Amplitude equation for under water sand-ripples in one dimension

Teis Schnipper (Author), Keith Mertens (Author), Clive Ellegaard (Author), Tomas Bohr (Author)

Research output: Non-textual formSound/Visual production (digital)Research

Abstract

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.
Original languageEnglish
Publication date2007
Publication statusPublished - 2007
Event60th Annual Meeting of the Division of Fluid Dynamics - Salt Lake City, UT, United States
Duration: 18 Nov 200720 Nov 2007
Conference number: 60
http://meetings.aps.org/Meeting/DFD07/Content/912

Conference

Conference60th Annual Meeting of the Division of Fluid Dynamics
Number60
CountryUnited States
CitySalt Lake City, UT
Period18/11/200720/11/2007
Internet address

Cite this

Schnipper, T. (Author), Mertens, K. (Author), Ellegaard, C. (Author), & Bohr, T. (Author). (2007). Amplitude equation for under water sand-ripples in one dimension. Sound/Visual production (digital), Retrieved from http://flux.aps.org/meetings/YR07/DFD07/all_DFD07.pdf
Schnipper, Teis (Author) ; Mertens, Keith (Author) ; Ellegaard, Clive (Author) ; Bohr, Tomas (Author). / Amplitude equation for under water sand-ripples in one dimension. [Sound/Visual production (digital)].
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title = "Amplitude equation for under water sand-ripples in one dimension",
abstract = "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.",
author = "Teis Schnipper and Keith Mertens and Clive Ellegaard and Tomas Bohr",
year = "2007",
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Schnipper, T, Mertens, K, Ellegaard, C & Bohr, T, 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 formSound/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 -

Schnipper T (Author), Mertens K (Author), Ellegaard C (Author), Bohr T (Author). Amplitude equation for under water sand-ripples in one dimension 2007.