HOME >> SeaCAMEL Home >> Science Modules >> Module 5

Background:

Everything on the surface of the Earth, or in the sea, lives in a boundary layer. Boundary layers are slower moving layers of air or water that form over surfaces. They form for a couple of reasons. One is that fluids like air and water have internal friction, viscosity, which Isaac Newton called a “lack of slipperiness between adjacent layers of fluid”. Fluid right next to an object is bound to the solid surface by intermolecular forces. This is called the ‘no-slip condition of fluid mechanics’ and its existence wasn’t fully accepted till the beginning of the last century. (You can can see this condition for yourself in a sink at home. Put a drop of food coloring in the sink, and then turn on the faucet. Immediately most of the dye goes down the sink with the water, but if you look really closely right next the bottom of the sink you will see a stained layer of water that persists.) The next layer of fluid that tries to slide by is held back by intermolecular forces between the fluid particles themselves (in water, these are hydrogen bonds). Further away the effect diminishes as more flow energy is available to overcome the internal friction of the fluid. Eventually one reaches (asymptotically) what is called the free-stream flow.

>>>Fig. 1. A boundary layer over a kelp blade. The length of the arrows denotes the speed of the flow. Note there is no arrow right at the surface, where the speed is zero! ∂ is the boundary layer thickness, the distance over which the speed goes from zero to freestream. As the environmental flow speed goes up, ∂ shrinks.

The distance over which the velocity goes from zero at a surface to 99% of the freestream velocity is termed the boundary layer height (Fig. 1).

As we see in Figure 1, boundary layers can form around organisms like kelps and corals. We have already seen in Module 3 the importance of boundary layer thickness in regulating metabolic processes like respiration and photosynthesis that depend on movements of dissolved chemicals through the boundary layer to and from the organism. But there are even larger boundary layers that form in the geophysical fluid layers of the Earth itself. The regions of reduced flow arise because of the dissipation of energy by turbulence. Turbulence is a disordered type of flow where eddies, spinning packets of water or air, form that can greatly increase the mixing in the direction perpendicular to the surface. (The other type of flow, rarer in nature except at very small sizes and speeds, is called laminar. Fig. 1 is a laminar flow idealization.)

<<< Fig. 2. Example of a geophysical boundary layer in air. Similar situations hold in water. The roughness height, z0, can vary from habitat to habitat. Aquarius itself is a roughness element that affects the velocity profile downstream of it. Image courtesy UC
Davis.

Why and how turbulence arises is still not completely understood by physicists. But in the boundary layer over a coral reef, the knobby bumps and protuberances of the reef itself, formed by all the boulders and coral heads and sponges, lead to the formation of turbulent eddies that rob moving seawater of kinetic energy (it gets turned to heat). An boundary layer scientist named Richardson coined a poem about this process in 1920. “Big whorls have little whorls, That feed on their velocity, And little whorls have lesser whorls, And so on to viscosity.” This leads to a turbulent boundary over the seafloor that is thicker than the laminar case, but behaves qualitatively the same way.

In essence, on a coral reef, there are boundary layers around individual organisms like corals, and there is a boundary layer around the reef itself, in which the smaller boundary layers around individual objects are embedded (Fig. 2). The bigger boundary layer is called the benthic boundary layer. The flow speed increases above the bottom with the logarithm of height. This log layer is common in geophysical boundary layers. The expression for velocity, u, as a function of height, z in Fig 2 is often give as

u* is called the shear velocity and is a measure of the strength and correlations of turbulent eddies tumbling along the bottom (see movie below). k is the von Kármán constant and is equal to 0.41. d₀ and z₀ are the roughness height and displacement height, respectively, which depend on the nature of the bottom upstream of the place we measure flow. (Under some conditions, we can actually get a log layer resulting from the roughness elements upstream and another log layer with a separate slope (set by u*) that results from the effects of waves passing overhead.) The thickness and nature of the boundary layer affect a host of processes on coral reefs including but not limited to the following: how far eggs and sperm and larvae travel during spawning events, how fast the entire reef metabolizes (flow-modulated metabolism - Module 3), how quickly the reef calcifies, and how destructive a storm event will be for corals on the bottom.

What students will see during the show:

We won’t measure the flow speed boundary layer directly, but instead will measure concentration boundary layers using the handheld profiler introduced in Module 4 (Fig. 3). We will test how variable the profiles are around the habitat and whether they conform to the predictions of an organized log layer that has been seen in other habitats for flow speed near the bottom. We also will see whether Aquarius itself, with the host of invertebrates that have settled on it (seen in Module 2), along with the stunning numbers of fishes that use it as an artificial reef (Module 6,coming up), affects the water column chemistry. Does all the biomass in and around the habitat (Fig. 4) lead to a measurable draw-down of dissolved oxygen?

Fig. 3. Dissolved oxygen in the bottom 2 meters over Conch Reef, showing unexpected
layering. Right: Diver using a hand-held oxygen profiler near Aquarius. Dissolved
oxygen, pH, and temperature are stored internally in a datalogger.

The aquanauts wills also release dye at various heights over the bottom around the habitat which will give us qualitative information on that nature of turbulent diffusion near the seafloor (see quantitative exercise #2 below).

Learning outcomes:

At the end of the module, students will have learned the following:

1. What distinguishes a laminar from a turbulent boundary layer and which type is more common in nature.
2. How boundary layers around individual objects differ from the logarithmic boundary layers over reefs.
3. How diffusive boundary layers for dissolved oxygen can form in the same way that flow speed boundary layers arise, and how these boundary layers affect water quality near the benthos.
4. Whether the boundary layers for dissolved oxygen differ on the upstream and downstream sides of the habitat, and over substrates of different types.
5. How different areas of the reef experience differing levels of turbulent diffusion and what this means for delivery of materials to and from the organisms on the bottom.

Fig. 4. Underside of Aquarius, showing the quadropod upon which the habitat sits. Note
the large populations of sessile invertebrates, mainly cnidarians and sponges, encrusting
every available square centimeter. This community attracts motile invertebrates
which in turn attracts large numbers of fishes. Does this large biomass extract enough
dissolved oxygen that we can detect it with our handheld profiler?

Quantitative exercises:

1. Gradient graphing (dissolved oxygen). During the classroom module, the aquanauts gathered data on dissolved oxygen concentration using the handheld profiler. The aquanauts made measurements on the upstream and downstream side of the habitat (relative to the tide and winddriven currents), as well as over different types of substrate (coral, sand, and mixed bottom type). The readings in the vertical direction were spaced logarithmically with more measurements near the seafloor than further away (Why was this done? Hint: think about how geophysical boundary layers for flow speed are organized.) Plot the data from the classroom module and see for yourself whether there is a discernible effect of bottom type, and presence of Aquarius, on the gradient of dissolved oxygen near the seafloor. If you plot the data using a log scales for height and dissolved oxygen concentration, what do the curves look like now? What is the significance of the slope of the plot when you use a double log scale?

2. Turbulent diffusion (advanced). By filming the dispersion of dye blobs, we can learn how turbulent the ocean is at different scales. During the classroom segment, we released dye packets at different heights over the reef, and at different locations. You probably saw that the rate of stretching of the dye differed in the horizontal vs. vertical direction; this is because turbulent diffusion is anisotropic, that is, different in different directions. The coefficient for turbulent diffusion (called the eddy diffusivity) in the vertical direction is usually much larger than that in the horizontal direction, because of the transport effects of eddies generated by the bottom roughness
of the reef. Using the movies posted on the web site, and your favorite media viewer, you can quantify the diffusion coefficient through some frame by frame analysis.

Here’s the recipe:

Calculation of eddy diffusivity (K_x,z, where K is the diffusion coefficient in the x, z directions,where z is the direction normal to the bottom):

A. Take a single video frame of dye blobs dispersing and measure location of x, y pairs (the more, the better) in the picture. This can be done by hand using an acetate overlay, translucent graph paper, and some manual labor or by using the NIH Image program available for free at the National Institutes of Health. Enter data in a statistical spreadsheet and calculate mean x, y positions to determine the location of the centroid of the blob. Determine the variance of x values and y values. Record the covariance between x and y from your stats program. Record these numbers in another spreadsheet with 3 elements as follows:

B. Run a principal components analysis using the above correlation matrix. Record the two eigenvalues of the two axes determined for the dye blob. These eigenvalues are a measure of the dispersion of the dye along the principal component axes, which are the x,y direction.

C. Repeat the above protocol for another video frame several seconds later in time. Determine the time between frames.

D. Now calculate the translation velocity (cm/s) of the centroid of the blob by taking the linear distance between centroid locations (use the square root of the sum of squares of the differences in the x and y values) and dividing by the time between frames. Remember, you will need to use the scale present in the video to get the actual flow speeds!

E. Finally, calculate the eddy diffusivities along the axes parallel to the principal component axes by subtracting the eigenvalues for the respective axes from each other and dividing by the time between frames. The eddy diffusivity is thus a measure of the time rate of change of the variance in dye location.

If you remember from high school science, the flux of something (moles diffusing through a surface per unit time) = the diffusion coefficient (length²/time) x the concentration gradient (dC/dz - moles/(volume•length) normal to the surface. When we multiply the diffusivity in the direction normal to the substrate by the concentration gradient we can compute from data acquired with the handheld profiling instrument, we can compute the flux, in moles of dissolved oxygen taken up, or given off, per square meter per second, to the bottom types around Aquarius. This sort of metabolic measurement is rarely done in reef environments and will provide some important baseline data for the reef near Aquarius.

Reading:

Boudreau, B.P., and B.B. Jørgensen. 2000. The benthic boundary layer: transport processes and biogeochemistry. Oxford University Press. - An excellent overview of how benthic boundary layers are formed, maintained, and their manifold effects on the biotic and abiotic components of the seafloor.

Shashar, N., S. Kinane, P.L. Jokiel, and M.R. Patterson. 1996. Hydromechanical boundary layers over a coral reef. Journal of Experimental Marine Biology and Ecology 199(1): 17-28. - An examination of the kinds of boundary layers found over living coral, both diffusive and momentum (flow speed), with some data collected at Aquarius.

Multimedia:

Movie from the Multimedia Fluid Mechanics project of flow past a cylinder showing the turbulent, recirculating wake on the downstream side. Aquarius sheds a similar wake (as do the corals we examined in Module 3).

Movie from the Multimedia Fluid Mechanics project of how a roughness element can make eddies which help transport fluid at right angles to the substrate. The graph shows a measurement of the shear stress (force/area) generated by the turbulence from the roughness element. Imagine how complex the flow over a real coral reef must look like!

PowerPoint presentation recently given m,y Dr, Patterson and his former graduate student (now Dr. Lawrence Carpenter) at a scientific meeting, on how dissolved oxygen varies near the bottom of Conch Reef. Most scientific talks must fit into a 15 minute window, with 5 minutes for questions.  Sometimes a movie is worth a thousand pictures so be sure to play the movie showing the dance of the oxygen profiles embedded in the presentation, and available below (DO.ppt,DO.pdf)

Movie showing 154 profiles of dissolved oxygen around Aquarius made during a saturation mission. Note how variable these profiles are, but with some common qualitative features.

Web Resources:

Concise Wiki overview of the phenomenon of turbulence -
(http://en.wikipedia.org/wiki/Turbulence)

Nice video of shear layer instability in a stream. Similar flow structures occur near the bottom of
a coral reef. (http://www.youtube.com/watch?v=zKRAHqS5Ys0)

Nice visualization of the ‘no slip condition’ of fluid mechanics!
(http://www.youtube.com/watch?v=cUTkqZeiMow)