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A progressive correction to the circular hydraulic jump scaling
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10.1063/1.4801836
/content/aip/journal/pof2/25/4/10.1063/1.4801836
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801836
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the experiment. The radii ( , , , ) and heights ( , , , ) are ordered as in the water case (see text, Eqs. (12) and (15)–(17) ). The position of the external wall of height is variable.

Image of FIG. 2.
FIG. 2.

Numerical height profiles ξ() for different values of the external depth for type I jumps (lines). Experimental data (circles) obtained from Ref. . Horizontal and vertical scales are normalized with the plate radius = 37.9 mm and the lowest final depth = 2.77 mm, respectively. Reproduced by permission from Bohr , Physica B , 1–10 (1996). Copyright 1996 Elsevier B.V.

Image of FIG. 3.
FIG. 3.

Schematic figures of type I and type II hydraulic jumps. A second roll is observed when the outer depth is increased.

Image of FIG. 4.
FIG. 4.

Horizontal and vertical coordinates (, ξ) are normalized with = 105 mm and = 4.1 mm, velocities are normalized using a supercritical speed = 2.14 m/s, given by experimental data. (Left) Free surface (line) and bulk velocity field (arrows). Dark areas denote low velocities. The velocity field shows a separation eddy causing the hydraulic jump. (Right) Surface velocity (line) compared with experimental data upstream (circles) and downstream (squares) the jump. Reproduced by permission from Bohr , Physica B , 1–10 (1996). Copyright 1996 Elsevier B.V.

Image of FIG. 5.
FIG. 5.

The free surface ξ (thick line) and its first three spatial derivatives ξ′ (dotted-dashed line), ξ′′ (dashed line), and ξ′′ (continuous line). is the jump position defined numerically, the jump definition ξ′′ = 0 is marked with a point. Numerical solutions were obtained using = 6.32 × 10 cm/s, = 11.57 cm in the water case. Variables are presented in the non-dimensional notation.

Image of FIG. 6.
FIG. 6.

Scalings for the circular hydraulic jump. Experimental data (points) for 3 different viscosities: ν (water viscosity, circles), ν = 15ν (squares), ν = 95ν (rhomboids) compared with (dotted-dashed line, Eq. (12) ), (dashed line, solution of Eq. (15) ), (thick dashed line, Eq. (16) (right), and (thick dotted-dashed line, Eq. (17) ). Hydraulic jump radii are scaled with = 16.5 cm (plate radius), the fluxes are scaled with = 100 cm/s. Reproduced by permission from Hansen , Phys. Rev. E , 7048–7061 (1997). Copyright 1997 American Physical Society.

Image of FIG. 7.
FIG. 7.

Radii dependence with outer fluid depth for = 0.031 l/s, ν = 0.97 × 10 m/s. Experimental results (type I curves (circles) and type II curves (squares)), (dashed line, solution of Eq. (15) ), (thick dashed line, Eq. (16) (right)), and (thick dotted-dashed line, Eq. (17) ) compared. Jump radii are normalized with = 37.9 mm and depths with = 2.77 mm. Reproduced by permission from Bohr , Physica B , 1–10 (1996). Copyright 1996 Elsevier B.V.

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/content/aip/journal/pof2/25/4/10.1063/1.4801836
2013-04-23
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A progressive correction to the circular hydraulic jump scaling
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801836
10.1063/1.4801836
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