Shallow convection over the oceans is responsible for the largest uncertainties in climate projections. Idealized simulations have shown decades ago that shallow clouds generate internal gravity waves, which under certain atmospheric background conditions become trapped inside the troposphere and influence the development of clouds. These feedbacks, which occur at horizontal scales of up to several tens of km are neither resolved, nor parameterized in traditional global climate models (GCMs), while the newest generation of GCMs (grid spacings < 5 km) is starting to resolve them. The interactions between the convective boundary layer and trapped waves have almost exclusively been studied in highly idealized frameworks and it remains unclear to what degree this coupling affects the organization of clouds in the real atmosphere or in the new generation of GCMs. Here, the coupling between clouds and trapped waves is examined in 2.5-km simulations that span the entirety of the tropical Atlantic and are initialized and forced by meteorological analyses. The coupling between clouds and trapped waves is sufficiently strong to be detected in these simulations of full complexity. Stronger upper-tropospheric westerly winds are associated with a stronger cloud-wave coupling. In the simulations this results in a highly-organized scattered cloud field with cloud spacings of about 19 km, matching the dominant trapped wavelength. Based on the large-scale atmospheric state wave theory can reliably predict the regions and times where cloud-wave feedbacks become relevant to convective organization. Theory, the simulations and satellite imagery imply a seasonal cycle in the trapping of gravity waves.