Open cavity flows are known to select and enhance locked-on modes or tones. High-energy self-sustained oscillations arise within the shear layer, impinging onto the trailing edge of the cavity. These self-sustained oscillations are subject to amplitude modulations (AMs) at multiple low frequencies. However, only a few studies have addressed the identification of the lowest modulating frequencies. The present work brings to light salient AMs of the shear layer waves and identifies their source as three-dimensional dynamics existing inside the cavity. Indeed, the recirculating inner flow gives rise to centrifugal instabilities, which entail broad-band frequencies down two orders of magnitude lower than those of the self-sustained oscillations. Using time-resolved PIV (TRPIV) in two planes, the nonlinearly saturated dynamics is analysed in both space and time by means of proper orthogonal decomposition, global Fourier decomposition and Hilbert–Huang transforms. The inner flow can be decomposed as three-dimensional waves carried by the main recirculation. Bicoherence distributions are computed to highlight the nonlinear interactions between these spanwise-travelling waves inside the cavity and the locked-on modes. The modulated envelope of the shear layer oscillations is extracted and investigated with regards to the inner-flow dynamics. Strong cross-correlations, in time rather than in space, reveal a global coupling mechanism, possibly related to the beating of the spanwise-travelling waves.