Bifurcation analysis of the transition of dune shape under unidirectional wind

TL;DR

This paper uses a reduced dune morphodynamics model to analyze how dune shapes transition under unidirectional wind, revealing bifurcation mechanisms that explain shape changes from straight to wavy dunes and then to barchans.

Contribution

It introduces a bifurcation analysis of dune shape transitions using a simplified model, clarifying the underlying transition mechanisms.

Findings

Transition from straight to wavy dunes via pitchfork bifurcation.

Shift from wavy dunes to barchans through Hopf bifurcation.

Decrease in sand amount and lateral flow influence dune shape stability.

Abstract

A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, dune skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found that the decrease in the total amount of sand in the system and/or the lateral sand flow shifts the stable state from a straight transverse dune to wavy transverse dune through a pitchfork bifurcation. A further decrease causes wavy transverse dunes to shift into barchans through a Hopf bifurcation. These bifurcation structures reveal the transition mechanism of dune shapes under unidirectional wind.