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Gravity currents produced by lock exchange

Published online by Cambridge University Press:  13 December 2004

J. O. SHIN ,
S. B. DALZIEL  and
P. F. LINDEN
J. O. SHIN
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
S. B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
P. F. LINDEN
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
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Abstract

The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of $\sqrt 2$. New experiments are reported for this case that support the new theoretical value.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 521 , 25 December 2004 , pp. 1 - 34
Copyright
© 2004 Cambridge University Press

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Shin et al. supplementary movie

Figure 9. Gravity current produced by lock exchange: full-depth release, vertical lock gate. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a vertical lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29.7 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents). The lower panel shows the effective depth in false colour plotted in the x-t plane. The lock gate is at x=0, and the propagation of the fronts of the dense current (x>0) and the light current (x<0) from this position are shown. The fact that the edges of the coloured regions are straight shows that the currents travel at constant (and almost equal) speeds. The horizontal line indicates the time corresponding to the image in the upper panel.

Download Shin et al. supplementary movie(Video)
Video 4.4 MB

Shin et al. supplementary movie

Figure 9. Gravity current produced by lock exchange: full-depth release, vertical lock gate. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a vertical lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29.7 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents). The lower panel shows the effective depth in false colour plotted in the x-t plane. The lock gate is at x=0, and the propagation of the fronts of the dense current (x>0) and the light current (x<0) from this position are shown. The fact that the edges of the coloured regions are straight shows that the currents travel at constant (and almost equal) speeds. The horizontal line indicates the time corresponding to the image in the upper panel.

Download Shin et al. supplementary movie(Video)
Video 32 MB

Shin et al. supplementary movie

Figure 18. Gravity current produced by lock exchange: partial-depth release. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a vertical lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents).

Download Shin et al. supplementary movie(Video)
Video 4.4 MB

Shin et al. supplementary movie

Figure 18. Gravity current produced by lock exchange: partial-depth release. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a vertical lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents).

Download Shin et al. supplementary movie(Video)
Video 19.5 MB

Shin et al. supplementary movie

Figure 10. Gravity current produced by lock exchange: full-depth release, tilted lock gate. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a tilted lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29.1 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents). The lower panel shows the effective depth in false colour plotted in the x-t plane. The lock gate is at x=0, and the propagation of the fronts of the dense current (x>0) and the light current (x<0) from this position are shown. The fact that the edges of the coloured regions are straight shows that the currents travel at constant (and almost equal) speeds. The horizontal line indicates the time corresponding to the image in the upper panel.

Download Shin et al. supplementary movie(Video)
Video 5.2 MB

Shin et al. supplementary movie

Figure 10. Gravity current produced by lock exchange: full-depth release, tilted lock gate. The upper panel shows a side view of the experiment. Initially, dense fluid (salt solution), marked with dye, is separated from less dense fluid (fresh water) by a tilted lock gate. When the gate is removed the dense fluid flows along the bottom boundary as a gravity current, and the fresh water flows along the surface forming a second gravity current. The total depth of the flow is 0.2 m and the initial reduced gravity of the two fluids is 29.1 mm/s. The effective depth of the current, determined by integrating the width-average density, is superimposed as the red curve. The side view also shows the initial lock position (the vertical yellow line) and the other lines correspond to the depths of the energy-conserving solution (blue) and of the current with maximum speed and dissipation (the two green lines, one each for the dense and light currents). The lower panel shows the effective depth in false colour plotted in the x-t plane. The lock gate is at x=0, and the propagation of the fronts of the dense current (x>0) and the light current (x<0) from this position are shown. The fact that the edges of the coloured regions are straight shows that the currents travel at constant (and almost equal) speeds. The horizontal line indicates the time corresponding to the image in the upper panel.

Download Shin et al. supplementary movie(Video)
Video 31.3 MB