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

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.