20
2. ENVIRONMENTALLY DRIVEN PLASTICITY
of the instantaneous velocity) also vary with time. In addition to lift and
drag, organisms in the accelerating flow in waves also are subjected to the
acceleration reaction force (A) ,
A = pC M dU V
dt
where C M is the inertia coefficient (which depends on shape), dU is the
dt
instantaneous water acceleration, and V is the volume of the organism (Koehl
1977a, Denny 1988). Bodies with shapes that deflect the path of the water
moving around them a lot (such as stiff, planar colonies normal to the flow)
have higher CM'S than do bodies that do not deflect the flow as much (such
as streamlined bodies). Since A depends on the volume of an organism (V is
proportional to length"), a small increase in body length can lead to a very
large increase in A. If water is trapped between the branches or blades of an
algal thallus or animal colony, the functional volume of the organism that
affects A is the volume of that water in addition to the volume of the organism's
body (Gaylord et al. 1994). Since A is proportional to the instantaneous water
acceleration, it varies with time as the water flows back and forth past an
organism;when water is speeding up, A acts in the same direction as drag, but
when water is slowing down, it acts in the opposite direction from drag. The
instantaneous net force on an organism in waves is the sum of the acceleration
reaction, drag, and lift at that instant.
Since the hydrodynamic forces on an organism depend on the magnitude
of the velocity and acceleration of the water relative to the organism, a flexible
organism that can move along with the water in waves can avoid being pulled
by hydrodynamic forces until it is fully extended in the direction of flow and
the water moves past it. The longer the organism relative to the distance the
water moves before it flows back the other way, the more likely the organism
is to avoid flow forces at times when accelerations and velocities are high
(Koehl 1999). However, a flexible wave-swept organism moving with the flow
can be jerked to a halt if it reaches the end of its rope before the water
in a wave begins to flow back in the opposite direction; when this occurs,
a brief inertial force (proportional to the mass, and hence to the V, of the
organism) pulls on the organism (Denny et al. 1998).The length of a flexible
macrophyte or colony relative to the distance X that the water in a wave flows
in one direction before stopping and accelerating in the opposite direction
can have a profound effect on the forces the organism experiences in waves
because it determines when in the wave cycle the organism is jerked to a halt
and begins to experience flow relative to its body. As flexible organisms that
are short relative to X grow, the total force they experience in waves increases
(e.g. Gaylord et al. 1994). However, once organisms grow long enough relative
to X that they reach the end of their rope only after the water in a wave has
begun to decelerate, further growth does not lead to an increase in force
on the holdfast, as demonstrated by experiments with model organisms
in an oscillating-flow tank and by measurements of forces on real kelp on
waveswept shores (Koehl 1999). Stretchy tethers such as the stipes of kelp can
act as shock absorbers whose stretching absorbs mechanical work , thereby
permitting the kelp to withstand the transient high loads they encounter in
turbulent or wave-swept habitats (Koehl and Wainwright 1977). Mathematical
models suggest that the tuning of the time-dependent material properties of
stretchy tethers relative to the frequencies at which these structures must
2. ENVIRONMENTALLY DRIVEN PLASTICITY
of the instantaneous velocity) also vary with time. In addition to lift and
drag, organisms in the accelerating flow in waves also are subjected to the
acceleration reaction force (A) ,
A = pC M dU V
dt
where C M is the inertia coefficient (which depends on shape), dU is the
dt
instantaneous water acceleration, and V is the volume of the organism (Koehl
1977a, Denny 1988). Bodies with shapes that deflect the path of the water
moving around them a lot (such as stiff, planar colonies normal to the flow)
have higher CM'S than do bodies that do not deflect the flow as much (such
as streamlined bodies). Since A depends on the volume of an organism (V is
proportional to length"), a small increase in body length can lead to a very
large increase in A. If water is trapped between the branches or blades of an
algal thallus or animal colony, the functional volume of the organism that
affects A is the volume of that water in addition to the volume of the organism's
body (Gaylord et al. 1994). Since A is proportional to the instantaneous water
acceleration, it varies with time as the water flows back and forth past an
organism;when water is speeding up, A acts in the same direction as drag, but
when water is slowing down, it acts in the opposite direction from drag. The
instantaneous net force on an organism in waves is the sum of the acceleration
reaction, drag, and lift at that instant.
Since the hydrodynamic forces on an organism depend on the magnitude
of the velocity and acceleration of the water relative to the organism, a flexible
organism that can move along with the water in waves can avoid being pulled
by hydrodynamic forces until it is fully extended in the direction of flow and
the water moves past it. The longer the organism relative to the distance the
water moves before it flows back the other way, the more likely the organism
is to avoid flow forces at times when accelerations and velocities are high
(Koehl 1999). However, a flexible wave-swept organism moving with the flow
can be jerked to a halt if it reaches the end of its rope before the water
in a wave begins to flow back in the opposite direction; when this occurs,
a brief inertial force (proportional to the mass, and hence to the V, of the
organism) pulls on the organism (Denny et al. 1998).The length of a flexible
macrophyte or colony relative to the distance X that the water in a wave flows
in one direction before stopping and accelerating in the opposite direction
can have a profound effect on the forces the organism experiences in waves
because it determines when in the wave cycle the organism is jerked to a halt
and begins to experience flow relative to its body. As flexible organisms that
are short relative to X grow, the total force they experience in waves increases
(e.g. Gaylord et al. 1994). However, once organisms grow long enough relative
to X that they reach the end of their rope only after the water in a wave has
begun to decelerate, further growth does not lead to an increase in force
on the holdfast, as demonstrated by experiments with model organisms
in an oscillating-flow tank and by measurements of forces on real kelp on
waveswept shores (Koehl 1999). Stretchy tethers such as the stipes of kelp can
act as shock absorbers whose stretching absorbs mechanical work , thereby
permitting the kelp to withstand the transient high loads they encounter in
turbulent or wave-swept habitats (Koehl and Wainwright 1977). Mathematical
models suggest that the tuning of the time-dependent material properties of
stretchy tethers relative to the frequencies at which these structures must