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