Lateral slopes and downflow obstacles Reflection, deflection and flow

Flow overspilling, reflection and deflection are dependent on flow properties and the height, geometry and orientation of topographic highs (Kneller and McCaffrey, 1999). Key flow properties include flow thickness, duration and acceleration, grain-size of the transported sediment and density stratification. A relationship has been noted between the Froude number (Fr) (1) of a flow and the relationship between obstacle height and flow thickness (Kneller and McCaffrey, 1999; Kneller and Buckee, 2000). Experimental studies can give insight into the effect of obstacles on flow capacity (Alexander and Morris, 1994; Lane-Serff et al., 1995; Morris et al., 1998; Kneller and McCaffrey, 1999).

For the same obstacle height, higher energy flows have a greater capacity whilst passing over obstacles. For flows with the same capacity, an obstacle height can be determined beyond which the entire flow will be blocked, causing reflection and deflection of the flow (Baines and Davies, 1980; Lawrence, 1987). Therefore, three main subdivisions of topographic control can be recognised: (i) when the obstacle height is significantly less than flow thickness, a change in Froude number may occur causing the flow to undergo hydraulic jump from super- to sub- critical flow conditions; (ii) when obstacle height and flow height are similar (< 2 x obstacle height, Alexander and Morris, 1994), the upper portion of the flow may breach the obstacle with the lower portion reflected and deflected; and (iii) when obstacle height greatly exceeds flow thickness (> 2 x flow thickness, Alexander and Morris, 1994) reflection and deflection of the entire flow will occur, and possibly a hydraulic jump will form (Edwards, 1993; Pantin and Leeder, 1987; Kneller and Buckee, 2000).

Even small obstacles will greatly effect flow dynamics. If the obstacle height is not sufficient to deflect lower denser portions of flow, the flow will still decelerate and rapidly deposit

sediments, while upper portions of flow continue down-dip. Kneller and Buckee (2000) describe four types of downflow effect on an obstacle (Fig. 2.5) based on the relationship between Froude number (Fr) (1), the velocity and stratification of the flow. With obstacle height increase relative to flow height, flow stratification increases and Froude number increase hydraulic jump are more likely to occur on the lee side of an obstacle (Fig. 2.6).

Figure 2.6 The effect of internal Froude number (Fri) on the behaviour of flows downstream of

topography (from Kneller and Buckee. 2000).

As discussed above, when moving over an obstacle, stratified layers within a flow act

independently, but this is subject to the Froude number (Fr) (1). When the Froude number is high, the flow tends to act as a unity, with the entire flow overtopping topography or

reflected/deflected (Fig. 2.7). For low Froude numbers there is a critical plane within the flow (dividing streamline, Baines, 1995), above which the flow and sediment particles can move up and over the obstacle, whereas in the denser lower regions of the flow, below the dividing streamline, the flow has insufficient energy to surmount topography, and is deflected around it (Fig. 2.7).

Figure 2.7 Schematic illustration of the joint effects of the dividing streamline, the Froude number and

the degree of confinement (h/z) (from Kneller and McCaffrey 1999).

When a flow obstacle is much larger than flow height the flow will run up and increase in height. For density-stratified flows, the maximum run up height is dependent on velocity and density profiles and can be highly variable (Kneller and Buckee, 2000). When a flow is fully confined a disturbance is generated upstream of the obstacle, consisting of an internal bore. An internal bore is an abrupt downstream increase in flow thickness and an associate decrease in flow velocity, which can migrate upstream (Rottman and Simpson, 1989; Edwards, 1993; Kneller and Buckee, 2000).

Figure 2.8 The three types of internal bores defined by Rottman and Simpson (1989) (From Kneller and

Buckee, 2000).

Kneller and Buckee (2000) differentiate types of bore (Fig. 2.8) based on the relationship between the height of the bore and the flow height. The weakest bore (Type A, fig. 2.8) is characterised by a group of internal solitary waves. The strongest bore (Type C, fig. 2.8) is generated by erosion at the head of the turbidity current, producing higher stratification through increased entrainment of ambient fluid. With an intermediary type (Type B, fig, 2.8) (Kneller and Buckee, 2000).

Flows will inevitably experience a decrease in competence and capacity associated with interaction with obstacles. Therefore, a marked localised increase in sedimentation is likely to occur (Alexander and Morris, 1994; Kneller, 1995; Kneller and McCaffrey, 1995), which may migrate upstream in steady currents (Kneller and Buckee, 2000). This increased deposition may also occur in the lee of the obstacle in association with a downstream hydraulic jump (Kneller and Buckee, 2000).

Figure 2.9 Depositional model for turbidity currents obstructed by a lateral slope that are (a) slow and

highly depositional or (b) fast and capable of erosion and/or bypass of sediment, and (c) and (d) their resulting cross-stream deposit thickness trends. SLFR= sediment load fallout rate, from Amy et al., 2004.

Three-dimensional models based on flume and numerical experiments have attempted to recreate turbidite thickness patterns where obstructed by lateral slopes (Kneller et al., 1991; Kneller, 1995; McCaffrey and Kneller, 2001; Amy et al., 2004). In the experimental currents obstructed by a lateral slope, flow velocity non-uniformity patterns consist of streamlines that are parallel close to the slope but diverge at positions away from the slope (Amy et al., 2004) (Fig. 2.9). In this pattern, flow is more depletive far from the slope than near to the slope and therefore higher suspended-load fallout rates and thicker deposits should be expected far from the slope beneath the most depletive portion of the flow (Amy et al., 2004). However, this is converse to the thinning-away-from-slope pattern of some experimental datasets (Amy et al., 2004), where maximum sediment thickness was attributed to sediment deposited on the slope transforming into a higher concentration flow and coming to rest at the base-of-slope (McCaffrey and Kneller, 2001). Therefore, an interpretation of deposit thickness based on flow velocity non-uniformity alone (e.g. Kneller 1995; Kneller and McCaffrey, 1999) cannot explain these experimental depositional patterns. To explain this using flow concentration a non- uniform mechanism is required where a current is weakly depletive close to the slope but is highly depletive far from the slope and thus maintains relatively high concentrations and high sediment load fallout rate close to the slope in medial and distal settings (Amy et al., 2004).

This pattern of flow concentration non-uniformity could arise if there were lower rates of deposition and/or entrainment in proximal regions close to the slope (Amy et al., 2004).