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.Google Scholar
Fung, J. C. H., Hunt, J. C. R., Malik, N. A. & Perkins, R. J. 1992 Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech. 236, 281–318.Google Scholar
Gardiner, C. W. 1983 Handbook of Stochastic Methods for Physics Chemistry and the Natural Sciences. Springer.
Hanna, S. R. 1981 Lagrangian and Eulerian time-scale relations in the daytime boundary layer. J. Appl. Met. 20, 242–249.Google Scholar
Kaplan, H. & Dinar, N. 1989 The interference of two passive scalars in a homogeneous isotropic turbulence field. J. Fluid Mech. 203, 273–287.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Novikov, E. A. 1963 Random force method in turbulence theory. Sov. Phys. JETP 17, 1449–1454.Google Scholar
Novikov, E. A. 1989 Two-particle description of turbulence, Markov property, and intermittency. Phys. Fluids A 1, 326–330.Google Scholar
Novikov, E. A. 1990 The effects of intermittency on statistical characteristics of turbulence and scale similarity of breakdown coefficients. Phys. Fluids A 2, 814–820.Google Scholar
Obukhov, A. M. 1959 Description of turbulence in terms of Lagrangian variables. Adv. Geophys. 6, 113–116.Google Scholar
Pope, S. B. 1985 Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.Google Scholar
Pope, S. B. 1987 Consistency conditions for random-walk models of turbulent dispersion. Phys. Fluids 30, 2374–2379.Google Scholar
Pope, S. B. 1994a On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys. Fluids 6, 973–985.Google Scholar
Pope, S. B. 1994b Lagrangian PDF methods for turbulent flows. Ann. Rev. Fluid Mech. 26, 23–63.Google Scholar
Pope, S. B. & Chen, Y. L. 1990 The velocity-dissipation pdf model for turbulent flows. Phys. Fluids A 2, 1437–1449.Google Scholar
Sawford, B. L. 1985 Lagrangian statistical simulation of concentration mean and fluctuation fields. J. Clim. Appl. Met. 24, 1152–1166.Google Scholar
Sawford, B. L. 1991 Reynolds number effects in Lagrangian stochastic models of dispersion. Phys. Fluids A 3, 1577–1586.Google Scholar
Sawford, B. L. & Borgas, M. S. 1994 On the continuity of stochastic models for the Lagrangian velocity in turbulence. Physica D (in press).Google Scholar
Sawford, B. L. & Guest, F. M. 1988 Uniqueness and universality of Lagrangian stochastic models of turbulent dispersion. Proc. 8th Conf. on Turbulence and Diffusion (San Diego), pp. 96–99. Am. Met. Soc.
Sawford, B. L. & Hunt, J. C. R. 1986 Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J. Fluid Mech. 165, 373–400.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–211.Google Scholar
Thomson, D. J. 1987 Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529–556.Google Scholar
Thomson, D. J. 1990 A stochastic model for the motion of particle pairs in isotropic high Reynolds number turbulence, and its application to the problem of concentration variance. J. Fluid Mech. 210, 113–153.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659–684.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar