The data contained in this dataset correspond to velocity spectra computed from long-term velocity measurements (6h) with the aim of exploring the existence of Large and Very-Large Scales Motions (LSMs and VLSMs) in the presence of a shallow mixing layer and the Kelvin-Helmholtz Coherent Structures (KHCSs) that populate it. The data corresponding to the auto-spectra of the 3 velocity components, as well as the cross-spectra between each of the velocity components, at each measurement point, are proposed in this dataset. This dataset also includes data corresponding to cross-spectra between two measurement points spaced across the width of the channel. Finally, five files containing longitudinal velocity profile measurements across the width of the channel are proposed. A README file is added to explain the construction of each available file.