The vast majority of parallel scientific applications distributes computation among processes that are in a busy state when computing and in an idle state when waiting for information from other processes. We identify the propagation of idle waves through processes in scientific applications with a local information exchange between the two processes. Idle waves are nondispersive and have a phase velocity inversely proportional to the average busy time. The physical mechanism enabling the propagation of idle waves is the local synchronization between two processes due to remote data dependency. This study provides a description of the large number of processes in parallel scientific applications as a continuous medium. This work also is a step towards an understanding of how localized idle periods can affect remote processes, leading to the degradation of global performance in parallel scientific applications.