Two-dimensional cross-spectrum of the streamwise velocity in turbulent boundary layers

Abstract

In this paper, we present the two-dimensional (2-D) energy cross-spectrum of the streamwise velocity (u) component and use it to test the notion of self-similarity in turbulent boundary layers. The primary focus is on the cross-spectrum (Φw cross) measured across the logarithmic (zo) and near-wall (zr) wall-normal locations, providing the energy distribution across the range of streamwise (λx) and spanwise (λy) wavelengths (or length scales) that are coherent across the wall-normal distance. Φw cross may thus be interpreted as a wall-filtered subset of the full 2-D u-spectrum (Φ), the latter providing information on all coexisting eddies at zo. To this end, datasets comprising synchronized t..