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Research Papers: Fundamental Issues and Canonical Flows

Front Condition for Gravity Currents in Channels of Nonrectangular Symmetric Cross-Section Shapes

[+] Author and Article Information
B. M. Marino

Instituto de Física Arroyo Seco, Universidad Nacional del Centro, Pinto 399, B7000GHG Tandil, Argentinabmarino@exa.unicen.edu.ar

L. P. Thomas

Instituto de Física Arroyo Seco, Universidad Nacional del Centro, Pinto 399, B7000GHG Tandil, Argentinalthomas@exa.unicen.edu.ar

J. Fluids Eng 131(5), 051201 (Apr 01, 2009) (6 pages) doi:10.1115/1.3089537 History: Received May 13, 2008; Revised January 21, 2009; Published April 01, 2009

We study the variation of the Froude number at the front of gravity currents developed in uniform channels whose cross-section shape depends on a parameter usually used in many numerical and theoretical models. The thickness and front velocity of the dense currents running on the bottom are greater for all the cases studied, resulting in a Froude number greater than that corresponding to the rectangular cross-section shape. The light currents developing along the upper boundary show the opposite trend. It is found that the results are not related to the depth and width of the channel. The relationships obtained agree with the results of laboratory experiments in which open and closed channels of different cross-section shapes are used.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of the lateral view of the lock-exchange gravity currents generated after removing the gate

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Figure 2

Schematic of the frontal zone of dense (a) and light (b) gravity currents

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Figure 3

Experimental setup to generate gravity flows in a channel of concave (a), triangular (b), and convex (c) cross-section shapes

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Figure 4

Instantaneous image of the counterflows generated in a parabolic cross-section shape tank after applying the image processing. A dense current (white) moving to the right and a light current (black) running in the opposite direction are clearly distinguished.

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Figure 5

Theoretical thickness of dense (solid line) and light (dashed line) gravity currents for different cross-section shapes. The experimental results obtained in closed and open channels are represented by solid and open symbols, respectively, and by triangles and diamonds for dense and light currents, respectively.

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Figure 6

Froude numbers of the dense F1 and light F2 currents as function of the respective heights H1 and H2 for different α. The energy-conserving solutions F1c(H1c) and F2c(H2c) given by Eqs. 15,23, respectively, are plotted by thin solid lines.

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