Flow dynamics and mixing processes in hydraulic jump arrays: Implications for channel-lobe transition zones

A detailed ﬁ eldinvestigation ofa saline gravity currentinthesouthwestBlack Sea hasenabled the ﬁ rstcomplete analysisofthree-dimensional ﬂ owstructureanddynamicsofaseriesoflinkedhydraulicjumpsinstrati ﬁ ed,den-sity-driven, ﬂ ows.These ﬁ eldobservationswerecollectedusinganacousticDopplercurrentpro ﬁ lermountedon anautonomousunderwatervehicle,andrevealthatinternalmixingprocessesinhydraulicjumps,including ﬂ ow expansion and recirculation, provide a previously unrecognised mechanism for grain-size sorting and segrega- tion in strati ﬁ ed density-driven ﬂ ows. Field observations suggest a newly identi ﬁ ed type of hydraulic jump, that is a strati ﬁ ed low Froude number ( b 1.5 – 2) subaqueous hydraulic jump, with an enhanced ability to trans- port sediment downstream of the jump, in comparison to hydraulic jumps in other subaerial and submarine ﬂ ows. These novel ﬁ eld data underpin a new process-based conceptual model of channel lobe transition zones (CLTZs) that explains the scattered offset nature of scours within such settings, the temporal variations in in ﬁ ll and erosion between adjacent scours, how bed shear stresses are maintained across the CLTZ, and why the locus of deposition is so far downstream of the scour zone.


Introduction
Hydraulic jumps are characterised by a sudden decrease in velocity and an increase in thickness of a flow. In the oceans, hydraulic jumps are thought to occur within gravity-driven flows located on the continental slope (Fildani et al., 2006;Fildani et al., 2013;Kostic et al., 2010;Maier et al., 2011), within submarine canyons and channels (Sumner et al., 2013;Covault et al., 2014;Symons et al., 2016), and in channel-lobe transition zones (Wynn et al., 2002;Kostic and Parker, 2006;Macdonald et al., 2011;Shaw et al., 2013;Hofstra et al., 2015). Hydraulic jumps in these contexts have been linked to a range of processes including: erosion and scour generation, bedform formation, flow mixing, and changes in sediment distribution and stratification (Wynn et al., 2002;Cartigny et al., 2011Cartigny et al., , 2014Sumner et al., 2013;Hofstra et al., 2015). The distribution of individual scours in linear trains on the continental slope and within canyons and channels, and in broader zones of erosion at the base-of-slope, has been linked in turn to the presence of multiple hydraulic jumps (Kostic et al., 2010;Macdonald et al., 2011).
Field measurements of hydraulic jumps in natural gravity currents are rare (Sumner et al., 2013). Given the paucity of field measurements, knowledge of subaqueous hydraulic jumps has been dominated by physical and numerical modelling (e.g., Komar, 1971;García and Parker, 1989;García, 1993). Research that follows these modelling approaches has focused on two distinct types of hydraulic jump: those formed by unsteady flows that occur in net depositional settings with chutes-and-pools and cyclic steps, and those that are formed by quasisteady flows (e.g., Waltham, 2004;Kostic and Parker, 2006;Spinewine et al., 2009;Kostic et al., 2010;Cartigny et al., 2011;Kostic, 2011Kostic, , 2014Sumner et al., 2013). Chutes-and-pools and cyclic steps are quasi-permanent features bounded by hydraulic jumps, with chutesand-pools differentiated by their mild slopes upstream of each hydraulic jump (e.g., Taki and Parker, 2005;Spinewine et al., 2009;. Unsteady flows forming cyclic steps and chutes-and-pools are associated with Froude numbers N1.5-2 characterised by breaking waves that form periodic surges, whilst quasi-steady flows have lower Froude numbers, typically b1.5-2 (Spinewine et al., 2009;Cartigny et al., 2011. Cyclic steps and chutes-and-pools have been linked to linear scour trains that are prominent on many continental slopes (e.g., Fildani et al., 2006;Kostic et al., 2010), however the formative processes of distributed scour fields in channel-lobe transition zones remain enigmatic (Macdonald et al., 2011).
To address this knowledge gap we: (i) present the first field measurements of an array of subaqueous hydraulic jumps; (ii) demonstrate that these hydraulic jumps are formed by interaction of a low Froude number, ≲ 1, flow with seafloor topography; and (iii) assess the flow processes within the hydraulic jumps in terms of mixing, fluid entrainment and their spatial influence downstream. We synthesize these observations to propose a novel conceptual model for low Froude number subaqueous hydraulic jumps over scours, and finally to propose a process-based model of channel-lobe transition zones (CLTZ) that addresses the nature of hydraulic jumps across these scour fields. These novel field data, and the new model of a stratified hydraulic jump derived from it, will inform geohazard risk assessment and hydrocarbon extraction in these complex environments.
The Black Sea shelf gravity current is confined within a sinuous channel (Fig. 1), achieves velocities of up to 1.5 m/s, is up to 30 m thick, and is sufficiently energetic to transport and rework coarse sand (Özsoy et al., 2001;Sumner et al., 2013). There has been extensive debate on the history of the Holocene reconnection of the Mediterranean and Black Seas, in particular on whether this was associated with a catastrophic flood into the Black Sea (e.g., Ryan et al., 1997Ryan et al., , 2003Thom, 2010), or gradual overtopping of the Black Sea into the Mediterranean via the Marmara Sea (e.g., Hiscott et al., 2002Hiscott et al., , 2007Aksu et al., 2016). The most recent connection has been estimated at N 8 ka to~11 ka BP (e.g. Ryan et al., 2003;Hiscott et al., 2007;Thom, 2010;Mertens et al., 2012;Aksu et al., 2016), and activation of the channel on the Black Sea Shelf (Fig. 1), constrained through levee development, has been dated to~7.5 ka BP suggesting that the channel formed subaqueously rather than via a subaerial catastrophic flood (Flood et al., 2009). The inflow to the Black Sea channel has a quasi-steady discharge, except when very strong onshore winds strengthen the Black Sea outflow, blocking the salinedriven inflow (Latif et al., 1991;Özsoy et al., 2001).
From the Strait of the Bosphorus, the main channel curves northwest following the seafloor slope. Upstream of the curved section, the flow passes over a series of steps and scours on the seafloor (Fig. 2). These seafloor features, and the varying width of the channel, force complex adjustment of the flow resulting in flow acceleration, deceleration and development of hydraulic jumps, as discussed in Sections 4 and 5. After this initial bend, the local channel relief decreases and the flow becomes progressively unconfined. Here the current separates into many smaller flows, forming multi-threaded channels and lobes on the seafloor (Fig. 1b).

Data and methods
The velocity of the gravity current was measured in three components using a downward looking 1200 KHz Acoustic Doppler Current Profiler (ADCP), with a vertical bin size of 1 m deployed from the autonomous underwater vehicle (AUV) Autosub3 (see Wynn et al., 2014). Seven transects of flow velocity data were collected, over the steps and scours on the seafloor. Transect A is composed of a single pass, providing an instantaneous time velocity field; Transects B-G are composed from multiple passes, providing time-mean velocity fields. Vertical salinity profiles were measured using a conductivity, temperature, depth (CTD) profiler deployed from a stationary research vessel that had dynamic positioning (R/V Pelagia). The velocity data presented in this study were collected between the 01-02 July 2013; 36 CTD profiles were collected between 02 and 09 July 2013 along the seven velocity transects. CTD profiles taken at the intersect of Transects A and B on the 2nd and 7th of July had a maximum absolute difference of b4%, indicating the flow was relatively steady during this period.
The velocity data were processed using the following steps: (i) Autosub3's inertial navigation system was corrected for drift using GPS fixes taken at the beginning and end of dives, when the AUV was on the surface. (ii) The component of velocity resulting from movement of the AUV was removed from the ADCP-derived flow velocity. (iii) Where large vertical motion was recorded throughout the water column, due to the motion of Autosub3 turning onto a new heading, the ADCP data were discarded. (iv) Vertical position was corrected, based on the offset of the downwards facing ADCP relative to the AUV's pressure sensor, then converted to depth relative to sea surface. (v) All data below the maximum ADCP backscatter intensity or within the blanking distance y b of the seafloor were removed, using y b = y a sin2θ, where y a was the altitude of the AUV with respect to the seabed and θ the angle of the profiling beam, 20°(e.g. Sumner et al., 2013). (vi) Flow velocity within the blanking region y b of the seafloor was extrapolated assuming a zero slip condition on the seafloor, using Matlab's "PCHIP" interpolation toolkit.
(vii) A single plane of best fit was generated from the repeat data at each transect; (viii) For each transect velocity vector data were rotated, using the right-hand-rule, and projected onto a single plane derived from the average path of Autosub3 (e.g. Parsons et al., 2010). From this projected cloud of data, a regular grid of flow velocity on each transect was extrapolated using Matlab's linear "griddata" function (determining the time-mean for Transects B-G).
The three components of the processed velocity data are: (i) along plane velocity, which is equivalent to downstream velocity in Transects A and E-G, and inner to outer bank velocity in Transects B-D; (ii) cross plane (normal) velocity, which is equivalent to inner to outer bank velocity in Transects A and E-G, and downstream velocity in Transects B-D; and (iii) vertical velocity. For each transect the flow-ambient fluid interface was defined by the contour of zero downstream flow velocity (Fig. 3a). Here the flow depth, H, is defined as the difference between the flow-ambientinterface and the bed depth, η.
The CTD profiles were processed to provide estimates of the density of the flow along each transect: (i) Density was derived from conductivity, temperature and depth data using the UNESCO (1983) formula; (ii) CTD data were mapped onto associated velocity transects using a linear least squares method to determine the optimal position to minimize distance to sample location; (iii) Depth was converted to relative height above seafloor, to allow comparison with the velocity data; and, (iv) to minimize topographic effects, the CTD data were interpolated between data points using the transformed phase space (x, (y-η)/H), where x is the along channel distance and y the vertical depth with respect to sea level (Sumner et al., 2013). Data interpolation was conducted using Matlab's™ linear "griddata" function, mapping concentration onto the grid describing the single plane of velocity data (Fig. 3b). For Transects D-G insufficient CTD data points meant that flow density profiles could not be generated.
A useful means of characterizing open channel flow behaviour is to compute the Froude number, Fr, which is the ratio of the depth-averaged inertial to gravitational forcing. For gravity currents where gravitational forcing depends on the excess density of the flow, this ratio is referred to as the densimetric Froude number, Fr d (Baines, 1997). For unstratified flows the Froude number is equivalent to the ratio of flow velocity to wave speed and thus a Froude number of unity specifies the transition point from super-to sub-critical flow necessary for a hydraulic jump.  derived from flow velocity and density measurements. The depthaveraged Froude number is calculated over the region between the seabed, y = η, and the flow-ambient fluid interface, y = η + H. The depth-averaged densimetric Froude number of the density-driven flow is defined as: Here g denotes specific gravity, |u| velocity magnitude, whilst ρ f and ρ a are the current and ambient fluid densities respectively, the latter here being taken as ρ a = 1014 kg/m 3 (Sumner et al., 2013). The first fraction on the right hand side of Eq. (1) describes the velocity averaged over the depth of the flow, according to the method of Ellison and Turner (1959), and the second fraction on the right hand side of Eq.
(1) describes the inverse of the gravitational force of the flow arising due to the excess density of the current.
A second useful means of characterizing the behaviour of a stratified, turbulent, current is to define the Richardson gradient number, Ri g , as the ratio of stratification induced stability of the fluid to shear induced turbulence production The first term of the right hand side of Eq.
(2) describes the square of the frequency of buoyancy driven fluctuations (Baines, 1997), whilst the second term describes the rate of turbulence production. Theoretically the stability of a steady stratified flow is defined by a value of Ri g N 0.25 (Miles, 1961). However, numerical analysis yields various criteria for stability that range between 0.2 and 1 (Galperin et al., 2007) and it is noted that instability may persist for Ri g ≫ 1 in unsteady flows (Majda and Shefter, 1998).

Results
Data from the Black Sea field site provide new insight into the dynamics of a stratified gravity driven flow as it passes through a series of hydraulic jumps. The following subsections discuss: the vertical structure of flow in the Black Sea channel and its dynamics  The gravity current formed by the exchange flow through the Strait of Bosphorus has a complex vertical structure as it enters the Black Sea channel system (see Fig. 1 and Sumner et al., 2014). The flow is accelerated by gravity acting on its excess density; and decelerated by frictional drag acting at both the bed, and the interface between the flow and surrounding ambient fluid. This results in the standard velocity profile of a stratified gravity current (Baines, 1997), with flow velocity increasing in magnitude with distance above the seafloor to a maximum near the mid-height of the flow (Fig. 3a). The decreasing cross-sectional shape of the channel (Fig. 2)   with mass conservation. Moreover, the flow is accelerated and decelerated by changes in the seafloor slope. As indicated in Figs. 3-5, these various forces together result in: flow expansion; vertical flow velocities of N 0.3 m/s, two orders of magnitude larger than the mean value; and depth-dependent flow acceleration and deceleration. These features are similar to those seen in super-to subcritical flow transitions in unstratified open-channel flows, with sudden changes in flow velocity and thickness, and it is therefore appropriate to characterise them as internal hydraulic jumps. The excess density of the flow is vertically stratified due to the entrainment of ambient fluid (Figs. 3-4). The lower half of the flow is approximately uniform with a density~1025 kg/m 3 , but above this the flow density drops rapidly to~1016 kg/m 3 before decreasing more slowly towards a value of~1014 kg/m 3 near the contour of zero flow velocity used to define the flow's interface with the ambient fluid (Figs. 3b and 4b). Given flow velocity and density profiles the depth-averaged Froude number of the flow may be calculated from Eq. (1), as shown in Figs. 3c and 4c. It is noted that whilst the depth-averaged Froude number changes abruptly across the internal hydraulic jumps shown in Figs. 3c and 4c, it is rarely greater than unity (Sumner et al., 2013).
Examining the hydraulic jumps in more detail shows that small recirculating flow cells are present above the preceding backwards-facing steps, as shown in Fig. 5a and, in greater detail, Fig. 5b-c for the recirculating flow cell above the largest scour. Flow streamlines, denoting the direction that an element of fluid travels in, at a given moment in time, are also shown in Fig. 5. Along Transect A (Fig. 5a-b), the streamlines show that the majority of the flow is closely orientated, parallel to the bed, in the downstream direction. However, over the seafloor scours the streamlines clearly show the recirculation of fluid, composed of fluid moving in the upstream direction, on the back of the internal hydraulic jumps (Fig. 5a-b). From the streamlines it is possible to observe that these recirculation cells are composed of several coherent vortices (Fig. 5b). These recirculation cells are thus similar in composition and formation to the surface rollers generated in open channel hydraulic jumps, as described by Long et al. (1991). At the top of the flow, at the contour of zero flow velocity, used here to define the flow-ambient fluid interface, the streamlines no longer become closely orientated to the bed (Fig. 5a-b). Here, the circular motion captured by the streamlines instead suggests the presence of Kelvin Helmholtz billows at the top of the current. Fig. 5c illustrates that structures with circular motion are also observed transverse to the primary flow.
Figs. 3-5 show that as the flow undergoes an internal hydraulic jump, mixing is enhanced due to the upwards flux of water. This mixing process results in stratification (the vertical variation of excess density) decreasing and flow thickness increasing. Moreover, from Figs. 3-5 it is seen that recirculation cells, described by the presence of upstream-directed flow, are formed as dense near-bed fluid is carried upwards by the expanding flow. Some of this locally denser than ambient fluid sinks under gravity, on the back of the expanding hydraulic jump. However, because relative density gradients are small within the stratified flow, inertia can carry this fluid for a large distance before it sinks. The result is a recirculating cell that extends beyond the upstream initiation of the internal hydraulic jump (Fig. 5b).

Internal hydraulic jumps and turbulent mixing
The development of the flow as it passes over the steps and scours at the upstream limit of the channel has a significant effect on turbulence and mixing processes within the flow. Here the relative magnitude of turbulence dampening to turbulence production is estimated by calculating the Richardson gradient number Eq. (2) of the flow (Fig. 6).  Fig. 6a shows that along the channel thalweg (Transect A, Fig. 2) the Richardson gradient increases vertically towards the centre of the flow and decreases towards both the lower and upper boundaries of the flow. This is due to the decrease in shear stress at the centre of the flow, near the flow velocity maximum. The large Richardson gradient numbers towards the centre of the flow suggest that shear production is minimized and stratification may act to dampen turbulence, whilst the small Richardson gradient numbers towards the flow-bed and flow-ambient fluid interfaces suggest that shear is generating large amounts of turbulent kinetic energy which may be advected, by fluid motion, into the central region of the flow.
In Fig. 6b and c the Richardson gradient number is also calculated for the cross-sectional Transects B and C. In Transect B (Fig. 6b), the flow is chaotic as the transect sits directly across the scour induced hydraulic jump. Here there is no uniform structure to mixing within the flow, however it is observed that near the flow-ambient fluid interface the Richardson gradient number becomes small as shear production dominates vertical density stratification. Moreover, within 1 km,~5 scour lengths, downstream of the hydraulic jump at Transect B, the flow has developed a more organized structure (see Transect C; Fig. 6c). Here the turbulent kinetic energy production at the sheared near-bed and flow-ambient fluid interfaces, is clearly separated by a region of low shear, high stratification, that surrounds the velocity maxima of the flow.

Bulk flow field behaviour over a hydraulic jump in a stratified density driven flow
Transects A-G (Fig. 1b) map the bulk flow behaviour of the internal hydraulic jump associated with the scour located at the intersection of Transects A and B. In Section 4.1 we discussed the bathymetry and depth-resolved flow velocity profiles for this scour and jump (Figs. 3-6). Here we compile the flow velocity profiles from Transects A-G to describe the flow velocity around the scour (Fig. 7). Specifically, Fig. 7a-c show flow behaviour in the basal 25%, the middle 50% and the upper 25% of the flow, respectively. Fig. 7d shows the depth-averaged velocity between the bed and the contour of zero flow velocity, the latter defining the flow-ambient fluid interface. In Fig. 7 the flow at all depths is seen to be predominantly orientated in the direction parallel to the channel sidewalls. Moreover, as frictional stresses diminish, the magnitude of the flow velocity increases away from the bed, away from the flow-ambient fluid interface and away from the channel walls. Whilst the denser than ambient flow is confined in-channel, outer-channel  flow velocities are negligible and predominantly orientated upstream (Fig. 7d). Lateral deflection of the flow towards the channel banks is observed above the internal hydraulic jump (Fig. 7). Within Transect B (Fig. 4a), the data show that, above the scour, the flow is orientated upstream thus obstructing up to 10% of the downstream flow. However, the deflection is greatest in the central 50% of the flow (Fig. 7b). This is because the recirculation cell associated with the hydraulic jump is elevated above the seafloor, allowing near-bed downstream flow to pass under it, but obstructing downstream flow at greater flow heights. In Fig. 7 the recirculation cell is evident by upstream flow velocities, see also Transect B (Figs. 3-5).
Lateral deflection around the scour diminishes for the top 25% of the flow (Fig. 7c) where flow is predominately bypassed over the scour and internal hydraulic jump (Fig. 5b). Although the recirculation zone sits within the middle reaches of the flow, as highlighted by the negative upstream flow velocities in Fig. 7b, there is no evidence for flow separation in the near-bed region which may influence step height and headwall slope (Allen, 1971). Such near-bed separation is unlikely in the observed stratified hydraulic jump, as if present it must be trapped within the unmeasured near-bed region of the flow, which is limited to 20-30% of the scour height (Section 3).

A new model for stratified subaqueous hydraulic jumps
Hydraulic jumps can be classified by the magnitude of the flow height expansion downstream of the jump, a variable that has been shown to be a function of the upstream Froude number in subaerial flows (Baines, 1997). Further, the dynamics of a flow both during and downstream of a hydraulic jump are dependent on the surrounding environment, for example: 1. A single subaerial or submarine hydraulic jump may be formed as flow slows and expands at a break of slope. In the subaerial case (Fig. 8a) surface rollers form a recirculation cell on the top of the flow (Rajaratnam, 1967;Komar, 1971;Long et al., 1991). Depending on water levels after the break in slope, this recirculation cell may extend upstream or downstream of the change in slope. 2. Arrays of linked hydraulic jumps, and co-dependent topography, are found in subaerial and submarine environments. Steep slopes, that generate high depth-averaged Froude number flows, Fr d N 1.5 − 2, provide sufficient motive force to reaccelerate the flow leading to super-to sub-to super-critical flow transition (see Fig. 8b and Kostic et al., 2010). Rapid expansion and reacceleration of the flow enables the flow to adjust within single scour lengths forming linear trains of scours, e.g. cyclic steps . Deposition on the lee side of these jumps progressively backfills them, whilst the steps move upstream (Lang and Winsemann, 2013).
In comparison to previous hydraulic jump models the flow dynamics of the observed hydraulic jumps are markedly different. Here the density-driven flow is gravitationally stratified with corresponding higher density, higher velocity flow nearer the bed (except in the near-wall region where flow velocity decreases due to friction). Thus a third type of hydraulic jump is postulated: Moreover, whilst a hydraulic jump in an unstratified flow requires an upstream Froude number greater than unity (i.e., commonly defined supercritical flow) and downstream Froude number less than unity (i.e., commonly defined subcritical flow), the depth-averaged Froude number observed in the stratified hydraulic jumps was rarely greater than unity (Figs. 3c and 4c). This is because the strict condition necessary for super-subcritical flow transition, and thus a hydraulic jump, is that the flow velocity is greater than the wave speed (Baines, 1997). Whilst the wave speed is equivalent to the denominator of (Eq. (1)) for unstratified open channel flow, this is not true for more complex flows where the wave speed is affected both by topography and flow stratification (see, e.g., Baines, 1997;Thorpe, 2010;Thorpe and Li, 2014). Thus, these observations highlight that the use of depthaveraged parameters to describe stratified density driven flow dynamics is of limited value (Waltham, 2004;Oğuz, 2005;Huang et al., 2009;Sözer, 2013;Sumner et al., 2013).
Stratification has a significant effect on a flow undergoing a hydraulic jump. Thorpe (2010) first reported how, across a hydraulic jump, internal expansion of a monotonically varying stratified flow can theoretically develop into a stratified twin layer flow with two velocity  Rajaratnam, 1967;Long et al., 1991); (b) cyclic steps (see, e.g., Kostic and Parker, 2006;Kostic et al., 2010;Postma et al., 2009;Postma and Cartigny, 2014); (c) stratified subaqueous flow discussed herein.
maxima. The development of twin layer flow behaviour is observed in expansion of the lowermost component of the flow as it undergoes hydraulic jumps in the Black Sea flow. The twin layer flow exists downstream of the hydraulic jumps, and concomitant backwards facing steps, and persists until destroyed by flow acceleration and recirculation at the scour ( Fig. 5a-b). The development of the twin layer flow is also observed in the Richardson gradient number description of turbulence within the flow (Fig. 6a). Here both the twin velocity maxima and the local velocity minima at the mid-height of the flow decrease turbulence production through shear.

Grainsize sorting and sediment transport across stratified hydraulic jumps
It is inferred from direct observation of the density driven Black Sea flow that flow stratification has an important effect on two fundamental sediment transport processes: grain-size sorting and downstream flow capacity. In sediment-laden flows, transitioning from super to subcritical, the majority of coarse-grained particles, carried near the bed, will pass through the hydraulic jump. Some of the material carried through the jump will be trapped in, and deposited from, the internal recirculation cell. In contrast, some of the finer-grained material, initially more evenly distributed in the water column, will bypass the hydraulic jump, in the upper reaches of the flow, as the flow separates upstream. Thus in the uppermost component of the flow, above the hydraulic jump, the net effect of stratification is to bypass a greater fraction of fine than coarse particulate material. However, within the lowermost component of the flow (containing the hydraulic jump) enhanced mixing and flow expansion will act to distribute sediment more evenly within the flow, thereby decreasing stratification downstream of the jump.
Flow expansion and large vertical flow velocities will rapidly decrease suspended sediment stratification immediately downstream of the hydraulic jump. After this rapid change in sediment stratification, the vertical distribution of suspended particulate material will slowly readjust to local flow conditions (Dorrell and Hogg, 2011). The length scale over which redistributed sediment readjusts determines the spacing of active internal hydraulic jumps. Within the field study site, observed changes in bed slope enabled reacceleration and thus linked hydraulic jumps. However, the length scales between individual jumps are large,~10 times the scour length (Fig. 6a). This is in contrast to cyclic steps where erosion and deposition appear within a single jump . Maintenance of the flow downstream of the hydraulic jump may be explained by the development of the twin velocity maximum, postulated by Thorpe (2010) and observed herein. As the twin velocity maxima are spread vertically over a wide region, the lower velocity maximum remains close to the bed. This enables near-bed shear stresses to be maintained at a similar value across single or multiple hydraulic jumps (Fig. 6a). The ability for flows downstream of a hydraulic jump to maintain near-bed shear stresses means they maintain erosion rates and thus flow capacity (Dorrell et al., 2013a). This mechanism of maintained sediment transport capacity is opposed to current models that suggest that downstream of a hydraulic jump flows are strongly depositional (Pantin and Franklin, 2009;Postma et al., 2009;Symons et al., 2016). Although, with a flow developing a twin velocity maximum, shear and thus turbulent mixing will decrease within the central region of the flow. Ultimately this implies that suspended material will become more concentrated near the seafloor downstream of the jump.

Implications for channel lobe transition zones (CLTZs)
In contrast to many previous studies which have described the dynamics of depth-averaged Froude number flows, Fr d N 1.5 − 2, found on steep slopes in the proximal reaches of submarine canyon and channel systems (e.g. Fildani et al., 2006Fildani et al., , 2013Lamb et al., 2008;Heinio and Davies, 2009;Normark et al., 2009;Maier et al., 2011), the depth-averaged Froude number flow, Fr d ≲ 1, described herein provides a suitable analogy with the decelerating flow dynamics of hydraulic jumps that are formed by stratified flow over scours, across lower slopes, in the channel lobe transition zone (CLTZ) (Komar, 1969(Komar, , 1977Wynn et al., 2002;Macdonald et al., 2011;Hofstra et al., 2015). CLTZs describe the region of change from confined channels to unconfined lobes, containing widely scattered erosional features and evidence for bypass of sediment (Mutti andNormark, 1987, 1991;Wynn et al., 2002;Hofstra et al., 2015). In particular, new observations presented in this paper provide a possible explanation for some previously enigmatic observations from modern CLTZs. One of these enigmas is the synchronous existence of deposition and erosion within adjacent scours that has recently been observed in CLTZs (Macdonald et al., 2011). Such lateral variations in scour dynamics are not easily interpreted in terms of: i) a single largescale hydraulic jump at the base of slope affecting the whole CLTZ, or, ii) all scours within a CLTZ exhibiting synchronous hydraulic jumps. The observations instead suggest that in a stratified gravity current, seafloor scours and their concomitant hydraulic jumps affect the flow velocity profile and turbulent mixing processes for multiple scour lengths downstream. Given the persistence of subcritical flow downstream of a hydraulic jump, hydraulic jumps over subsequent scour features may thus be suppressed (Fig. 9). Consequently, for a given input flow, only a proportion of scours in a channel lobe transition zone may exhibit active hydraulic jumps (see Fig. 9 and Sumner et al., 2013). The position and proportion of active hydraulic jumps within a CLTZ may vary between flows as a function of flow magnitude, or as an individual flow waxes and wanes. Moreover, given the negligible change in near-bed stresses downstream of a stratified hydraulic jump, the bulk flow capacity (Dorrell et al., 2013a) of sediment driven gravity currents may remain relatively unchanged. This provides an explanation for the locus of deposition being downstream of broad zones of scour in CLTZs (Wynn et al., 2002;Sumner et al., 2013); vertical turbulent mixing, and maintenance of bed shear stresses enables sediment bypass across these regions. The present work on low Froude number, here ≲1, but potentially b1.5-2, hydraulic jump arrays provides a coherent process- model for the geomorphological observations of channel lobe transition zones.

The absence of CLTZs in some systems: implications for hydraulic jumps in mud-rich channels
A further enigma is that channel-lobe transition zones are not universal, being associated in modern systems with a high sand/clay ratio, whilst being absent in many mud-rich (high clay/sand ratio) channelised systems such as the Zaire and Mississippi (Mulder and Etienne, 2010;Mulder, 2011). This observed relationship appears to differ to work derived from the ancient where Mutti (1985) defined detached (CLTZ present) and attached (no CLTZ) lobes in larger mud-rich, and smaller sand-rich systems respectively. Many of the observations from modern systems are at a different scale to those in the ancient, and are typically from less tectonically active settings, so there may be multiple parameters controlling CLTZ formation. Here we concentrate on the observations from modern systems. Many large mud-rich channelized systems such as the Zaire (Savoye et al., 2000) and Mississippi (Twichell et al., 1991) show no obvious gap, or scour fields, between channel and lobe. This suggests that the flows are already subcritical by the time they exit the channel, in agreement with modelling that suggests that flows in large submarine channels are subcritical in their distal reaches (Pirmez and Imran, 2003;Dorrell et al., 2013b). Yet, gravity currents in the upper reaches of such systems are thought to be typically supercritical, based on analysis and measurement of flow properties (Pirmez and Imran, 2003;Xu et al., 2004Xu et al., , 2010Talling et al., 2013), and the presence of linear scour trains (Fildani et al., 2006;Fildani et al., 2013;Heinio and Davies, 2009;Normark et al., 2009). So how do currents undergo the supercritical to subcritical transition and why is there no obvious morphological expression of these hydraulic jumps within these systems?
A number of factors may be responsible for this lack of morphological expression at the super-to sub-critical transition. The present work suggests that the nature of hydraulic jumps in thick, stratified, confined flows may be very different. Mud-rich submarine channels can exhibit strongly stratified flows many tens of metres, to well in excess of a hundred metres, thick (e.g., Peakall et al., 2000;Khripounoff et al., 2003;Savoye et al., 2009;Konsoer et al., 2013;Dorrell et al., 2014;Peakall and Sumner, 2015). Comparison with the Black Sea flows shown herein, suggests that only the lower parts of the flow may undergo a hydraulic jump, with potentially much of the fine-grained upper part of the flow bypassing the jump altogether. Furthermore, large-scale mud-rich submarine channels build towards a graded profile (Kneller, 2003), whilst simultaneously prograding (Normark et al., 1997), thus approaching but never truly reaching grade. These transient graded profiles act to minimize the rate of change of gradient along system, smoothing out areas such as the slope break. Consequently, successive flows may form internal hydraulic jumps at different points within a system, with these migrating downstream and upstream over time as a function of changing dynamics within individual flows (cf. Mulder et al., 2003;Giorgio Serchi et al., 2011;Peakall and Sumner, 2015), rather than being pinned at a specific point such as the slope break. In combination with these longitudinal movements, within an individual flow the thickness of the internal hydraulic jump, and the percentage of the flow involved in the jump, may also alter. Potentially, the net result of this type of internal hydraulic jump in mud-rich submarine channels is to reduce and broaden the zones of erosion and deposition within these systems, leaving no substantive morphological imprint of the super-to sub-critical transition.

Conclusions
Here for the first time we examine the three-dimensional flow dynamics of an array of subaqueous hydraulic jumps that are formed by a flow traversing a series of scours, in a natural field example. We demonstrate that these hydraulic jumps have depth-averaged Froude numbers around unity, and that the resulting flow dynamics are very different to higher depth-averaged Froude number (N 1.5-2) flows such as those associated with chutes-and-pools and cyclic steps. It is highlighted that in stratified flows depth-averaged Froude numbers do not give an accurate measure of flow criticality. Flows across the scours lead to significant upward velocities, thus aiding sediment suspension and mixing. This enhanced suspension of sediment is maintained downstream of the jump by a flow that exhibits two velocity maxima, that acts to keep high basal shear stresses downstream. The resulting velocity profiles and turbulent mixing profiles are maintained for~10 scour lengths downstream, in marked contrast to cyclic steps which scale with the scour/bedform length. The persistence of mixing processes and near-bed velocity structure for many scour lengths downstream suggests that the development of hydraulic jumps and concomitant bedform features in close proximity may be suppressed. These observations enable a process-model to be developed for channel lobe transition zones in the deep ocean, suggesting that only a proportion of scours exhibit active hydraulic jumps at any one point in time, and that these may change between flows, and within individual events, as flows wax and wane. The new insights afforded into these processes provide a new explanation of how channel-lobe transition zones typically exhibit an areal distribution of scattered offset scours, rather than the individual linear arrays associated with higher Froude number (N1.5-2) flows associated with cyclic steps. Some mud-rich submarine channel systems do not exhibit channel-lobe transition zones, or an obvious morphological zone associated with the super-to sub-critical transition. The Black Sea results herein suggest that this may in part be due to the development of spatially and temporally varying internal hydraulic jumps in stratified flows, where the hydraulic jump may only affect the lower part of the flow. These results will therefore inform geohazard assessment for placement of seafloor infrastructure (e.g. telecommunications cables and oil/gas pipelines) and hydrocarbon exploration and production (e.g. reservoir connectivity between channel and lobes) in these complex and dynamic environments.