A new Entrainment Parameterization for Mixing in Oceanic Overflows and Dense Gravity Currents
Overflows are generated by dense currents and have been observed to mix with the surrounding waters at specific locations, like sills and constrictions, but also along the descent over the continental slope. The final properties of these currents are dictated by the amount of entrained fluid. Dense currents are an integral part of the thermohaline circulation and their water properties are of global importance. For example, one of the most important sources of deep water in the oceans is the North Atlantic Deep Water (NADW), which is formed in the Greenland Seas and its water properties are modified by the entrainment occurring at Denmark Strait, Faroe Bank Channel, and along the descent over the continental slope. The amount of entrainment occurring is therefore of fundamental importance to the understanding of the formation of deep water masses. Even when resolving the overflows, coarse resolution global circulation and climate models cannot resolve the entrainment processes that are often parameterized. A review of current parameterizations will be presented together with a new empirical parameterization that has been obtained using a data set which includes oceanic and laboratory data. The new parameterization proposed by the authors presents two novelties when compared to the present available parameterizations. First, it depends on both the Froude number, Fr, and Reynolds number of the flow. Second, it takes into account subcritical (Fr < 1) mixing. The subcritical mixing observed in previous laboratory experiments has been suggested to be of fundamental importance for the water mass characteristics, such as density, of a dense current descending the continental slope. A weak, but non zero, entrainment can change the final density and, consequently, the depth and location of important water masses in the open ocean. This is especially true when the dense current follows a long path over the slope in a subcritical regime, as observed occurring in the southern Greenland Deep Western Boundary Current. A stream tube model employing this new parameterization gives results that are more consistent with previous laboratory and oceanographic observations than when a classical parameterization is used. Finally, the new parameterization predictions are compared to recent oceanographic measurements of entrainment and turbulent diapycnal mixing rates, using scaling arguments to relate the entrainment ratio to diapycnal diffusivities.
A theory to Explain the Entrainment Ratio of Gravity Currents
The dynamics of both density and turbidity currents are determined by mixing and drag due to turbulence at the upper and lower interface. The magnitude the mixing and interfacial drag is often parameterized in terms of a dimensionless entrainment ratio E in gravity currents, but there has not previously been any unifying theory to predict either the magnitude of E or to determine how E depends upon the stability of the flow. Such a theory would then predict when the bottom drag co-efficient CD would be greater of less than the interfacial drag E, for different Reynolds and Froude numbers. We present an explanation of the functional dependence of E upon the Froude number and Reynolds number of a gravity current. Our theory is based upon the observed variation of the flux coefficient Γ (sometimes known as the mixing efficiency). Our main theoretical result is that E= 0.25 Γ Fr2 cos(θ), where θ is the angle of the slope over which the gravity current flows, and Fr the Froude number. In the case of high Froude numbers we find that E ~ 0.1, consistent with observations of a constant entrainment ratio in unstratified jets and weakly stratified plumes. For Froude numbers close to one, Γ is constant and has a value in the range of 0.1 - 0.3, which means that E ~ Fr2, again in agreement with observations, and previous experiments. For Froude numbers less than one, Γ decreases rapidly with Froude number, explaining the sudden decrease in entrainment ratios that has been observed in all field and experimental observations. We also show that the functional form of the stratified turbulent diffusivity Kρ has the same dependence upon the Froude number as the entrainment ratio.
Secondary Flow in Meandering Channels: Rivers Versus Turbidity Currents
Classical analyses of secondary flow in river bends indicate that the flow should be directed toward the outer bank near the surface and the inner bank near the bed. This secondary flow plays an important role in sculpting the bed of meandering channels, with shallow water near the inner point bar and deep water near the outside of the bend. Turbidity currents sculpt meandering channels with similar planforms on submarine fans in the deep ocean. It has recently been suggested that the secondary flow of turbidity currents in meandering channels may be reversed compared to rivers, with the near-bed flow directed toward the outer bank. The conditions for this reversal are investigated in the context of steady, uniform flow in a bend of constant curvature. It is found that such a reversal is associated with flows of sufficiently high Froude number. In the case of most Froude-subcritical flows, such a reversal would not be expected. We present a threshold line dividing the two regimes. We use this threshold line in combination with reconstructions of turbidity currents in a canyon-fan system and seismic images to infer where each regime might be expected to occur.
Secondary Circulation in Sinuous Submarine Channels: First Results from the Black Sea
Sinuous submarine channels are important features on ocean floors, and are key conduits for sediment, carbon and other nutrients into the deep-sea. Their gross planform similarity to river channels has long led to comparison with their subaerial meandering river counterparts. However, they are formed by the action of gravity flows and therefore might be expected to exhibit different processes from the open-channel, single phase flows of river channels. Changes in their morphology and deposits have been observed, however, little is known about the flow processes that occur in these channels. The best available data from modern systems have been limited to single at a point downstream velocity profiles; the best of these being from submarine canyons rather than channels. In order to understand flow dynamics and how they relate to channel processes, sedimentary dynamics and channel evolution, more detailed 2D and 3D flow data is required. Here we report the first such data from a sinuous channel on the Black Sea shelf, and examine the nature of secondary circulation in submarine channels. River channels have long been known to exhibit a three-dimensional helical flow comprising both a dominant downstream component, and a secondary (cross-stream) flow. Such secondary flows are the result of centrifugal acceleration induced by bend curvature, and an inwardly directed radial pressure gradient, which results from a super-elevation of the water surface at the outside of the bend. In river bend apices these secondary flows are directed towards the inner bend at the base of the flow, and towards the outer bank at the top of the flow. Until very recently, it was assumed that submarine channels showed a similar distribution. However, theoretical analysis of the governing equations for river channels, with the incorporation of an appropriate downstream velocity distribution for gravity currents, indicated that submarine channels could display reversed secondary circulation orientation with respect to meandering rivers (Corney et al. 2006, 2008). This theory was backed up by an extensive physical modeling program that also showed reversed secondary circulation in all cases (Keevil et al., 2006, 2007). Other experiments though have shown examples of secondary circulation similar to river channels, and there has been intense debate on the validity of different approaches and datasets. Immediately north of the exit of the Bosphorus Strait, north of Istanbul there is a spectacular sinuous channel network on the Black Sea shelf. This channel network is created by the higher density of seawater of Mediterranean origin as it flows into the much lower salinity Black Sea. The near-constant gravity currents that run through these channels provide the perfect laboratory for studying the detailed fluid dynamics of submarine channel flows. Here we report results from the apex of a major sinuous channel bend that is 20-30 m deep. An acoustic Doppler current profiler (ADCP) towed across the bend recorded a maximum velocity of ~1 m/s. There, the saline underflow is density-stratified, exhibits marked outer-bank super-elevation, and the sense of secondary flow is opposite to that in rivers. Future 3D flow monitoring will use the British autonomous vehicle AutoSub3.
Submarine Currents and Subaerial Intuition: Comparing Flow Characteristics Inferred From Deposit Morphology to Constraints From Inverted Grain-Size Data
Turbidity currents exert fundamental controls on the evolution of continental margins, yet their physical properties remain poorly constrained because they are difficult to observe directly in nature. We develop a method for inverting geometric and grain size data from turbidites to constrain turbidity current flow conditions. Grain-size distributions were obtained for over fifty samples from two single-event deposits collected within a submarine channel cross section preserved in the Miocene-Pliocene Capistrano Formation, San Clemente, California. The deposits include fine-sand beds of relatively uniform thickness and grain size that drape preexisting channel topography and sandy beds that onlap the channel side-walls and fine upwards. Based on observations from subaerial deposits, the drape morphology suggests deposition by a thick current that far exceeded the height of the channel. The onlap morphology suggests a relatively thinner flow, largely confined to the channel. Spatial variations in particle size are used to constrain the instantaneous vertical flow-structure and depositional conditions at a single point through time. A simple sediment transport model connects suspended-sediment concentration profiles and local flow conditions to the observed variations in deposit grain-size and sorting. Modeled profiles for the two deposits constrain the down-channel spatial evolution of the flows that produced them, indicating current velocities of up to 10-20 meters per second and flow durations on the order of minutes to hours. The disparate morphologies of the two deposits suggest deposition from flows with dissimilar thicknesses and sediment concentration profiles. However, constraints based on observed grain size distributions indicate that the velocity and thickness of the flows were comparable. Our results suggest that interpretations based on deposit morphology and intuition from subaerial flows can be misleading when applied to submarine environments and that turbidite morphology cannot be related directly to turbidity current physical properties.
Sediment Lofting From Melt-Water Generated Turbidity Currents During Heinrich Events as a Tool to Assess Main Sediment Delivery Phases to Small Subpolar Ocean Basins
Small subpolar ocean basins such as the Labrador Sea received a major portion (25%) of their sediment fill during the Pleistocene glaciations (less than 5% of the basin's lifetime), but the detailed timing of sediment supply to the basin remained essentially unknown until recently. The main sediment input into the basin was probably not coupled to major glacial cycles and associated sea-level changes but was related to Heinrich events. Discovery of the depositional facies of fine-grained lofted sediment provides a tool which suggests that the parent-currents from which lofting took place may have been sandy-gravelly turbidity currents that built a huge braided abyssal plain in the Labrador Sea (700 by 120 km underlain by 150 m on average of coarse- grained sediment) which is one of the largest sand accumulations (104 km3) on Earth. The facies of lofted sediment consists of stacked layers of graded muds that contain ice-rafted debris (IRD) which impart a bimodal grain-size distribution to the graded muds. The texturally incompatible grain populations of the muds (median size between 4 and 8 micrometers) and the randomly distributed coarse silt and sand-sized IRD require the combination of two transport processes that delivered the populations independently and allowed mixing at the depositional site: (i) sediment rafting by icebergs (dropstones) and (ii) the rise of turbid freshwater plumes out of fresh-water generated turbidity currents. Sediment lofting from turbidity currents is a process that occurs in density currents generated from sediment-laden fresh-water discharges into the sea that can produce reversed buoyancy, as is well known from experiments. When the flows have traveled long enough, their tops will have lost enough sediment by settling so that they become hypopycnal (their density decreasing below that of the ambient seawater) causing the current tops to lift up. The turbid fresh-water clouds buoyantly rise out of the turbidity current to a level of equal density in the stratified water column, presumably the pycnocline, where they spread out laterally, even up-current, and generate interflows that deposit graded layers. The process is slow enough to allow incorporation into the graded layers of debris melting out of drifting icebergs. The hyperpycnal portion of individual discharge events that generated these currents might have had an estimated volume on the order of 103 km3x(1012 m3) which would have flowed for 10-15 days or less, assuming estimated discharge ranges for subglacial outburst floods of up to 106 m3/s. Turbidites are deposited much too fast to incorporate any substantial fraction of IRD, whereas deposition from lofted interflows may take months. The most likely candidates for the parent currents from which lofting occurred were the sandy flows that formed the sand abyssal plain The observed lofted depositional facies is exclusively found in Heinrich layers at distances of up to 300 km from the presumed terminus of the Hudson Strait ice stream. Through this stratigraphic relationship the lofted facies ties the main pulses of Late Pleistocene sediment supply in the Labrador Basin to Heinrich events. Heinrich events are known as Late Pleistocene ice-rafting episodes of unparalleled intensity in the North Atlantic that were associated with major melt-water discharge pulses and, as it appears now, also were the times of the main sediment delivery. Other potential basin candidates where lofting may have occurred are the Bering Sea and Maury Channel in North Atlantic.