Role of the Manning Coefficient on Progressive Inundation by a Megaflood

Introduction: Estimations of peak discharge rates and durations of floods will play critical roles in discussions about megafloods and their relevance to the history of water on Earth and Mars. However, the movement of the floodwater is not easily modeled in an exact form because it strongly correlates to turbulent forces. In addition to that, actual floods progressively inundate complicated rough terrains, which introduces an additional complexity on the movement of the megaflood. For these reasons, empirical equations, especially the Manning equation developed in the fluvial hydrology field, are widely used to analyze megafloods [e.g., 1-3]. Nevertheless, the Manning resistant coefficient of a megaflood is not easily estimated by extrapolation from measured stream flows of much smaller floods. Here we discuss its theoretical background and its role in megaflood inundation processes by numerical calculations of our new flood simulation code (see [4] for a detail of our code). Theoretical view of the Manning coefficient: First, we follow the traditional discussion of turbulence [e.g., 5, 6] to derive a theoretical expression of the Manning equation. Considering a time-averaged velocity ua and a velocity fluctuation u, the velocity u at a certain depth can be written as: