Modified Thermal Theory for Gravity Currents on Sloping Boundaries
Publication: Journal of Hydraulic Engineering
Volume 136, Issue 10
Abstract
In this study, we generalize the classic thermal theory to account for both entrainment and detrainment effects occurring in the acceleration and deceleration phases of gravity current motion. Although the original thermal theory qualitatively captures the two phases of gravity current motion, the pure entrainment model appears to underpredict the gravity current velocity and the distance before the maximum velocity is reached. We theoretically show that detrainment increases the predicted maximum velocity of gravity current and extends the predicted distance before the maximum velocity is reached. Furthermore, based on the experimental data reported in the literature, the detrainment coefficient appears to increase as the bottom slope increases.
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Acknowledgments
The research was supported by the National Science Council of Taiwan through Project No. NSCTNSC 98-2218-E-032-007.
References
Baines, P. G. (2001). “Mixing in flows down gentle slopes into stratified environments.” J. Fluid Mech., 443, 237–270.
Baines, P. G. (2005). “Mixing regimes for the flow of dense fluid down slopes into stratified environments.” J. Fluid Mech., 538, 245–267.
Beghin, P., Hopfinger, E. J., and Britter, R. E. (1981). “Gravitational convection from instantaneous sources on inclined boundaries.” J. Fluid Mech., 107, 407–422.
Britter, R. E., and Linden, P. F. (1980). “The motion of the front of a gravity current travelling down an incline.” J. Fluid Mech., 99, 531–543.
Dade, W. B., Lister, J. R., and Huppert, H. E. (1994). “Fine-sediment deposition from gravity surges on uniform slopes.” J. Sediment Res., 64, 423–432.
Dai, A., and Garcia, M. (2010). “Gravity currents down a slope in deceleration phase.” Dyn. Atmos. Oceans, 49, 75–82.
Maxworthy, T., and Nokes, R. I. (2007). “Experiments on gravity currents propagating down slopes. Part 1. The release of a fixed volume of heavy fluid from an enclosed lock into an open channel.” J. Fluid Mech., 584, 433–453.
Monaghan, J. J., Cas, R. A. F., Kos, A. M., and Hallworth, M. (1999). “Gravity currents descending a ramp in a stratified tank.” J. Fluid Mech., 379, 39–69.
Morton, B. R., Taylor, G. I., and Turner, J. S. (1956). “Turbulent gravitational convection from maintained and instantaneous sources.” Proc. Roy. Soc. A, 234, 1–23.
Ross, A. N., Dalziel, S. B., and Linden, P. F. (2006). “Axisymmetric gravity currents on a cone.” J. Fluid Mech., 565, 227–253.
Ross, A. N., Linden, P. F., and Dalziel, S. B. (2002). “A study of three-dimensional gravity currents on a uniform slope.” J. Fluid Mech., 453, 239–261.
Shin, J., Dalziel, S., and Linden, P. (2004). “Gravity currents produced by lock exchange.” J. Fluid Mech., 521, 1–34.
Simpson, J. (1997). Gravity currents, 2nd Ed., Cambridge Univ. Press, Cambridge, Mass.
Tickle, G. (1996). “A model of the motion and dilution of a heavy gas cloud released on a uniform slope in calm conditions.” J. Hazard. Mater., 49, 29–47.
Webber, D., Jones, S., and Martin, D. (1993). “A model of the motion of a heavy gas cloud released on a uniform slope.” J. Hazard. Mater., 33, 101–122.
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© 2010 ASCE.
History
Received: May 20, 2009
Accepted: Mar 29, 2010
Published online: Sep 15, 2010
Published in print: Oct 2010
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