Biomechanics

There are many aspects of biomechanics that can be seen and studied in nature. However, this lecture focuses on how moving fluids affect organisms. In order to approach this topic it is necessary to first talk about the boundary layer. All life occurs in boundary layers, in the case of marine ecosystems, this can be seen as a flow gradient and the velocity you experience depends on where you are in the boundary layer. The following image explains better than I can what a boundary layer is.

(Image obtained from http://www.grc.nasa.gov/)

As it can be seen in the image above, the velocity increases as you move closer to the top. At the very bottom, the velocity is practically zero. This is known as the no slip condition. This means that fluid immediately in contact with the solid surface does not slip or move relative to the surface. 

With this knowledge, we can talk about the force that acts upon on organisms. Newton's third law states that an action produces an equal and opposite direction. This means that fluid exerts force on an object and an organism responds by exerting equal force on the fluid but in the opposite direction. The force exerted by a fluid is known as drag. Drag can be calculated using the following equation:

Fd=0.5*p(U^ß)AcCd

Fd = drag force

p = (Greek letter ro) = density of fluid

U = velocity of fluid

ß = usually 2

Ac = area perpendicular to flow, also known as characteristic area

Cd = drag coefficient

There are two types of drag: pressure drag and skin friction drag. Pressure drag is due to upstream/downstream differences in pressure. The pressure builds up on one side of the body. This is the most ecologically important type of drag. Skin friction drag refers to the fact that the more surface or 'skin' the organism has, the greater its drag will be. This type of drag is mostly relevant at low velocities.

Nature is smart and organisms have developed drag minimizing strategies. Some of them are:

• Increased flexibility
• This can be seen in sea fans, which bend over with the current. They become parallel to flow and manage to go down near the boundary layer. This is helpful because even though they have a great characteristic area, they are able to be near the low velocity zone of the boundary layer.
• Another example is the strategy seen in holly leaves, which bundle up and collapse as flow increases. 
• A sea anemone's tentacles collapse in high velocities.
• Intertidal and subtidal seaweed also exhibits great flexibility.
• Drag resistance
• This property is related to material strength, such as that seen in wood. Large tropical trees have wide bases (buttress), which gives them support. Having a great basal width offers drag resistance because the center of gravity is distributed over a large area. Basal width increases the distance from the rotation point. Trees also have a considerable weigh that would require great force in order to uproot them.
• Reduced drag coefficient
• A streamlined body shape results in a lower drag coefficient. This can be seen in animals such as dolphins, fish, sharks, among others. Streamlining affects fitness and is an example of convergent evolution.
• Another strategy is to transcend the air/water barrier, as seen in dolphins and flying fish. Since air is roughly 830 times less dense than water, moving temporarily out of the water is a valid strategy to reduce drag.

In order to study pressure-flow relations it is necessary to look at the principle of continuity and Bernoulli's principle. The principle of continuity states that velocity is inversely proportional to cross-sectional area. Bernoulli's principle states that velocity is inversely proportional to pressure.

The principle of continuity can be seen in sponges and their 'biological nozzle'. These organisms reduce the area of aperture to increase excurrent velocity. They expel water at great velocities to minimize the chance of refiltering the same water.

Bernoulli's principle allows us to compare velocities and pressure at different points in an ecosystem. At a point with high pressure, there will be low velocity and vice versa, at a point with low pressure there will be high velocity.  

Induced flow is the coupling of external to internal flow which results in the fluid being drawn passively through an object or organism. An example of this is the prairie dog burrow, in which a reduction in pressure between two points allows air to be passively drawn in through the structure. This is also seen in sponges, where a change in pressure passively draws food-laden water into sponge and augments filter feeding.

Other examples of pressure-flow relationships include fish experiencing pressure flow differentials across their bodies. This allows water to passively enter mouth and go through gills. It also offer advantages for respiration and visual acuity (there is zero pressure at the eyes).

Another force to be considered when taking about pressure is lift. Lift is concerned with pressure differences between the top and the bottom. There is also an equation that can be used to quantify the lift force experienced by an organism. 

Fl = 0.5p(U^2)AcCl

Fl = lift force

p = ro = density of fluid

U = velocity

Cl = lift coefficient

Ac = characteristic area (projected fluid perpendicular to flow)

As with drag, there are lift minimizing strategies (e.g. limpets), but unlike drag there are also lift maximizing strategies (e.g. flight)

Lift can be generated with an oncoming wind and a circulation. In stationary organisms, an adaptation is to have a body tapered in direction of lift so as to decrease the characteristic area and thus reduce the lift force.

However, it is important to consider that velocity is not always stationary. 

acceleration reaction = pCmVa

p = density of fluid

Cm = added mass coefficient (inertia)

V = volume of organism

a = acceleration

With these three equation, one can calculate the total (net) force on an organism, which is the sum of forces due to drag, lift, and acceleration. It is calculated by the Morrison equation.

Morrison equation:

Total net force = √[(Fd+Fa)^2 + Fl^2]

Biomechanics and the principles of drag and lift are also important because of the ecological consequences of high flow forces. Some ecological manifestations and effects are:

1. Hurricane impacts
• Hurricanes have restructured forests by reshaping species distribution and abundance. 
• Example: 1983 hurricane
• There have been species-specific effects, such as tallest trees experiencing the highest velocities.
• Landscape can be predictable as to how wind speed will impact it.
2. Wind speed effects
• Wind speed has had a negative effect on barn swallow fitness.
• Survival rate of birds depends on wind speed.
• Intertidal snails survived perfect storm because of smaller body size.
• smaller drag and lift forces
• High flow forces have selection of a population
3. Distribution of organisms
• Hypothesis: Sea urchins could not occupy shallow areas in exposed site because they get dislodged. 
• Conclusion: Sea urchins did not occupy shallow areas because they could not move and feed.
4. Size and reproduction of organisms
• Seaweed blade area reduced in high flow (lower area)

Conclusion -  High flow affects:

• Shape and performance
• Exchange processes
• Fitness and survival
• Distribution of organisms
• Transport processes
• dispersal
• recruitment
• nutrient transport