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Lagrangian analysis of fluid transport in empirical vortex ring flows
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View: Figures


Image of FIG. 1.
FIG. 1.

Streamlines of Hill's spherical vortex.

Image of FIG. 2.
FIG. 2.

Cartoon of the heteroclinic tangle of the upper unstable and stable manifolds of the front and rear stagnation points.

Image of FIG. 3.
FIG. 3.

Cartoon of heteroclinic intersections for a perturbed elliptical vortex. The interior of the vortex is given by the shaded region.

Image of FIG. 4.
FIG. 4.

Panel (a) illustrates the process of vortex ring fluid entrainment; panel (b) illustrates the process of fluid detrainment from the vortex ring.

Image of FIG. 5.
FIG. 5.

Water tank and imaging apparatus for quantitative studies of jellyfish swimming and feeding.

Image of FIG. 6.
FIG. 6.

(Color online) Contour plots of the FTLE fields computed from DPIV at time , with an integration times and in panels (a) and (b), respectively. Position coordinates are specified in centimeters.

Image of FIG. 7.
FIG. 7.

(Color online) Intersection of aLCS (blue curve) and rLCS (red curve) define the vortex interior. Shown for .

Image of FIG. 8.
FIG. 8.

(Color online) Looping of the rLCS. Superimposed is a rectangular parcel of fluid.

Image of FIG. 9.
FIG. 9.

(Color online) Evolution of lobes in empirical vortex rings.

Image of FIG. 10.
FIG. 10.

Cross-sectional area of the vortex interior as a function of time as measured from the streamline method (Ref. 30 ) and the LCS method described in Sec. IV .

Image of FIG. 11.
FIG. 11.

Panel (a) shows DPIV measurements of the velocity field surrounding a free-swimming Aurelia jellyfish at an arbitrary time in its swimming motion. Panel (b) shows the instantaneous streamlines of the flow in the wake of a jellyfish similar to the one in panel (a).

Image of FIG. 12.
FIG. 12.

(Color online) Panel (a) shows the FTLE field ( , grid spacing of ) at the same time as the measurement in Fig. 11(a) . The FTLE field reveals an LCS, that is superimposed over the jellyfish at a slightly later time in panel (b). The evolution of the LCS indicates which regions of fluid are entrained and shows a recirculation zone behind the jellyfish.

Image of FIG. 13.
FIG. 13.

(Color online) Evolution of lobes about jellyfish. The lobes distinguish which fluid is entrained into the subumbrellar region.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lagrangian analysis of fluid transport in empirical vortex ring flows