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 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/Territory | United States |
| City | Salt Lake City, UT |
| Period | 18/11/2007 → 20/11/2007 |
| Other | We present the simulation of the swimming medusa by capturing the outline of the motion from video taped experiments. A three dimensional body with constant mass distribution and divergence solid velocity field is ensured under the assumption of a rotationally symmetric medusa. The simulations are carried out using the vortex-in-cell algorithm in three dimensions with one-way coupling from the medusa motion. The boundaries of the deforming solid body are enforced using Brinkmann penalization. The flow is discretized by 67M vortex particles and the computations carried out on 256 cores with a 80% parallel efficiency. The simulation is visualized in a fluid dynamics video. To different strokes, A and B, are captured, simulated and studied. Stroke A produces a starting vortex ring as fluid is being expelled from the bell and produces yet a vortex ring of opposite sign when the bell opens and recovers its shape. Stroke B is more brisk and differs from A by producing two vortex rings during the recovery stroke. Both strokes propel the medusa but stroke B produces a higher velocity. The crusing velocity scales with the square root of the Reynolds number. |
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