Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer

Abstract

An experimental study of a turbulent boundary layer at R_θ≈1070 and R_τ≈543 was conducted. Detailed measurements of the velocity vector and the velocity gradient tensor within the near-wall region were performed at various distances from the wall, ranging from approximately y⁺=14 to y⁺=89. The measured mean statistical properties of the fluctuating velocity and vorticity components agree well with previous experimental and numerically simulated data. These boundary layer measurements were used in a joint probability density analysis of the various component vorticity and vorticity–velocity gradient products that appear in the instantaneous vorticity and enstrophy transport equations. The vorticity filaments that contribute most to the vorticity covariance Ω[bar]_xΩ [bar]_y in this region were found to be oriented downstream with angles of inclination to the wall, when projected on the streamwise (x, y)-plane, that decrease with distance moving from the buffer to the logarithmic layer. When projected on the planview (x, z)- and cross-stream (y, z)-planes, the vorticity filaments that most contribute to the vorticity covariances Ω [bar]_xΩ [bar]_z and Ω [bar]_yΩ [bar]_z have angles of inclination to the z-ordinate axis that increase with distance from it. All the elements of the Ω_iΩ_j ∂U_i/∂x_j term in the enstrophy transport equation, i.e. the term that describes the rate of increase or decrease of the enstrophy by vorticity filament stretching or compression by the strain-rate field, have been examined. On balance, the average stretching of the vorticity filaments is greater than compression at all y⁺ locations examined here. However, some individual velocity gradient components compress the vorticity filaments, on average, more than they stretch them.