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.

## 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.

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

(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

- Vogel, S. 1994. Life in Moving Fluids. Princeton

University Press, Princeton, NJ -
Wikipedia entries

on Hydrodynamics, Reynold’s

Number and Boundary

Layers. - Zingmark, Richard. “Life in a Fluid Environment

(Hydrodynamics).” Marine Ecology 575. University of South

Carolina, Columbia. October 2005.