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Conditions under which a supercritical turbidity current traverses an abrupt transition to vanishing bed slope without a hydraulic jump

Published online by Cambridge University Press:  14 August 2007

SVETLANA KOSTIC  and
GARY PARKER
SVETLANA KOSTIC
Affiliation:
Ven Te Chow Hydrosystems Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USAskostic@uiuc.edu; parkerg@uiuc.edu
GARY PARKER
Affiliation:
Ven Te Chow Hydrosystems Laboratory, University of Illinois, Urbana-Champaign, IL 61801, USAskostic@uiuc.edu; parkerg@uiuc.edu
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Abstract

Turbidity currents act to sculpt the submarine environment through sediment erosion and deposition. A sufficiently swift turbidity current on a steep slope can be expected to be supercritical in the sense of the bulk Richardson number; a sufficiently tranquil turbidity current on a mild slope can be expected to be subcritical. The transition from supercritical to subcritical flow is accomplished through an internal hydraulic jump. Consider a steady turbidity current flowing from a steep canyon onto a milder fan, and then exiting the fan down another steep canyon. The flow might be expected to undergo a hydraulic jump to subcritical flow near the canyon–fan break, and then accelerate again to critical flow at the fan–canyon break downstream. The problem of locating the hydraulic jump is here termed the ‘jump problem’. Experiments with fine-grained sediment have confirmed the expected behaviour outlined above. Similar experiments with coarse-grained sediment suggest that if the deposition rate is sufficiently high, this ‘jump problem’ may have no solution with the expected behaviour, and in particular no solution with a hydraulic jump. In such cases, the flow either transits the length of the low-slope fan as a supercritical flow and shoots off the fan–canyon break without responding to it, or dissipates as a supercritical flow before exiting the fan. The analysis presented below confirms the existence of a range associated with rapid sediment deposition where no solution to the ‘jump problem’ can be found. The criterion for this range is stated in terms of an order-one dimensionless parameter involving the fall velocity of the sediment. The criterion is tested and confirmed against the experiments mentioned above. A sample field application is presented.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 119 - 145
Copyright
Copyright © Cambridge University Press 2007

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