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The link between intrinsic shear-flow instability of longshore currents and their mean cross-shore profiles has long been suggested. Yet, recent investigations give increasing credit to extrinsic wave forcing mechanisms, downplaying the role of shear waves on the observed variability. Our results for Grand Popo beach, Benin, provide an original attempt to map mean longshore currents forced by an oblique swell. A 3D model investigation shows that their broad mean flow and the frequency band of eddy variability are consistent with shear instability, conversion of mean to eddy kinetic energy and eddy mixing of momentum. Their turbulent dynamics do not clearly fit in any classical 2D or 3D paradigms but show large transfer of energy across the wavenumber spectrum, to both larger and smaller scales.