Modeling the Dynamics of Flutes and Scallops: Preliminary Results

Abstract

Our aim is to develop a computational model of the corrosion forms known as scallops and flutes, common in karst environment. This model is designed to take in account dynamical interactions between successive forms, which has previously never be done, and to be as simple as possible. We present preliminary results corresponding to numerical simulations that have been run during February 2018. The evolution of scallops and flutes is summarized in some simple equations that model how the length of a form evolves, how too large forms split into smaller forms and how too small forms are erased by larger ones. These equations are used in programs written in C language. They enable to investigate how a system of numerous scallops or flutes evolves and to investigate the corresponding statistical distribution. The preliminary results we present are very encouraging because of their good quantitative agreement with the well-known Curl relationship in the case of steady flows. When the velocity of the water (or air) responsible for the formation of scallops or flutes change, the model predicts that the average size of the forms changes too. However, in such a situation, the Curl relationship is not always accurately verified. This progressive model depends upon few parameters and does not require huge computing power. Further comparisons with field data may render it even more realistic, particularly regarding the statistical distributions it generates.