Statistical Properties for Trigonometric Random Fields


  • Eduardo S. Schneider



Random velocity fields, Gaussian, Fourier modes, passive trace transport.


This work presents a general form for a scalar random field which is written as a sum of finitely many Fourier modes. We get some of its statistical proprieties and analyze its geometry. Additionally, we derive a model for a Gaussian, two dimensional, mean-zero, homogeneous, steady, and incompressible random velocity field and provide numerical evidence about the non-normality of the joint distribution of the Lagrangian velocity process.


Não há dados estatísticos.

Biografia do Autor

Eduardo S. Schneider

Universidade Federal de Pelotas, Pelotas, RS, Brazil


M. Avellaneda and A. J. Majda. “Mathematical models with exact renormalization for turbulent transport”. In: Communications in Mathematical Physics 131.2 (1990), pp. 381– 429.

G. E. P. Box and M. E. Muller. “A note on the generation of random normal deviates”. In: The Annals of Mathematical Statistics, 29 (1958), pp. 610–611.

R. A. Carmona and L. Xu. “Homogenization for time-dependent two-dimensional incompressible Gaussian flows”. In: The Annals of Applied Probability 7.1 (1997), pp. 265– 279.

S. Corrsin. “Atmospheric diffusion and air pollution”. In: Advances in Geophysics, 6 (1959), p. 161.

F. W. Elliott and A. J. Majda. “Pair dispersion over an inertial range spanning many decades”. In: Physics of Fluids, 8.4 (1996), pp. 1052–1060.

S. C. Port and C. J. Stone. “Random measures and their application to motion in an incompressible fluid”. In: Journal of Applied Probability 13.3 (1976), pp. 498–506.

E. S. Schneider. “Exact calculations for the Lagrangian velocity”. PhD thesis. Bowling Green State University, 2019.

E. S. Schneider and C. L. Zirbel. “Using symbolic expressions to get the Taylor expansion of the Lagrangian auto-covariance function”. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 8.1 (2021). doi: 10.5540/03.2021.008. 01.0504.

G. I. Taylor. “Statistical theory of turbulence”. In: Proceedings of the Royal Society of London.Series A, Mathematical and Physical Sciences 151.873 (1935), pp. 421–444.

W. A. Woyczynski. “Passive tracer transport in stochastic flows”. In: Stochastic Climate Models, 49 (2012), pp. 385–396.

C. L. Zirbel. “Lagrangian observations of homogeneous random environments”. In: Advances in Applied Probability 33.4 (2001), pp. 810–835






Trabalhos Completos