The world of High-Performance Computing (HPC) currently stands on the edge of the ExaScale. The supercomputers are growing ever more powerful, requiring power-efficient components and ever smarter tool-suites to operate them. One of the key features of those frameworks will be their ability to monitor and predict the behavior of executed applications to optimize resources utilization, and abide by the operating constraints, notably on power consumption. In this context, this article presents Phase-TA, an offline tool which detects and characterizes the inherent periodicities of iterative HPC applications, with no prior knowledge of the latter. To do so, it analyzes the evolution of several performance counters at the scale of the compute node, and infers patterns representing the identified periodicities. As a result, Phase-TA offers a nonintrusive mean to gain insights on the processor use associated with an application, and paves the way to predicting its behavior. Phase-TA was tested on a panel of 3 applications and benchmarks from the supercomputing field: HPCG, NEMO, and OpenFoam. For all of them, periodicities, accountable for on average 78% of their execution time, were detected and represented by accurate patterns. Furthermore, it was demonstrated that there is no need to analyze the whole profile of an application to precisely characterize its periodic behaviors. Indeed, an extract of the aforementioned profile is enough for Phase-TA to infer representative patterns on-the-fly, opening the way to energyefficiency optimization through Dynamic Voltage-Frequency Scaling (DVFS).