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criticial Shields numbers cannot be respected at
the same time as is usual in aerodynamics or fluid
flow modelling (Peakall et al ., 1996; Paola, 2000;
Postma et al ., 2008; Martin et al ., 2009). As classi-
cal full-scale-modelling procedures are too restric-
tive and unsuited to geomorphologic and
stratigraphic experiments, Hooke (1968) proposed
to focus on the similarity of processes rather than
the true and full dynamic similarity. A geomor-
phic experiment should be considered as a small
natural system in its own right and not just as a
small model. Flume experiments have been used
over the last decades to understand the qualitative
behaviour of natural systems and have been
proven to yield stratigraphic responses that are
consistent to natural systems, opening up new
ways to calibrate stratigraphic forward models
(Whipple et al ., 1998; Heller et al . 2001; Muto &
Steel, 2001; Van Heijst et  al ., 2001a, b; Strong &
Paola, 2008; Postma et al . 2008; Van den Berg van
Saparoea & Postma, 2008; Martin et al ., 2009; Van
Dijk et al ., 2009; Martin et al ., 2010). The passive-
margin and source-to-sink models built from
the  flume experiments are thus extreme models.
In particular, sea-level cycles (110 m in 20 ka) cor-
respond to really extreme glacial cycles. Although
they may be not common in real world systems,
these extreme values have the benefit to enhance
the role of sediment transport on the stratigraphic
architecture, both in the flume and numerical
experiments.
Table 2. Transport coeficients used in the non-linear
water-driven (Fig. 6A), linear water-driven (Fig. 6B)
and linear slope-driven simulations (Fig. 6C).
Case a:
non-linear
water-driven
transport
Case b:
linear
water-driven
transport
Case c:
slope-
driven
transport
n (−)
1.5
1.0
0.0
Transport
equation
1.
QKQS
sm
=
QKQS
sw
=
Q sw = K w   S
w
w
w
w
K sand (m 2 y −1 )
400
1100
9000
K silt (m 2 y −1 )
1200
3300
27,000
slope in each simulation (Table 2). Sediment trans-
port in marine environments was simulated using
the same avalanching code: all sediment grains
above the static angle of repose move downslope
until the depositional slope angle is lower than this
dynamic angle of repose.
The basin-scale evolution of the three simulated
passive margins is very similar, both in terms of
total sediment volume distribution and in terms
of sand/silt distribution (Fig.  8). This large-scale
architecture is controlled by sediment transport in
marine environments, which acts as a vacuum
cleaner at the mouth of the fluvial systems. The
large-scale internal stratigraphic architecture is
also very similar. The three main sedimentary
units controlled by the extreme sea-level cycles
were reproduced in each simulation. A first, thick,
sedimentary unit was deposited during the slow
cycle (unit 1 on Fig. 2). A second and smaller unit
exhibited erosional surface, toplap truncation and
steep downlap onto unit 1 (unit 2 on Fig.  2). A
composite and complex third unit was composed
of a series of smaller units similar to the second
unit (unit 3 on Fig. 2).
Despite the large-scale similitude of these three
simulations, the detailed internal stratigraphic
architectures were very different. The classical
slope-driven diffusion transport equation assumes
that sediment transport is only controlled by the
local slope. During each sea-level fall, this slope-
driven diffusion induced widespread subaerial
erosion from the source point downslope to a uni-
form shoreline parallel to the strike direction
(Fig.  8C). The water-driven diffusion equation
assumes that a local slope, but also a water flow,
are required to transport sediment. As soon as a
valley was created in the simulated domain,
water flow locally converged towards this valley.
As the sediment transport was linearly proportional
Linear vs. non-linear fluvial transport
Numerical models provide an ideal method to test
assumptions on transport laws and causal relation-
ships between parameters and stratigraphy. The
application of the linear slope-driven, non-linear
water-driven diffusion model demonstrates that
the simulation results are consistent with the flume
experiment. Not only the large-scale behaviour of
the flume experiment was reproduced, but the
complex stratigraphic details were also simulated:
the broad and composite erosional surface during
the slow long-term eustatic sea-level fall, the nar-
row and deep incised valley during the fast short
term eustatic sea-level fall. To control the influence
of the non-linearity, two simulations were per-
formed using a linear-water driven and slope-
driven transport equation (Q sw = K w Q w S, Fig.  8B)
and using only the classical linear slope-driven dif-
fusion equation (Q sw = K w S, Fig.  8C). Transport
coefficients were modified to obtain similar fluvial
 
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