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Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows
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10.1063/1.3270045
/content/aip/journal/chaos/20/1/10.1063/1.3270045
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/1/10.1063/1.3270045
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

White light flow visualization of the wake of a rectangular pitching panel. From Buchholz and Smits. (a) and (b) (Ref. 29). [Reprinted with permission from J. H. J. Buchholz and A. J. Smits, Phys. Fluids 17, 091102 (2005). Copyright 2005, American Institute of Physics.]

Image of FIG. 2.
FIG. 2.

Hill’s spherical vortex and its negative- and positive-time DLE fields with red and blue showing maximum values. (a) Streamlines with a green circle indicating the vortex boundary at ; (b) nDLE, short integration time; (c) nDLE, long integration time; (d) pDLE, short integration time; and (e) pDLE, long integration time.

Image of FIG. 3.
FIG. 3.

Hyperbolic pLCS (blue) and nLCS (red) field for Hill’s spherical vortex. Black circles highlight saddle points.

Image of FIG. 4.
FIG. 4.

Two-dimensional nDLE plots of the isolated hairpin: (a) 10% max superimposed on location of the three planes, (b) constant-streamwise cut, (c) constant wall-normal cut, and (d) constant-spanwise cut (Ref. 16). [Reprinted with permission from M. A. Green, C. W. Rowley, and G. Haller, J. Fluid Mech. 572, 111 (2007). Copyright 2007, Cambridge University Press.]

Image of FIG. 5.
FIG. 5.

Hyperbolic pLCS (blue) and nLCS (red) of the isolated hairpin head in a two-dimensional cross section of the hairpin vortex. (a) Constant-spanwise plane, plotted as regions of maximum value that satisfy the corresponding hyperbolicity criteria, and (b) constant wall-normal plane, plotted as regions of maximum value that satisfy the corresponding hyperbolicity criteria. Time-dependent saddle points are highlighted using a black box.

Image of FIG. 6.
FIG. 6.

Hyperbolic pLCS (blue) and nLCS (red) of the isolated hairpin head in a two-dimensional slice in a constant-spanwise plane through the fully turbulent channel, plotted as regions of maximum value that satisfies the corresponding hyperbolicity criteria. A possible hairpin vortex is highlighted by a white box.

Image of FIG. 7.
FIG. 7.

Hyperbolic pLCS (blue) and nLCS (red) of the secondary hairpin head (a) before formation and (b) after formation LCS is plotted as regions of maximum value that satisfies the corresponding hyperbolicity criteria. Time-dependent saddle points are highlighted with a black box.

Image of FIG. 8.
FIG. 8.

Fairing and panel assembly (Ref. 28). (From J. H. J. Buchholz, Ph.D. thesis, Princeton University, 2006. Reprinted with permission.)

Image of FIG. 9.
FIG. 9.

(a) Panel and fairing position in water channel test section (Ref. 28). (From J. H. J. Buchholz, Ph.D. thesis, Princeton University, 2006. Reprinted with permission.) (b) Diagram of trapezoid dimensions.

Image of FIG. 10.
FIG. 10.

Two-dimensional planes of spanwise vorticity in the midspan plane at four phases of the panel motion for : (a) , (b) , (c) , and (d) .

Image of FIG. 11.
FIG. 11.

Two-dimensional planes of spanwise vorticity in the midspan plane at four phases of the panel motion for : (a) , (b) , (c) , and (d) .

Image of FIG. 12.
FIG. 12.

nLCS (red) and pLCS (blue), plotted as regions of maximum value, superimposed on two-dimensional planes of spanwise vorticity at the midspan for : (a) , (b) , (c) , and (d) .

Image of FIG. 13.
FIG. 13.

Hyperbolic nLCS (red) and pLCS (blue), plotted as regions of maximum value that satisfies the corresponding hyperbolicity criteria, in the midspan of the panel pitching at with . Black boxes highlight saddle points that are part of individual vortex core boundaries.

Image of FIG. 14.
FIG. 14.

nLCS (red) and pLCS (blue), plotted as regions of maximum value, superimposed on two-dimensional planes of spanwise vorticity at the midspan for : (a) , (b) , (c) , and (d) .

Image of FIG. 15.
FIG. 15.

Hyperbolic pLCS and nLCS, plotted as regions of maximum value that satisfies the corresponding hyperbolicity criteria, at the midspan of the panel pitching at . Black boxes highlight the merging of two nearby saddle points: (a) , (b) , (c) , and (d) .

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2010-01-05
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/1/10.1063/1.3270045
10.1063/1.3270045
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