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Published on: February 3, 2014
Bifurcation analysis of the transition of dune shapes under a unidirectional wind
Hirofumi Niiya1, Akinori Awazu, Hiraku Nishimori
1Department of Mathematical and Life Sciences, Hiroshima University, Higashihiroshima, Hiroshima 739-8526, Japan.
Abstract:
A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, the 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 a 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.
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