Page 89 - Caldera Volcanism Analysis, Modelling and Response

64 Roberto Sulpizio and Pierfrancesco Dellino

Figure 3 Di¡erent sediment support mechanisms and related deposits in a diluted, fully tur-
bulent PDC. (a) Di¡erent mechanisms of £uid support of particles with di¡erent shapes (after
Branney and Kokelaar, 2003; modi¢ed); (b) theoretical mechanism of formation of lithofacies
lensL (n,i) at the very base of the current; (c) e¡ect of £uid drag and £uid lift on saltation and
rolling mechanisms of particle transport (lithofacies xsA); (d) gentle settling (direct fallout
regime) of ¢ne particles from the ash cloud that accompanies the waning phase of the current
(lithofacies maccrA); (e) real deposit left by a dilute, fully turbulent PDC of the Pollena erup-
tion (AD 472, Somma-Vesuvius, Italy).

(Pn i ; Rouse, 1937; Valentine, 1987) defines suspension conditions for particles of a
given grain size:
w i
Pn i ¼ (1)
ku
where w i is the settling velocity of particles of a given grain size, k the von Karman’s
coefficient (~0.4) and u * the shear velocity. Low Rouse numbers (Pn i ~o0.5)
correspond to small or light particles that can be efficiently transported in
suspension by fluid turbulence, while Rouse numbers W2.5 characterise coarser or
heavier particles transported by mechanisms other than suspension (Valentine,
1987).
Recently, Leeder et al. (2005) proposed a dimensionless criterion, L, needed to
maintain suspension for a given load. L is defined as the ratio of the maximum
vertical turbulent stress to the immersed weight of the suspended load above a unit
bed area:
rðv Þ max
02
L ¼ 1 (2)
mðs r=sÞg
where vu is fluctuating (instantaneous) vertical turbulent velocity, s and r are solid
and fluid densities, respectively, m the suspended load dry mass and g the
acceleration of gravity.