## Separation vortices and pattern formation

Publication: Research - peer-review › Journal article – Annual report year: 2010

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**Separation vortices and pattern formation.** / Andersen, Anders Peter; Bohr, Tomas; Schnipper, Teis.

Publication: Research - peer-review › Journal article – Annual report year: 2010

### Harvard

*Theoretical and Computational Fluid Dynamics*, vol 24, no. 1-4, pp. 329-334., 10.1007/s00162-009-0102-0

### APA

*Theoretical and Computational Fluid Dynamics*,

*24*(1-4), 329-334. 10.1007/s00162-009-0102-0

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*Theoretical and Computational Fluid Dynamics*. 2010, 24(1-4). 329-334. Available: 10.1007/s00162-009-0102-0

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TY - JOUR

T1 - Separation vortices and pattern formation

AU - Andersen,Anders Peter

AU - Bohr,Tomas

AU - Schnipper,Teis

PB - Springer

PY - 2010

Y1 - 2010

N2 - In this paper examples are given of the importance of flow separation for fluid patterns at moderate Reynolds numbers—both in the stationary and in the time-dependent domain. In the case of circular hydraulic jumps, it has been shown recently that it is possible to generalise the Prandtl–Kármán–Pohlhausen approach to stationary boundary layers with free surfaces going through separation, and thus obtain a quantitative theory of the simplest type of hydraulic jump, where a single separation vortex is present outside the jump. A second type of jump, where an additional roller appears at the surface, cannot be captured by this approach and has not been given an adequate theoretical description. Such a model is needed to describe “polygonal” hydraulic jumps, which occur by spontaneous symmetry breaking of the latter state. Time-dependent separation is of importance in the formation of sand ripples under oscillatory flow, where the separation vortices become very strong. In this case no simple theory exists for the determination of the location and strengths of separation vortices over a wavy bottom of arbitrary profile. We have, however, recently suggested an amplitude equation describing the long-time evolution of the sand ripple pattern, which has the surprising features that it breaks the local sand conservation and has long-range interaction, features that can be underpinned by experiments. Very similar vortex dynamics takes place around oscillating structures such as wings and fins. Here, we present results for the vortex patterns behind a flapping foil in a flowing soap film, which shows the interaction and competition between the vortices shed from the round leading edge (like the von Kármán vortex street) and those created at the sharp trailing edge.

AB - In this paper examples are given of the importance of flow separation for fluid patterns at moderate Reynolds numbers—both in the stationary and in the time-dependent domain. In the case of circular hydraulic jumps, it has been shown recently that it is possible to generalise the Prandtl–Kármán–Pohlhausen approach to stationary boundary layers with free surfaces going through separation, and thus obtain a quantitative theory of the simplest type of hydraulic jump, where a single separation vortex is present outside the jump. A second type of jump, where an additional roller appears at the surface, cannot be captured by this approach and has not been given an adequate theoretical description. Such a model is needed to describe “polygonal” hydraulic jumps, which occur by spontaneous symmetry breaking of the latter state. Time-dependent separation is of importance in the formation of sand ripples under oscillatory flow, where the separation vortices become very strong. In this case no simple theory exists for the determination of the location and strengths of separation vortices over a wavy bottom of arbitrary profile. We have, however, recently suggested an amplitude equation describing the long-time evolution of the sand ripple pattern, which has the surprising features that it breaks the local sand conservation and has long-range interaction, features that can be underpinned by experiments. Very similar vortex dynamics takes place around oscillating structures such as wings and fins. Here, we present results for the vortex patterns behind a flapping foil in a flowing soap film, which shows the interaction and competition between the vortices shed from the round leading edge (like the von Kármán vortex street) and those created at the sharp trailing edge.

U2 - 10.1007/s00162-009-0102-0

DO - 10.1007/s00162-009-0102-0

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 1-4

VL - 24

SP - 329

EP - 334

ER -