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  • 1
    Electronic Resource
    Electronic Resource
    Very large-scale motion in the outer layer (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 417-422 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Very large-scale motions in the form of long regions of streamwise velocity fluctuation are observed in the outer layer of fully developed turbulent pipe flow over a range of Reynolds numbers. The premultiplied, one-dimensional spectrum of the streamwise velocity measured by hot-film anemometry has a bimodal distribution whose components are associated with large-scale motion and a range of smaller scales corresponding to the main turbulent motion. The characteristic wavelength of the large-scale mode increases through the logarithmic layer, and reaches a maximum value that is approximately 12–14 times the pipe radius, one order of magnitude longer than the largest reported integral length scale, and more than four to five times longer than the length of a turbulent bulge. The wavelength decreases to approximately two pipe radii at the pipe centerline. It is conjectured that the very large-scale motions result from the coherent alignment of large-scale motions in the form of turbulent bulges or packets of hairpin vortices. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869889
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  • 2
    Electronic Resource
    Electronic Resource
    Karhunen–Loéve expansion of the derivative of an inhomogeneous process (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2233-2235 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The properties of the Karhunen–Loéve (KL) expansion of the derivative ux(x) of an inhomogeneous random process possessing viscous boundary-layer behavior are studied in relation to questions of efficient representation for numerical Galerkan schemes for computational simulation of turbulence. Eigenfunctions and eigenvalue spectra are calculated for the randomly forced one-dimensional Burgers' model of turbulence. Convergence of the expansion of ux is much slower than convergence of the expansion of u(x), and direct expansion of ux is not significantly more efficient than differentiating the expansion of u. The ordered eigenvalue spectrum of ux is proportional to the square of the order parameter times the eigenvalue spectrum of u. The underlying cause of slow convergence is the earlier onset of locally sinusoidal behavior of the KL eigenfunctions when the expansion is performed over the entire domain of the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868173
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  • 3
    Electronic Resource
    Electronic Resource
    Reynolds number similarity of orthogonal decomposition of the outer layer of turbulent wall flow (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2815-2819 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Experimental evidence is presented to show that in the outer region of wall-bounded turbulent flow, both the eigenfunctions and the eigenvalue spectra of the one-dimensional proper orthogonal decomposition have forms that are independent of Reynolds number when scaled by the wall friction velocity and the outer length scale.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868169
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Convergence of Galerkin solutions using Karhunen–Loève expansions of inhomogeneous 1-D turbulence (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1695-1697 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The rate of convergence of the Karhunen–Loève expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers' equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority of the Karhunen–Loève expansion, especially for high Reynolds number flows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857948
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  • 5
    Electronic Resource
    Electronic Resource
    Approximation of turbulent conditional averages by stochastic estimation (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 992-998 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Conditional averages of turbulent flow quantities can be approximated in terms of unconditional correlation data by means of stochastic estimation. The validity and accuracy of this procedure are investigated by comparing stochastic estimates to conditional averages measured in four turbulent flows: grid turbulence, the axisymmetric shear layer of a round jet, a plane shear layer, and pipe flow. Comparisons are made for quantities that are separated from the conditional data in time or space, and for turbulent pressures, as well as turbulent velocities. In each case, the linear estimate accurately represents large scale structure. Nonlinear quadratic estimation shows little improvement over linear estimation, because the second-order terms are small for probable values of the turbulent fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857411
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  • 6
    Electronic Resource
    Electronic Resource
    Karhunen–Loéve expansion of Burgers' model of turbulence (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 2573-2582 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Characteristics of the Karhunen–Loéve expansion of a strongly inhomogeneous random process possessing small viscous length scales and a large outer scale have been investigated in relation to the application of the expansion to turbulent flow fields. Monte Carlo simulations of a randomly forced Burgers' equation with zero velocity boundary conditions generate the random process numerically and the Karhunen–Loéve (KL) eigenfunctions and the eigenvalue spectra are computed for different Reynolds numbers. The eigenfunctions possess thin viscous boundary layers at the walls and are independent of Reynolds number in the core, where the random process is quasihomogeneous. The eigenfunctions and eigenvalues of the outer, large scale motions obey a principle of Reynolds number similarity. Eigenvalue spectra contain much of the energy in the first few modes, but they are as broad as ordinary trigonometric power spectra. The rate at which the expansion converges to within 90% of the total energy decreases with increasing Reynolds numbers and the expansion of the mean plus the fluctuation converges more rapidly than the expansion of the fluctuation alone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866535
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Particle-Imaging Techniques for Experimental Fluid Mechanics (1991)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 23 (1991), S. 261-304 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.23.010191.001401
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  • 8
    Electronic Resource
    Electronic Resource
    Turbulent and Transition Pipe Flow of Dilute Aqueous Polymer Solutions (1969)
    s.l. : American Chemical Society
    Industrial and engineering chemistry 8 (1969), S. 498-502 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/i160031a021
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  • 9
    Electronic Resource
    Electronic Resource
    Structure extraction by stochastic estimation with adaptive events (1993)
    Springer
    Theoretical and computational fluid dynamics 5 (1993), S. 243-257 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Various aspects of turbulence structure can be found by a new class of stochasticestimation methods in which the conditional events that define the stochastic estimate are systematically varied. Methods are presented to find the length scale of large periodic structures, the form of structures that have specified geometric constraints such as two-dimensionality, and the structure of small-scale motions embedded in large-scale motions. These methodologies are demonstrated in high Rayleigh number turbulent convection by extracting both the large-scale roll-cell and coherent thermal plumes. A method of compressed representation using a stochastic estimate given data on optimally chosen points is also demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00271661
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  • 10
    Electronic Resource
    Electronic Resource
    Thirteenth U.S. national congress of theoretical & applied mechanics (1997)
    Springer
    Computational mechanics 20 (1997), S. 282-282 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050249
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