142
4. SIMULATING GROWTH AND FORM
this is due to the relatively low number of branches which have developed in
the objects in Fig. 4-41 close to Pe ::::: 0, which makes the objects too small for
an accurate estimation of Dj,ox. Growth of the object in the diffusion-limited
regime is relatively much slower than growth in the flow-limited conditions,
resulting in smaller objects for the same number of growth steps in the simulations. In the range with branching objects, the object gradually transforms
from a thin-branching form in Fig. 4-41 for the value Pe ::::: 0, into a compact
shape for Pe = 3.0. In the range with lobed objects in Fig. 4.39 the more or
less columnar objects for lowPenumbers transform more abruptly into more
spherical forms. The gradual increase in compactness for an increasing influence of hydrodynamics in Fig. 4.41 corresponds to observations of ranges
of growth forms of marine sessile organisms collected along a gradient of increasing influence of exposure to water movement (see Sect. 3.3). In the same
ranges it is also observed that Dbox values, estimated from two-dimensional
pictures, tend to decrease with an increasing degree of compactness. A similar observation was done in three-dimensional aggregates, where the growth
process was controlled by the local availability of simulated nutrients (see
Sect. 4.5): for increasing Penumbers more compact aggregates develop, while
the Dj,ox value decreases from 2.27 to 2.05.
In both ranges shown in Figs. 4.39 and 4.41 the average absorption Ii (see
Tables 4.4 and 4.5) in the sink nodes of the simulated objects increases going
from the diffusion-limited (Pe ::::: 0) to the flow-limited regime (Pe = 3.0). The
exponent Dabs> which can be interpreted as a measure of the uniformity of the
nutrient distribution, decreases for the range of branching objects in Fig. 4.41;
for increasing hydrodynamics the nutrient is distributed more evenly over the
system. The same phenomenon is not observed in the range oflobed objects
in Fig. 4.39; the underlying reason could be the complex geometry of these
objects where an intricate system of narrow crevices is formed preventing
a uniform distribution of nutrients. In Figs. 4.40 and 4.42 slices in the xzplane through the simulation box are shown where the nutrient distribution
is visualized around the object for Pe ::::: 0 and Pe = 3.0. The most obvious
difference between the diffusion-limited nutrient distribution and the flowlimited distribution is the asymmetry due to the flow. In the diffusion-limited
case for the lobed and the branching objects a roughly radial symmetric
nutrient pattern is found; when comparing the left-to-right and the rightto-left flow phases there are hardly any effects of the flow to be seen. In the
flow-limited case for both experiments there is a clear difference between
the two phases; a depleted region downstream of the object is observed,
while upstream the nutrient pattern is not disturbed by the object. In the
more open branching objects in Fig. 4.42 more nutrient arrives between the
branches compared with the lobed objects in Fig. 4.40, where hardly any
nutrient arrives between crevices. This may explain the relatively high Dabs
for high Pe numbers in Table 4.4. In Figs. 4.43 and 4.44 it can be seen that
in the average nutrient distribution, depletion zones develop at both the left
and the right side of the simulated object, for the flow-dominated case. Both
zones emerge at certain distances from the object; close to the object there is
still a region with a relatively high nutrient concentration.
For both experiments there is also a clear difference in the absorption patterns (see Figs. 4-40 and 4.42) for the diffusion-limited and the
flow-limited case. In the Pe ::::: 0 case most nutrients are being absorbed at
protruding parts of the object, while in the Pe = 3.0 case most nutrients are
4. SIMULATING GROWTH AND FORM
this is due to the relatively low number of branches which have developed in
the objects in Fig. 4-41 close to Pe ::::: 0, which makes the objects too small for
an accurate estimation of Dj,ox. Growth of the object in the diffusion-limited
regime is relatively much slower than growth in the flow-limited conditions,
resulting in smaller objects for the same number of growth steps in the simulations. In the range with branching objects, the object gradually transforms
from a thin-branching form in Fig. 4-41 for the value Pe ::::: 0, into a compact
shape for Pe = 3.0. In the range with lobed objects in Fig. 4.39 the more or
less columnar objects for lowPenumbers transform more abruptly into more
spherical forms. The gradual increase in compactness for an increasing influence of hydrodynamics in Fig. 4.41 corresponds to observations of ranges
of growth forms of marine sessile organisms collected along a gradient of increasing influence of exposure to water movement (see Sect. 3.3). In the same
ranges it is also observed that Dbox values, estimated from two-dimensional
pictures, tend to decrease with an increasing degree of compactness. A similar observation was done in three-dimensional aggregates, where the growth
process was controlled by the local availability of simulated nutrients (see
Sect. 4.5): for increasing Penumbers more compact aggregates develop, while
the Dj,ox value decreases from 2.27 to 2.05.
In both ranges shown in Figs. 4.39 and 4.41 the average absorption Ii (see
Tables 4.4 and 4.5) in the sink nodes of the simulated objects increases going
from the diffusion-limited (Pe ::::: 0) to the flow-limited regime (Pe = 3.0). The
exponent Dabs> which can be interpreted as a measure of the uniformity of the
nutrient distribution, decreases for the range of branching objects in Fig. 4.41;
for increasing hydrodynamics the nutrient is distributed more evenly over the
system. The same phenomenon is not observed in the range oflobed objects
in Fig. 4.39; the underlying reason could be the complex geometry of these
objects where an intricate system of narrow crevices is formed preventing
a uniform distribution of nutrients. In Figs. 4.40 and 4.42 slices in the xzplane through the simulation box are shown where the nutrient distribution
is visualized around the object for Pe ::::: 0 and Pe = 3.0. The most obvious
difference between the diffusion-limited nutrient distribution and the flowlimited distribution is the asymmetry due to the flow. In the diffusion-limited
case for the lobed and the branching objects a roughly radial symmetric
nutrient pattern is found; when comparing the left-to-right and the rightto-left flow phases there are hardly any effects of the flow to be seen. In the
flow-limited case for both experiments there is a clear difference between
the two phases; a depleted region downstream of the object is observed,
while upstream the nutrient pattern is not disturbed by the object. In the
more open branching objects in Fig. 4.42 more nutrient arrives between the
branches compared with the lobed objects in Fig. 4.40, where hardly any
nutrient arrives between crevices. This may explain the relatively high Dabs
for high Pe numbers in Table 4.4. In Figs. 4.43 and 4.44 it can be seen that
in the average nutrient distribution, depletion zones develop at both the left
and the right side of the simulated object, for the flow-dominated case. Both
zones emerge at certain distances from the object; close to the object there is
still a region with a relatively high nutrient concentration.
For both experiments there is also a clear difference in the absorption patterns (see Figs. 4-40 and 4.42) for the diffusion-limited and the
flow-limited case. In the Pe ::::: 0 case most nutrients are being absorbed at
protruding parts of the object, while in the Pe = 3.0 case most nutrients are