2. Environmentally Driven Plasticity
2.1 The Physical Environment
T
he two major environmental parameters which have the greatest impact on the growth forms of marine sessile organisms are light, required
for photosynthesis, and hydrodynamics. A full discussion of the physics of
underwater light distributions and hydrodynamics could easily cover a few
textbooks. In Box 2.1 the basic hydrodynamic laws are summarized, together
with two dimensionless parameters, the Reynolds number Re (2.3) and the
Peeler number Pe (2-4), which can be used to characterize the impact of the
flow on the organism. In Sect. 2.1.1 "Growing and flowing" we will focus on
the biomechanical impact of hydrodynamics on the growth process and try
to construct a number oflaws for the biomechanical impact ofhydrodynamics using an engineering approach. In Sect. 4.3 we will return to the topic of
hydrodynamics, from a modeling point of view and try to construct a computational method capable of capturing the influence of hydrodynamics in
models of growth and form of marine sessile organisms. In Box 2 .2 the basic equations, in a highly simplified form, of underwater light distributions
are shown. Toa certain extent, in contrast with the hydrodynamic equations,
these simplified equations can more or less straightforwardly be included in
computational models; this will be discussed in Chap. 4.
Box 2.1 Hydrodynamics
Flow of water in space can be captured through two fundamental
equations:
iJp + . pU =0
iJt
iJU =_(U . ) U - 1. P + V 2U
iJt
p
In the e equation p repre ent the rna density, t the time, U the flow
velocity, P the pre ure, and v the kinematic vi co ity. The ymbols and
2 are re pectively the del and Laplacian operator (in three dimen ions
respectively: iJ/ iJx+ iJ/ iJy+ iJ/ iJz and iJ 2/ iJx 2 + iJ 2/ iJy2+ iJ2/ iJz2). The
fir t equation (the continuity equation) expresse the con ervation of
mas, and tate that the density can change at a point in space only due
to a net in- or outflow of matter. The second equation, the avier-Stokes
equation, expre ses the conservation of momentum, and states that the
J. A. Kaandorp et al., The Algorithmic Beauty of Seaweeds, Sponges and Corals
© Springer-Verlag Berlin Heidelberg 2001
2.1 The Physical Environment
T
he two major environmental parameters which have the greatest impact on the growth forms of marine sessile organisms are light, required
for photosynthesis, and hydrodynamics. A full discussion of the physics of
underwater light distributions and hydrodynamics could easily cover a few
textbooks. In Box 2.1 the basic hydrodynamic laws are summarized, together
with two dimensionless parameters, the Reynolds number Re (2.3) and the
Peeler number Pe (2-4), which can be used to characterize the impact of the
flow on the organism. In Sect. 2.1.1 "Growing and flowing" we will focus on
the biomechanical impact of hydrodynamics on the growth process and try
to construct a number oflaws for the biomechanical impact ofhydrodynamics using an engineering approach. In Sect. 4.3 we will return to the topic of
hydrodynamics, from a modeling point of view and try to construct a computational method capable of capturing the influence of hydrodynamics in
models of growth and form of marine sessile organisms. In Box 2 .2 the basic equations, in a highly simplified form, of underwater light distributions
are shown. Toa certain extent, in contrast with the hydrodynamic equations,
these simplified equations can more or less straightforwardly be included in
computational models; this will be discussed in Chap. 4.
Box 2.1 Hydrodynamics
Flow of water in space can be captured through two fundamental
equations:
iJp + . pU =0
iJt
iJU =_(U . ) U - 1. P + V 2U
iJt
p
In the e equation p repre ent the rna density, t the time, U the flow
velocity, P the pre ure, and v the kinematic vi co ity. The ymbols and
2 are re pectively the del and Laplacian operator (in three dimen ions
respectively: iJ/ iJx+ iJ/ iJy+ iJ/ iJz and iJ 2/ iJx 2 + iJ 2/ iJy2+ iJ2/ iJz2). The
fir t equation (the continuity equation) expresse the con ervation of
mas, and tate that the density can change at a point in space only due
to a net in- or outflow of matter. The second equation, the avier-Stokes
equation, expre ses the conservation of momentum, and states that the
J. A. Kaandorp et al., The Algorithmic Beauty of Seaweeds, Sponges and Corals
© Springer-Verlag Berlin Heidelberg 2001