Water Flow is More Important for Corals Than Light Part 4: Basics of Hydrodynamics

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I began this article series with a basic introduction to the
mechanisms by which water flow affects the gas
exchange rate of corals. I followed the introduction with a
review of scientific papers on the interaction of water flow
and corals as well as my own research demonstrating the effect
of water flow speed on the respiration and photosynthesis rates
of corals. My first article on gas exchange introduces the key
points of small scale hydrodynamics as applies to the
dissolution rate of gases. This article revisits the
topic of hydrodynamics, at a larger scale, in order to give
readers background understanding on the big picture of water
movement. More specifically, I will discuss the properties of
fluids which govern how moving water behaves at the site of
interaction between corals and the surrounding water. In next
month’s final installment of the water flow series, I will
elaborate on how aquarists can produce optimal
water movement in their aquaria by applying the properties of
moving fluids to their advantage.

Introduction: What is a Fluid
Dynamics?

The study of how objects are affected by moving fluid is called
fluid dynamics. Fluid dynamics may also be used to describe the
particles, nutrients and gases which are transported by moving
fluids. But what does it really mean to be a fluid?
Dictionary.com
defines the noun fluid as “1. a substance, as a
liquid or gas, that is capable of flowing and that changes its
shape at a steady rate when acted upon by a force tending to
change its shape.”
While the definition of fluids
includes gases and liquids, this is a discussion about
water flow. As such I will use the terms “water”
and ”fluid” more or less interchangeably. Whether
we are discussing a stationary coral, free floating plants or
swimming fish, hydrodynamics can help us relate the properties
of water motion to the lifestyle of a particular aquatic
organism.

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Viscosity and Inertia

A fluid can be described by the properties of density,
pressure, buoyancy and viscosity. Of these, viscosity is the
most significant property governing the behavior of fluid
motion. Viscosity is the resistance of a fluid to a change of
shape or a resistance to flow and it can be thought of as fluid
friction. Viscosity can be either dynamic or kinematic but for
our purposes, I will only discuss fluid motion in terms of
dynamic viscosity which is a measure of the molecular
stickiness (thickness) of a fluid. The stickiness of a fluid is
caused by the attraction of the molecules which make up a
fluid. Honey would be an example of a fluid with a very high
viscosity, whereas pure alcohol is an example of a fluid with a
very low viscosity. Within the narrow range of reef
aquarium temperatures, the effect of temperature on the
viscosity of seawater is very minimal so it is not critical to
consider temperature when discussing hydrodynamics in reef
aquaria.

The other important factor governing hydrodynamics is
inertia which is the resistance of a body to a change of
motion. Whether an object or fluid is stationary or moving,
both will tend to keep still or to keep moving. The effect of
inertia is solely dependent on mass so if scale is increased
then both size, mass and inertia will increase.
Therefore, viscous forces are strongest at small scale and
inertial forces are strongest at large scales. To a copepod,
seawater is very sticky and it will stop moving immediately if
it stops swimming. At this scale, viscosity is the dominant
force. To a whale, seawater provides very little resistance and
it will keep moving for quite a distance if it stops swimming.
At this scale, inertia is the dominant force. Since the
properties of viscosity and inertia dictate how a fluid motion
behaves, the transition from viscosity dominated scale to
inertia dominated scale also marks the transition from laminar
to turbulent flow.

Turbulent and laminar flow

Turbulence has long been the characteristic which aquarists use
to describe the desired water motion for reef aquariums. The
trouble with that description is that when circulating seawater
in volumes larger than a test tube it is very difficult
to produce anything but turbulent flow. With that in
mind, all water flow which aquarists produce in their aquaria
would be described as directional turbulence or turbulent flow
which is mostly laminar.

Turbulent flow is characterized by randomness and it is
generally thought of as being rough and chaotic. Laminar or
streamline flow is basically the opposite of turbulent flow and
it is characterized by an evenness of direction of water
movement even though parallel streamlines of flow can be moving
in relation to each other. The smooth motion of laminar flow
occurs because viscous forces cause parallel streamlines to
stick to each other. In this situation the viscous forces of
the fluid are dominant over inertial forces. If the velocity of
the fluid is increased inertial forces will increase, the
sticky effect of viscosity will be dampened and the evenness of
the laminar flow will progress into chaotic and turbulent
flow.

Likewise, as turbulent water flow approaches a solid
surface, viscous forces transmit friction between the
water flow and the surface. The friction causes a decrease in
velocity so that the flow becomes more laminar as it approaches
the surface. As water flow approaches a solid surface, viscous
friction increases and the flow velocity continually decreases.
The fine micro-layer of water which is in contact with the
surface has zero velocity, it does not move and it exhibits a
“no-slip” condition. The region above a surface
where the characteristics of water flow change in type and
speed is called the boundary layer.

Boundary Layers

The boundary layer describes the actual region of
interaction between a surface and a fluid. When the boundary
layer is defined by the type or speed of the flow it is called
a momentum boundary layer. The momentum boundary layer
defined by flow type is the region between a surface and the
point where flow changes from laminar to turbulent. The
momentum boundary layer can also be defined by water flow speed
as the region above a surface which ranges from 0% to 99% of
mainstream flow. Stated simply it is the region where flow
slows down. In some cases the boundary layer may be more
turbulent than laminar so the definition of a boundary layer in
terms of velocity is preferred.

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There is another separate boundary layer which can be described
in terms of the concentration of a particular substance which
is called a diffusion boundary layer. The diffusion
boundary layer is (arbitrarily) defined as the region above a
surface which contains the change in the concentration of a
particular substance. Organisms continually absorb and release
substances from their surfaces into the water column so the
concentration of a substance can either increase or decrease as
you move away from the surface.

Regardless of the definition used, the thickness of the
momentum and diffusion boundary layers depends on the velocity
water flow. In fast, turbulent flow there will be more mixing
and the boundary layers will be thinner. In slow, laminar flow
there will be less mixing. Depending on the criteria being
examined, the size of a boundary layer can be anywhere from
millimeters to meters. For benthic organisms such as corals,
the boundary layer is the most critical region of water
movement because it will determine how a coral feeds, the
forces it must endure and the rates of diffusion which drive
respiration and photosynthesis.

The consequences of the boundary layer are obvious to anyone
who has ever grown out a fragment of stony coral. When first
attached, small fragments of coral tend to grow at a moderate
rate but once they gain height above the substrate, growth rate
tends to increase. We’ve all had that one fragment which grew
at a crawling pace but once it reached a certain size, it
projected out of the boundary layer and then grew at break neck
speed. Once a coral attains a certain profile, it will
experience more turbulent flow, increasing diffusion rates and
maximizing the corals respiration and photosynthesis. This
phenomenon is well known to the coral farmers who attach coral
fragments to projecting bases or suspend them in the water
column using string. Although they may not be aware of the
boundary layer, these attachment techniques effectively
minimize boundary layer effects and it maximizes growth by
exposing coral fragments to optimal flow.

Reynold’s Number (Re)

Reynold’s number (Re) is used to relate the forces of viscosity
and inertia in order to predict how fluids will behave. I try
to exclude as much math as possible but knowing the simple
calculation of Reynold’s number using relative values
can go a long way to understanding what happens to water flow
around corals as they vary polyp extension and colony
expansion. The Reynold’s number (Re) is the ratio of inertial
forces to viscous forces such that Re = Inertia/Viscosity.
Inertia is equal to the product of velocity, surface area
and density and viscosity is measured directly.

(Eq 1) Re =
Inertia / Viscosity

(Eq 2) Inertia =
Velocity * Surface

Area of Object * Density

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(Eq 3) Re =
Velocity * Area * Density / Viscosity

Within the same fluid, density and viscosity is constant so
changes in velocity and surface area have the most effect on
Reynold’s number.
In a situation where viscosity is
dominant over inertia, laminar flow occurs because viscosity
cause streamlines to stick to each other. This scenario is an
example of flow with a low Re. If one were to increase the
velocity of the same fluid, inertia would overtake viscosity
and this would lead to turbulent flow with a high Re.
Corals and other benthic organisms cannot change water velocity
but they can change the way they interact with water
flow. Just because corals are non-motile does not mean
that they are helpless. On a short time scale, corals can
expand polyps and colony tissue to increase surface
area. When surface area is increased, the Re value is larger
and flow becomes more turbulent. The increased turbulence
reduces the local boundary layer and it increases diffusion
rates. Similarly, corals can extend and retract their polyps
into the part of the boundary layer which best suits the
colony. If the water flow speed is too fast, retracting polyps
into lower parts of the boundary layer reduces velocity,
reducing the Re value and decreasing the amount of turbulence
to which the coral is exposed. Although corals rely mostly on
passive existence, they can actively alter their shape and
texture in order to fine-tune their interaction with the water
flow around them.

Drag, Lift and the Bernoulli
Principle

Drag and lift are forces which result from the interaction
between fluid motion and the surface of objects. Drag is the
resistance that results from the sum of viscous friction and
differences in pressure. Just as there is viscous friction
between streamlines of flow, viscosity also transmits friction
between a fluid and an object which are moving in relation to
each other. The force of drag which is produced by pressure
depends greatly upon the shape of the object which is in
contact with the water flow. If the fluid contacts a
surface which increases turbulence, smaller cells of turbulent
flow called eddies will occur downstream of the object. When
eddies form, they produce a pulling force from negative
pressure downstream of the object. If the fluid contacts a
surface which minimizes turbulence, it will reduce or eliminate
the formation of downstream eddies. This type of shape is said
to be aero- or hydrodynamic and it reduces the effect of drag
by effectively diverting and recombining streamline flow. The
ideal hydrodynamic shape is similar to a teardrop; smooth and
rounded upstream with a smooth tapering downstream end. This is
a common shape of fast and active fish like tuna. Some types of
hydrodynamic shapes will generate forces on the object which is
perpendicular to the direction of flow. This perpendicular
force is called lift and it occurs when a solid shape turns the
direction of a moving fluid. If the direction of flow is turned
in one direction, the force of lift is generated in the
opposite direction. The cross-section of an airplane wing is a
shape which was designed to maximize lift. The force of lift
can also be caused by a difference of pressure caused by the
Bernoulli principle. If streamline flow passes over an orifice
in a surface, negative pressure will occur in the orifice,
causing fluid to be sucked out. The form of many animals takes
advantage of the Bernoulli principle by growing shapes which
optimize the passive movement of water through their filter
feeding mechanisms.

Summary

Viscosity and inertia are the most important properties of
fluid motion. Viscosity is the resistance of liquids to flow
and inertia is the resistance of a body to a change of motion.
The ratio of inertial to viscous forces is called the Reynold’s
number (Re). At small scales (Re<1), the effect of viscosity
dominates and at large scales (Re>1), the effect of inertia
is more important. The motion of a moving fluid can be
described as being turbulent or laminar. Turbulent flow is
characterized as uneven in velocity and direction whereas laminar flow can
be defined as being non-turbulent. Laminar flow is characterized as having
even, parallel streamlines of motion. At lower velocities, water flow tends
to be laminar and at higher velocities, water flow tends to become
turbulent. Since fluid velocity is included in the calculation of the
Reynold’s number, the value of Re can predict the transition from laminar
to turbulent flow. Fluid motion can break down into smaller cells of
turbulent flow called eddies. If the formation of eddies occurs
from the contact of fluid motion with an object, the eddies
will produce a pulling force called drag. If laminar flow is
redirected by a surface, the surface will experience a
perpendicular force called lift.

References

  1. Vogel, S. 1994. Life in Moving Fluids. Princeton
    University Press, Princeton, NJ
  2. Wikipedia entries
    on Hydrodynamics, Reynold’s
    Number
    and Boundary
    Layers
    .
  3. Zingmark, Richard. “Life in a Fluid Environment
    (Hydrodynamics).” Marine Ecology 575. University of South
    Carolina, Columbia. October 2005.
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