Free-overfall structures such as weirs and crest gates are commonly used as control structures for a variety of applications including irrigation, water treatmentand dam safety. The gravity-driven free falling jet on the downstream side of these structures, called the nappe, may display a variety of behaviors and instabilities among which, under relatively low heads/discharges, nappe oscillations, also known as nappe vibrations. This oscillating phenomenon is characterized by oscillations of the thin flow nappe cascading downstream of the crest and results in a significant disturbing noise production that increases negatively the environmental and societal impacts of the hydraulic structure. Given the lack of quantitative information reported in literature and the inchoate understanding of the dominant processes underpinning nappe oscillations occurrence and development, the global objective of this PhD thesis was to improve the knowledge of the nappe oscillation phenomenon. To that end, experimental modelling was seen as the best way to analyse the problem. First, a prototype scale model of a linear weir has been specifically designed and made flexible with respect to the main parameters of the weir. Then, two original characterization methods of the nappe oscillations properties have been developed based on the distinct audio and visual traits of the phenomenon. The application of these methods allowed the determination of the occurrence and development of the oscillations and their associated frequencies. Both were used systematically to assess the influence of various hydraulic and geometric parameters on the nappe oscillation phenomenon. Secondly, given the importance of scale physical modelling for hydraulic structure design, the possible scale effects affecting nappe oscillation were studied by considering a 1:3 scale model of the aforementioned prototype scale facility. The operation of this second model showed that nappe oscillations cannot be scaled according to the traditional similitude for weirs (Froude similitude). Instead, they always occur within the same unit discharge range independent of size scale, although they are prone to hysteretic behaviour and are less stable over time for smaller weir dimensions. Third, considering the data collected from the study of 52 geometric configurations and the expertise gained from hours of nappe oscillation observations and analysis, necessary conditions for nappe oscillation occurrence have been defined. Along with geometrical criteria regarding the fall height and width of the structure, these conditions, although not sufficient, allow to predict the occurrence of the oscillation in many cases. Finally, original mitigation techniques have been developed with the help of practicing engineers and contractors. Identified with respect to constructability, durability, performance and maintenance, these solutions were tested and optimized regarding disturbing noise reduction without impacting the hydraulic efficiency of the structure. Beside these extensive experimental works, in-situ measurements at two Belgian dams proved the applicability and robustness of the measurement methodologies developed in the framework of this thesis and the utility of the results to solve real world problems.