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On the weak viscous effect of the reflection and transmission over an arbitrary topography
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10.1063/1.4799099
    + View Affiliations - Hide Affiliations
    Affiliations:
    1 Department of Marine Environmental Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan
    2 Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
    a) Author to whom correspondence should be addressed. Electronic mail: twhsu@mail.ntou.edu.tw. Telephone: +886-6-2372315. Fax: +886-6-2741463. Present address: Research Center of Ocean Energy and Strategy, National Taiwan Ocean University, Keelung 202, Taiwan.
    Phys. Fluids 25, 043103 (2013); http://dx.doi.org/10.1063/1.4799099
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View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Waves propagating over a series of steps.

Image of FIG. 2.
FIG. 2.

Typical examples of horizontal velocity profiles for a water wave solved by LWT and VPWA.

Image of FIG. 3.
FIG. 3.

Horizontal velocity profiles with different phases for waves propagating over a constant depth. (a) Different wave phases; (b) velocity profiles at different wave phases.

Image of FIG. 4.
FIG. 4.

Diagram of friction factor and Reynolds number compared with experimental data.

Image of FIG. 5.
FIG. 5.

Horizontal velocity profiles with different phases for waves propagating over a sloping bottom. (a) Different wave phases; (b) velocity profiles at different wave phases.

Image of FIG. 6.
FIG. 6.

A comparison of viscous waves elevations (a) pure water, ν = 1.12 × 10 m/s; (b) fictitious fluid, ν = 1.0 × 10 m/s; (c) SAE-30, ν = 4.2 × 10 m/s; and (d) glycerin, ν = 1.19 × 10 m/s.

Image of FIG. 7.
FIG. 7.

Trapezoid symmetric trench with the same slopes on both sides.

Image of FIG. 8.
FIG. 8.

Comparison of reflection coefficients versus for a symmetric trapezoid trench with the same fluid depth.

Image of FIG. 9.
FIG. 9.

Viscous wave scattering over a symmetric trapezoid trench ( = 1.0); (a) reflection and (b) transmission coefficients.

Image of FIG. 10.
FIG. 10.

Energy loss of viscous wave scattering over a symmetric trapezoid trench ( = 1.0).

Image of FIG. 11.
FIG. 11.

Trapezoid trench with the same slope on both sides and different fluid depths.

Image of FIG. 12.
FIG. 12.

Reflection coefficients versus for waves propagating over an asymmetric trapezoid trench with different fluid depths.

Image of FIG. 13.
FIG. 13.

Viscous wave scattering over an asymmetric trapezoid trench ( = 1.0); (a) reflection and (b) transmission coefficients.

Image of FIG. 14.
FIG. 14.

Energy loss of viscous wave scattering over an asymmetric trapezoid trench ( = 1.0).

Image of FIG. 15.
FIG. 15.

Parabolic trench with the same fluid depth.

Image of FIG. 16.
FIG. 16.

Reflection coefficients versus / for parabolic trenches with different center depths ( = 0.167).

Image of FIG. 17.
FIG. 17.

Viscous wave scattering over a parabolic trench ( / = 4, = 1.0); (a) reflection and (b) transmission coefficients.

Image of FIG. 18.
FIG. 18.

Gaussian trench with the same slope on both sides and different fluid depths.

Image of FIG. 19.
FIG. 19.

Reflection coefficients versus for a Gaussian trench with the same fluid depth.

Image of FIG. 20.
FIG. 20.

Viscous wave scattering over a Gaussian trench ( = 1.0); (a) reflection and (b) transmission coefficients.

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/content/aip/journal/pof2/25/4/10.1063/1.4799099
2013-04-11
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the weak viscous effect of the reflection and transmission over an arbitrary topography
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4799099
10.1063/1.4799099
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