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to the water discharge, the sediment transport
efficiency along this valley increased whilst
almost no transport was possible along the sides
of this valley. This convergence of the water flow
was more sensitive during sea-level fall. Each
sea-level fall induced a fluvial base level fall. The
drainage network could not escape this valley
and a narrow shallow incised valley was formed
(Fig. 6B).
As the transport equation was linear and as the
simulated domain was symmetric, the incised val-
ley was straight and fed a symmetric broad delta.
The non-linear water driven diffusion equation
behaves in a similar way but has a more explosive
behaviour due to the non-linearity. Basin-scale
water flow structure has a major influence on the
sediment transport. In the case of channel con-
fluences in the simulated domain, water flow
increased leading to local erosion to satisfy the
increased sediment transport capacity. On the
contrary, in the case of bifurcations or diffluences,
water flow decreased leading to fast sedimenta-
tion due to the loss of transport capacity. It should
be noted here that no avulsion or confluence rules
were used in our numerical model. This chaotic
behaviour arose from the water flow routing and
the non-linear equation itself. It was amplified
during extreme sea-level fall such as during the
fast cycle (Figs 3A-4, 5 & 6 and Fig. 6A): water
flow focused in a single sinuous channel, which
deeply incised the previously deposited sedimen-
tary units.
This analysis of the linear versus non-linear
water-driven diffusion equation demonstrates
that the three sediment transport equations
tested here gave similar results along a 2D dip-
section. The detailed fluvial architecture and, in
particular, the water flow structure calculated by
these equations were completely different. These
simulations were characterised by a uniform
shoreline parallel to the strike direction without
any delta (slope-driven transport, Fig. 6C) or by
a broad delta fed by a straight and shallow chan-
nel (linear water-driven transport, Fig. 6B) or a
small shelf-edge delta fed by a sinuous narrow
and deeply incised channel (non-linear water-
driven transport, Fig. 6A). The linear slope-
driven, non-linear water-driven diffusion
equation led to realistic fluvial evolution with
sinuous channels, but more studies of real-world
systems are still required to calibrate all the
transport parameters such as the exponent or
diffusion coefficients.
Passive margin vs. source-to-sink model
The above analysis of the non-linear water-driven
transport equation is focused on the passive-margin
model that is on the lower catchment to sink
areas. It has been recently recognised that these
areas are not alone but part of a full source-to-
sink system (Martinsen & Helland-Hansen, 2009;
Somme
et al
., 2009b; Martinsen
et al
., 2010). The
second simulation performed at a source-to-sink
scale allowed exploration of the importance of
the drainage area that fed the passive margin. The
evolution of the sedimentary systems of the
source-to-sink model (Fig. 6) was quite similar to
that of the passive margin model, as illustrated by
the evolution of the centroid (Fig. 8-1).
A long transitory phase (0 ka to 80 ka) was
observed at the beginning of the simulation. During
this transitory phase, the upper catchment area
evolved progressively from an immature to a mature
landscape. To better explore the distribution of sed-
iment, the total erosion of the source area and the
sedimentation rate in the transition area were calcu-
lated. These erosion and sedimentation rates were
compared to the boundary condition defined in the
passive margin model (1820 km
3
My
−1
). The first-
order evolution of the erosion and sedimentation
rates was quite similar in the two simulations and
mimicked the sea-level cycles.
In detail, the evolution of the source-to-sink
model was far more complex than the passive
margin model. In particular, each sea-level fall
was characterised by two phases (Fig. 8-3). During
the first phase (T1-T2), sea-level fall steepened the
fluvial base level. This induced an increase of the
erosion rate of the source area. In the transition
area, this fall induced either a decrease of the sed-
imentation rate in the transition area when sea-
level fall was slow, or a major erosion of this
transition area when sea-level fall was very fast.
During the second phase (T2-T3), sea-level con-
tinued to fall up to a minimum value but at a
slower rate than during the first phase. Erosion of
the catchment area continued to increase, while
in the transition area erosion decreases or even
sedimentation starts again. These first results on a
source-to-sink system illustrate the importance
of simulating the full sedimentary system. A con-
stant boundary condition hides high-frequency
variations of the erosion along the drainage area
and thus of the sediment inflow into the sink area.
These simulations also illustrate the diachro-
nicity of erosional surfaces, as already noticed in
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