The Probability Density Functions of Velocity Fluctuations Inside Steady Pressure-Driven Three-Dimensional Turbulent Boundary Layers

One-point time-averaged velocity correlations and joint probability density functions (p.d.f.s) are analyzed with a multi-step method for steady three-dimensional turbulent boundary layers (3DTBLs). The data are derived from a time series of velocity fluctuations measured along the measurement axes ( ₁, ₂, ₃). The method includes a Monte Carlo (MC) technique in which, firstly, the 3×3 Reynolds stress tensors are diagonalized locally in order to obtain the experimental eigenvalues or principal values and the experimental eigenvectors or principal axes ( ₁, ₂, ₃). Secondly, trial independent p.d.f.s are MC-generated along these are projected from system into and the built-in hypotheses are tested for validity, using stringent self-consistency tests. All p.d.f. investigations are made with “perturbed centered-Gaussians” hypotheses, in which the “centered-Gaussians” are experimentally defined and the “perturbations” are trial drift velocities. Our MC-analysis method [1-3] is applied to the first [4] and second [5] generation “S-duct” experiments performed at the école Polytechnique Fédérale de Lausanne (EPFL). Additionally, two complementary algebraic self-consistency tests are developed for the double and the triple correlations separately. New results in the p.d.f. properties of 3DTBLs are presented, using Kinetic Theory as background. Received 6 November 2001 and accepted 27 August 2002 Published online 28 February 2003 Communicated by J.R. Blake