On an adjustment to the Fowler equation

TL;DR

This paper presents an adapted version of Fowler's equation for nonlinear dune dynamics, incorporating an additional term through variable changes and scalings to better model dune morphodynamics.

Contribution

It introduces a modified Fowler equation with an extra term, derived via variable transformations and scalings, enhancing the modeling of dune morphodynamics.

Findings

The adapted equation captures key features of dune evolution.

The additional term improves the model's accuracy.

The approach simplifies the derivation process.

Abstract

Following closely the analysis performed by Andrew C. Fowler to derive the first canonical equation for nonlinear dune dynamics, but considering some appropriate changes of variables, suitable scalings, and by neglecting higher order terms, we obtain an adaptation of the aforementioned equation, which contains an additional term, to describe dune morphodynamics.