Range expansions have been common in the history of most species. Serial founder effects and subsequent population growth at expansion fronts typically lead to a loss of genomic diversity along the expansion axis. A frequent consequence is the phenomenon of "gene surfing," where variants located near the expanding front can reach high frequencies or even fix in newly colonized territories. Although gene surfing events have been characterized thoroughly for a specific locus, their effects on linked genomic regions and the overall patterns of genomic diversity have been little investigated. In this study, we simulated the evolution of whole genomes during several types of 1D and 2D range expansions differing by the extent of migration, founder events, and recombination rates. We focused on the characterization of local dips of diversity, or "troughs," taken as a proxy for surfing events. We find that, for a given recombination rate, once we consider the amount of diversity lost since the beginning of the expansion, it is possible to predict the initial evolution of trough density and their average width irrespective of the expansion condition. Furthermore, when recombination rates vary across the genome, we find that troughs are over-represented in regions of low recombination. Therefore, range expansions can leave local and global genomic signatures often interpreted as evidence of past selective events. Given the generality of our results, they could be used as a null model for species having gone through recent expansions, and thus be helpful to correctly interpret many evolutionary biology studies.