Spatially compounding extreme events such as concurrent heatwaves pose a growing risk to society. The distance between concurrent events, or more generally their distribution in longitude, can be described in terms of a zonal wavenumber. Estimates of this wavenumber are typically based on stationary Rossby wave dynamics and the properties of a mid-latitude waveguide. A potential link to transient waves remains largely unexplored. We investigate the zonal structure of concurrent heatwaves through a composite analysis, comparing idealized numerical experiments and reanalysis data. In particular, we compare summer and winter in the Northern and the Southern hemispheres. Defining concurrent events on a weekly time scale, the composite mean shows a central peak in concurrent heatwave frequency corresponding to a spatially extended heatwave object, adjacent minima with reduced concurrent heatwave probability, and, depending on the degree of zonal symmetry in the atmosphere, more or less pronounced secondary maxima. Such wavy structures can be interpreted as the temporal mean of a downstream-developing transient wave packet. The distance between the adjacent minima or secondary maxima can be inferred from the stationary wavenumber, which we derive by calibrating a simple dispersion relation with the phase speed and group velocity of the associated wave packets. By linking the structure of the quasi-stationary flow to the local properties of downstream-developing Rossby waves, we offer a new perspective on spatially compounding climate extremes.