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72                                         Roberto Sulpizio and Pierfrancesco Dellino


          4.2. Development of self-organised pulses in a PDC and stepwise
               aggradation
          Recently, Sulpizio et al. (2007) proposed a model for small-scale PDCs that joins
          together the en masse and aggradation approaches. This model successfully explains
          characteristics of small-scale PDCs from the subplinian eruption of Pollena from
          Somma-Vesuvius (Rosi and Santacroce, 1983; Rolandi et al., 2004; Sulpizio et al.,
          2005), but it can also satisfactorily describe some general characteristics of PDC
          deposits.
             The model assumes that most PDC deposits originate from stratified flows, in
          which the segregation of particles with higher terminal velocities in the lowermost
          part of the flow can develop a high-concentration zone (Valentine, 1987; Branney
          and Kokelaar, 2002; Dellino et al., 2004). This basal portion of the flow can move
          down-slope as a succession of high-concentration pulses whose thickness varies as a
          function of turbulence and kinematics of different density waves (Figure 7a, d and f ).
          This allows consideration of a single-pulse as a flow-boundary zone for its entire
          thickness, in which the interplay among shear-rate, rate of deposition and
          concentration of particles determines the depositional regime (fallout, fluid-escape,
          granular flow and traction; Figure 7n). Pulse stoppage occurs en masse when
          resistance forces overpass the driving ones (e.g. when grain interlocking forces
          overpass gravitational forces). The four types of flow-boundary zones are completely
          intergradational (Burgissier and Bergantz, 2002; Branney and Kokelaar, 2002)and
          mixed regimes are common (Sulpizio et al., 2007).
             This implies that, due to the masking effect of the phoenix cloud on the
          underflow, the current appears to move as a steady mass flow, but, in reality,
          the main body is segmented into different pulses that run very close to each other.
          The development of multiple pulses within a gravity current have been observed
          during large flume experiments (Major, 1997; Iverson, 1997), small-scale
          laboratory experiments (Savage, 1979; Brennen et al., 1983; Huppert et al.,
          1986) and hypothesised for both volcaniclastic and pyroclastic deposits on the basis
          of field evidence (Chough and Sohn, 1990; Schwarzkopf et al., 2005; Sulpizio
          et al., 2006, 2007). The mechanisms responsible for pulsating behaviour in a
          gravity-driven current are still not completely understood, but can be related to the
          successive release of material during generation (i.e. during column or dome
          collapse and failure of soils or slopes; Pierson, 1980; Scott et al., 2001; Cole et al.,
          2002; Loughlin et al., 2002) and/or to the inhomogeneous mass distribution within
          the current that induces development of kinetic waves (Lee and Leibig, 1994;
          Major and Iverson, 1999; Schwarzkopf et al., 2005). Lee and Leibig (1994)
          numerically demonstrated how a system with an initially random density field
          evolves to a configuration in which neighbouring regions have a high-density
          contrast. At the early stage of development, the density contrast between nearby
          regions increases linearly with time. In a gravitational field, this results in different
          velocities in adjacent portions of the current:


                                             jðr Þ  jðr Þ
                                               1
                                                      2
                                     Uð1; 2Þ¼                                   (4)
                                               r   r
                                                1   2
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