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.

No abstract

Abstract.A new method of interpreting the signals from triplesensor thermal anemometer probes has been developed based on fast solution for all the roots of the non-linear Jorgensen (1971) equations describing the directional response of each cylindrical sensor. The sensors can be oriented at arbitrary angles to each other, but always within a range of probe geometries that keep prong interference and thermal wake interference below acceptable levels. The properties of a class of non-orthogonal symmetric tetrahedral probe geometries are studied in relation to the range of flow vector angles that can be measured, the sensitivity of the probe with respect to changes in flow angle, and the sensitivity of the computed velocity components due to angular errors associated with the construction of the probe. The solutions of Jorgensen's equations are inherently multiple-valued, but if the velocity vector is restricted to be within a cone of angles, they are unique. It is shown that measurements with non-orthogonal triple sensor signals are sensitive to angular deviations of a few degrees of the sensor angles from the nominally orthogonal probe geometry, indicating the need of a non-orthogonal algorithm. The mean, rms, Reynolds stress, and power spectrum of the velocity in fully developed turbulent pipe flow were measured using a specially designed triple sensor probe and the proposed algorithm.

No abstract

No abstract