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Physics of Fluids / Volume 5 / Issue 10

Phys. Fluids A 5, 2525 (1993); doi:10.1063/1.858765 (8 pages)

Skewed, exponential pressure distributions from Gaussian velocities

Mark Holzer and Eric Siggia

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853‐2501

(Received 17 February 1993; accepted 18 June 1993)

A simple analytical argument is given to show that the distribution function of the pressure and that of its gradient have exponential tails when the velocity is Gaussian. A calculation of moments implies a negative skewness for the pressure. Explicit analytical results are given for the case of the velocity being restricted to a shell in wave number. Numerical pressure distributions are presented for Gaussian velocities with realistic spectra. For real turbulent flows, one expects that the pressure distribution should retain exponential tails while the pressure gradients should develop stretched‐exponential distributions. In the context of the theory, available numerical and laboratory data are examined for the pressure, along with data for the wall shear stress in a boundary layer.

KEYWORDS and PACS

Keywords

PRESSURE, DISTRIBUTION FUNCTIONS, TURBULENT FLOW, MOMENTS METHOD, GAUSSIAN PROCESSES, ANALYTICAL SOLUTION, NUMERICAL SOLUTION, VELOCITY FIELDS, PRESSURE GRADIENTS, BOUNDARY LAYERS, WALL EFFECTS, STRESSES

PACS

  • 47.27.Sd

    Turbulence generated noise

  • 47.27.Gs

    Isotropic turbulence; homogeneous turbulence

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.858765

PUBLICATION DATA

ISSN:

0899-8213 (print)  
1089-7666 (online)

For access to fully linked references, you need to log in.
    G. S. Patterson and S. A. Orszag, “Spectral calculations of isotropic turbulence: Efficient removal of aliasing interactions,” Phys. Fluids 14, 2538 (1971PFLDAS000014000011002538000001).

    See, e.g., R. H. Kraichnan, “Inertial ranges in two-dimensional turbulence,” Phys. Fluids 10, 1417 (1967PFLDAS000010000007001417000001).

    S. Douady, Y. Couder, and M. E. Brachet, “Direct observation of the intermittency of intense vorticity filaments in turbulence,” Phys. Rev. Lett. 67, 983 (1991).

    D. P. Lathrop, J. Fineberg, and H. L. Swinney, “Transitions to shear-driven turbulence in Couette-Taylor flow,” Phys. Rev. A 46, 6390 (1992).

    R. H. Kraichnan, “Models of intermittency in hydrodynamic turbulence,” Phys. Rev. Lett. 65, 575 (1990).


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