Page 101 - Caldera Volcanism Analysis, Modelling and Response

76 Roberto Sulpizio and Pierfrancesco Dellino

resisting stress that occurs as bed slopes decline (Figure 8a). The other component
takes into account that, where the bed slope decreases in the downstream direction,
2
part of the depth-averaged momentum flux per unit area rv is directed into the
bed and resisted by the reaction force provided by the underlying Earth (assumed
to be infinitely massive and immobile). This external reaction force redirects the
flow’s depth-averaged momentum flux to keep it parallel to the bed. However, the
action–reaction at the bed also locally increases the normal stress at the bed by an
2
2
amount (rhv )/r, where r is the radius of local bed curvature, v /r the associated
centripetal acceleration, r the density of the flow and h the flow height (Figure 8a;
Iverson and Denlinger, 2001). Hence, a strong change in slope increases the normal
stress (small r value) more than a weaker change (high r value), resulting in greater
normal bed frictional forces. Similar evaluation of such an influence of break
in slope on depositional behaviour of gravity-driven currents was claimed by
Zanchetta et al. (2004a) for volcaniclastic flows in the Vesuvian area. They
demonstrated how, at equal (or similar) flow characteristics and boundary
conditions, the distance travelled was related to the value of the slope ratio (SR),
defined as the ratio between the downflow and the upflow slopes (Figure 8a). The
deceleration of the current due to an increase in normal bed stress and lowering of
the slope enhances the turbulence (Gray et al., 2005), which may increase the
elutriation of fines and lofting (Figure 8a).
Deposition induced by change in slope has been documented in many papers
for dry granular flows (e.g. Denlinger and Iverson, 2001; Felix and Thomas, 2004)
volcaniclastic flows (e.g. Zanchetta et al., 2004a), PDCs (e.g. Macias et al., 1998;
Cole et al., 2005; Sulpizio et al., 2007) and turbidites (e.g. Mulder and Alexander,
2001; Gray et al., 2005). However, changes imposed by deposition in proximity of a
break in slope may also induce major flow transformations in fluid-bearing currents.
Beyond the break in slope, the flow braking induces deposition of material in the
flow-boundary zone and partial transfer of momentum to turbulence generation
and elutriation of fines (Figure 8a). At this point, the part of the flow above the
flow-boundary zone can respond in two ways: (i) its bulk density is still greater than
the surrounding ambient fluid and it propagates further as an independent gravity-
driven current (Figure 8b); or (ii) its bulk density is less than the surrounding
ambient fluid and it lofts convectively and stops (Figure 8c). The fate of a gravity-
driven current is then function of its mass and grain-size, the local curvature at the
break in slope and efficiency in energy transformation. All these parameters control
both the amount of material remaining in the transport system as the flow crosses
the break in slope and the subsequent physical characteristics of the surviving
gravity-driven current. Natural examples of PDC decoupling in proximity of a
break in slope were observed during the 1991 eruption of Colima volcano
(Saucedo et al., 2004) and inferred for the Avellino eruption of Somma-Vesuvius
(Figure 9; Sulpizio et al., 2008a).

4.3.2. Ability to surmount a ridge
When the path of a gravity-driven flow includes a steepening of the slope, the
change in local curvature lessens the partition between driving and resisting forces,