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The Critical Densimetric Froude Number of Subaqueous Gravity Currents Can Be Non-Unity or Non-Existent

¹ School of Architecture and Civil Engineering, Anhui University of Technology, 59 Hudong Road, Maanshan City, Anhui 243003, China; heqing{at}ahut.edu.cn
² Department of Civil and Environmental Engineering, University of South Carolina, 300 Main Street, Columbia, South Carolina 29208, U.S.A.
³ Shell International Exploration and Production, P.O. Box 481, Houston, Texas 77001, U.S.A.
⁴ School of Architecture and Civil Engineering, Anhui University of Technology, 59 Hudong Road, Maanshan City, Anhui 243003, China
⁵ School of Architecture and Civil Engineering, Anhui University of Technology, 59 Hudong Road, Maanshan City, Anhui 243003, China

For decades, the critical densimetric Froude number of subaqueous gravity flows has been regarded to be unity or close to unity, the same as the critical Froude number for open-channel flows. Based on the analysis of specific energy, a concept borrowed from hydraulic engineering, it is shown that two correction terms, the discharge correction and the concentration correction, appear in the formulation of the critical densimetric Froude number for subaqueous gravity flows in a channel. As a result, the critical densimetric Froude number of a subaqueous gravity flow in a channel can be non-unity or non-existent depending on the degree of entrainment of ambient fluid and the density variation in the currents. Furthermore, it is shown that the lower the critical densimetric Froude number is in a supercritical subaqueous gravity flow, the bigger the internal jump is if the flow experiences a change in flow regime.