### Abstract

Original language | English |
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Publication date | 2007 |

Publication status | Published - 2007 |

Event | 60th Annual Meeting of the Division of Fluid Dynamics - Salt Lake City, UT, United States Duration: 18 Nov 2007 → 20 Nov 2007 Conference number: 60 http://meetings.aps.org/Meeting/DFD07/Content/912 |

### Conference

Conference | 60th Annual Meeting of the Division of Fluid Dynamics |
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Number | 60 |

Country | United States |

City | Salt Lake City, UT |

Period | 18/11/2007 → 20/11/2007 |

Internet address |

### Cite this

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*Amplitude equation for under water sand-ripples in one dimension*, 2007, Sound/Visual production (digital).

**Amplitude equation for under water sand-ripples in one dimension.**Schnipper, Teis (Author); Mertens, Keith (Author); Ellegaard, Clive (Author); Bohr, Tomas (Author). 2007. Event: 60th Annual Meeting of the Division of Fluid Dynamics, Salt Lake City, UT, United States.

Research output: Non-textual form › Sound/Visual production (digital) › Research

TY - ADVS

T1 - Amplitude equation for under water sand-ripples in one dimension

A2 - Schnipper, Teis

A2 - Mertens, Keith

A2 - Ellegaard, Clive

A2 - Bohr, Tomas

PY - 2007

Y1 - 2007

N2 - Sand-ripples under oscillatory water flow form periodic patterns with wave lengths primarily controlled by the amplitude d of the water motion. We present an amplitude equation for sand-ripples in one spatial dimension which captures the formation of the ripples as well as secondary bifurcations observed when the amplitude $d$ is suddenly varied. The equation has the form h_t=- ε(h-mean(h))+((h_x)^2-1)h_(xx)- h_(xxxx)+ δ((h_x)^2)_(xx) which, due to the first term, is neither completely local (it has long-range coupling through the average height mean(h)) nor has local sand conservation. We argue that this is reasonable and that this term (with ε = d^(-2)) stops the coarsening process at a finite wavelength proportional to $d$. We compare our numerical results with experimental observations in a narrow channel.

AB - Sand-ripples under oscillatory water flow form periodic patterns with wave lengths primarily controlled by the amplitude d of the water motion. We present an amplitude equation for sand-ripples in one spatial dimension which captures the formation of the ripples as well as secondary bifurcations observed when the amplitude $d$ is suddenly varied. The equation has the form h_t=- ε(h-mean(h))+((h_x)^2-1)h_(xx)- h_(xxxx)+ δ((h_x)^2)_(xx) which, due to the first term, is neither completely local (it has long-range coupling through the average height mean(h)) nor has local sand conservation. We argue that this is reasonable and that this term (with ε = d^(-2)) stops the coarsening process at a finite wavelength proportional to $d$. We compare our numerical results with experimental observations in a narrow channel.

M3 - Sound/Visual production (digital)

ER -