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Electrified free-surface flow of an inviscid liquid past topography
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10.1063/1.4758812
/content/aip/journal/pof2/24/10/10.1063/1.4758812
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/10/10.1063/1.4758812
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of a typical electrode or point charge and liquid flow configuration.

Image of FIG. 2.
FIG. 2.

Supercritical flow with a single electrode, We = 0.04, A = 0.009, r = 0.1, z = 1.0 and x 1 = 0. The topography is flat everywhere, with σ(x) ≡ 0. The broken and solid curves in (a), (c), and (d) correspond to the boundary element method and formula (13) for the electric pressure, respectively. (a) Nonlinear free-surface profiles with F = 1.10. The elevation of the free-surface in the top two curves is η(0) = 0.20 (solid curve) and η(0) = 0.19 (broken curve). The elevation of the free-surface in the bottom two curves is η(0) = 0.02 (solid curve) and η(0) = 0.02 (broken curve). (b) Weakly nonlinear phase plane diagram for (a) with F = 1.10 and Q 1 = 0.014. From left-to-right, the first and second jumps occur at η(0) = 0.03 and η(0) = 0.20, respectively. (c) Pressure distributions. The top and bottom broken curves correspond to the top and bottom broken curves in (a). The bottom solid curve corresponds to formula (13) and was used to produce both solid curves in (a). (d) Plot of y(0) = η(0) + 1 versus F.

Image of FIG. 3.
FIG. 3.

Supercritical flow with two point charges, F = 1.10, A = 0.009, λ1 = λ2 = 1.0, and z = 1.0. The electric pressure is given by (15). (a) Nonlinear free-surface profile with x 1 = −6.5, x 2 = 2.5, η(x 1) = 0.02, and η(x 2) = 0.20. (b) Weakly nonlinear phase plane diagram for (c) with Q 1 = Q 2 = 0.014, η(x 1) = 0.03, and η(x 2) = 0.20. (c) Nonlinear free-surface profile with x 1 = −10, x 2 = 10, η(x 1) = η(x 2) = 0.02, and η(0) = 0.21. (d) Pressure distributions. The solid and broken curves correspond to the profiles (a) and (c).

Image of FIG. 4.
FIG. 4.

Generalised hydraulic and hydraulic falls with a single electrode, F = 1.10, h = −0.01, η(0) = 0.20, r = 0.1, and z = 1.0. (a) Nonlinear free-surface profile with no electrode. (b) Weakly nonlinear phase plane diagram for (a), Q 1 = 0.019. (c) Nonlinear free-surface profile with A = 0.012 and x 1 = −6.32. (d) Weakly nonlinear phase plane diagram for (c). (e), and (f) Nonlinear free-surface profiles with A = 0.012. (e) x 1 = −13.32. (f) x 1 = −10.12.

Image of FIG. 5.
FIG. 5.

Subcritical flow with no electrodes, F = 0.50 and h = 0.1. (a) Nonlinear free-surface profile for a bump length of b = 8.38. (b) Sketch of phase plane diagram for (a). (c) Nonlinear free-surface profile for a bump length of b = 8.81. The bump length came as part of the solution. (d) Sketch of phase plane diagram for (c).

Image of FIG. 6.
FIG. 6.

Subcritical flow with a single electrode, F = 0.50, h = 0.1, r = 0.1, and z = 1.0. (a) Nonlinear free-surface profile, A = 0.018, b = 8.40, and x 1 = −7.66. (b) Sketch of phase plane diagram for (a). (c) Nonlinear free-surface profile for A = 0.008, b = 8.38, and x 1 = −0.32. (d) Sketch of phase plane diagram for (c).

Image of FIG. 7.
FIG. 7.

Subcritical flow with two point charges, F = 0.50, h = 0.1, , , and z = 1.0. (a) Nonlinear free-surface profile, b = 8.15, x 1 = −7.78, and x 2 = 0.22. (b) Sketch of phase plane diagram for (a). (c) Nonlinear free-surface profile, b = 8.12, x 1 = −4.60, and x 2 = 2.40. (d) Sketch of phase plane diagram for (c).

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/content/aip/journal/pof2/24/10/10.1063/1.4758812
2012-10-26
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electrified free-surface flow of an inviscid liquid past topography
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/10/10.1063/1.4758812
10.1063/1.4758812
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