3D Dune Skeleton Model as a Coupled Dynamical System of 2D Cross-Sections

TL;DR

This paper introduces a coupled dynamical system model of 3D dunes based on 2D cross-sections to analyze their shape stability and migration behavior.

Contribution

It proposes a novel skeleton model representing 3D dunes through coupled 2D cross-section dynamics, enabling theoretical analysis of dune stability and deformation.

Findings

Model captures essential dune dynamics with coupled differential equations

Stability depends on sand availability and flow directions

Predicts deformation from dunes to barchans

Abstract

To analyze theoretically the stability of the shape and the migration process of transverse dunes and barchans, we propose a {\it skeleton model} of 3D dunes described with coupled dynamics of 2D cross-sections. First, 2D cross-sections of a 3D dune parallel to the wind direction are extracted as elements of a skeleton of the 3D dune, hence, the dynamics of each and interaction between them is considered. This model simply describes the essential dynamics of 3D dunes as a system of coupled ordinary differential equations. Using the model we study the stability of the shape of 3D transversal dunes and their deformation to barchans depending on the amount of available sand in the dune field, sand flow in parallel and perpendicular to wind direction.