We combine observations of stratigraphy, morphology, and atmospheric processes to relate the spiral troughs on Mars' polar layered deposits to a class of features known as cyclic steps. Cyclic steps are quasi-stable, repeating, and upstream-migrating bed forms that have been studied in terrestrial and submarine environments. The repeating pattern is bounded by hydraulic jumps, which act to stabilize the form. We use radar stratigraphy from the Shallow Radar instrument on Mars Reconnaissance Orbiter to examine trough evolution and constrain lateral transport. We examine visible images from the Thermal Emission Imaging System and observe low-altitude clouds that we interpret to be the result of katabatic jumps, i.e., the Aeolian counterpart of hydraulic jumps in open channel flow. We then devise a theoretical framework for understanding the origin of the spiral troughs that agree with 10 criteria that should be explained for any scenario to satisfactorily model the spiral troughs. Finally, we use Froude and geometrical analysis to estimate the rate of upstream migration caused by katabatic winds for the spiral troughs.