VENICE, LA - MAY 04: A boat drives navigates the grassy wetlands near the South Pass of the Mississippi River on May 4, 2010 in Venice, Louisiana. The Deepwater Horizon wellhead operated by BP is still leaking up to 5,000 barrels of oil a day into the Gulf of Mexico. (Photo by Chris Graythen/Getty Images)
Controlling the Mississippi River has proved to be as bedeviling of a quandary as it has been necessary and valuable. The river rearranges itself in small scale ways, such as the formation of sandbars or cutoffs, and in large, regional shifts, such as the movement of the entire terminus of the river. Hence, the river is notoriously chaotic and difficult to predict and control.
Despite the difficulties posed by the Mississippi’s movements, Americans must control the river in order to maintain the nation’s thriving economics by all means necessary.
However, accounting for the infinite details and fluctuations in the Mississippi’s geology and hydrology requires a god-like knowledge, memory, and energy. Fortunately, chaos theory, a newer branch of mathematics, philosophy, and science, has helped engineers begin to unravel the mysterious interaction of forces driving the river and build more effective, long-lasting river control mechanisms.
In particular, chaos theory has advanced the erection of jetties, a man-made structure with an integral role in maintaining the navigability and current course of the Mississippi. The Eads Jetties are precariously positioned in the environment; they were built to harness these chaotic forces, and yet the jetties may succumb to them soon.
The Eads Jetties
Chaos Theory: The Butterfly Effect
The butterfly effect is classically defined as, “sensitive dependency on initial conditions” (Gleick, 1987). Mathematically speaking, the butterfly effect appears in nonlinear systems, those being systems where the result of an equation is not proportional to the input factors. Small changes in such systems can result in significantly large differences in a later state (1987). Water is famously dependent on initial conditions. Its movement and its ability to fill a space are dependent upon the conditions imposed upon the movement and the qualities of the space.
A pendulum sensitive to initial conditions
The Butterfly Effect and Moving Terminus of the Mississippi
An example of the butterfly effect is the movement of the terminus of the Mississippi River across southern Louisiana.
The processes generating the Mississippi’s movement along the Louisiana coasts begin small. As the river flows around a bend, carrying a load of sediment, the energy of the current on the outside of the curve is greater than that on the inside of the curve. Therefore, sediment on the outside curve moves faster and is likely to be deposited at an angle more perpendicular to the radius of the turn. Over time, billions of sediment particles accumulate on the outside curve, and slowly, the river builds a sandbank. Eventually the sandbank will alter the gradient advantage, and the river will be cutoff. The flow will flow at right angles along the new gradient advantage.
Deltaic Lobes of the Mississippi
Left to play out unhindered, the land building processing of the Mississippi will cause the course to shift to the most proximate gradient advantage. Over the course of 2 million years, the Mississippi has writhed across the North American continent innumerable times in dance of buildup, cutoffs, and flooding. Combined with the shifting global climate that characterized the Pleistocene, these conditions altered the magnitude of the Mississippi’s flow and the sea level of the Gulf of Mexico. This broadly changed the location of the terminus of the Mississippi at least seven times, resulting in the formation of at least seven deltaic lobes that form southern Louisiana.
In terms of the movement of the terminus of the Mississippi, the numerous, continuously shifting inputs, even those fluctuations that seemed minute or distant, interacted with each other and created a surprising present and a nearly indiscernible future. The fluctuations started small, perhaps a stubborn rock protuberance on the bottom of the river or a grain of sand deposited on the outer curve of a river bend. However, each of these changes, when multiplied to an infinitely large number, matters. These changes have far-reaching interactions that beget dramatic results.
The Eads Jetties were built to constrain the small and large scale movements of the Mississippi River. It is important to remember, however, that the jetties themselves represent an initial condition. The erection of the jetties has successfully kept the Mississippi on the same course, but doing so has led to disastrous results, including catastrophic floods, salt water encroachment, vulnerability to hurricanes and tropical storms, and severe land erosion.
Chaos Theory: Turbulence
“Something shakes a fluid, exciting it…When you shake it, you add energy at low frequencies or large wavelengths, and the first thing to notice is that the large wavelengths decompose into small ones. Eddies form, and smaller eddies within them, each dissipating the fluid’s energy and each producing a characteristic rhythm” ( Gleick, 1987).
Turbulence is a flow order that is powered by low momentum diffusion of the material’s particles, high momentum of their collective movement, and rapid variation of pressure and velocity as the material moves (Gleick, 1987). When water is at rest or running smoothly, the flow remains orderly. But after the velocity of the flow increases, the water stops behaving neatly. Disruptions begin to appear, where the dynamic fluid starts forming strange, shifting patterns. The order that characterized the smooth running flow deteriorates into whorls, vortices, and eddies at all levels.
Turbulent Flow and the Eads Jetties on the South Pass
Waves, currents, and cross-currents act upon the Eads Jetties on the Gulf of Mexico, and create fluid turbulence along and around the jetties. As waves crash into a jetty, the energy of the wave pushes the fluid out through the path of lease resistance. As the energy behind the wave disperses, the whorl unfurls into infinitely smaller whorls. At some point, the energy in these small tendrils become overpowered by other forces and change shape…
However, the system becomes even more complex, because the rebounding wave is always obstructed by other rebounding waves or another incoming wave. Even super computers cannot keep track of all the interactions taking place within a cubic inch of this turbulent flow in one second. The cacophony of interactions between waves, between different strains of flow, and between individual water molecules create intricate vortices and eddies on all scales.
Turbulence along a jetty
Turbulence resists the linear descriptions that are adequate for labeling simple systems. Mathematicians have developed fractals as a measure for tracking the area of dynamic movement and convoluted patterns in turbulent flow. Fractals are mathematical sets that repeat themselves infinitely. Where geometrical measurements are able to account for complete dimensions, (think squaring the length of a side of a two-dimensional square to find its area or cubing the same side to attain the area of a cube) fractals allow mathematicians and scientists to explore half dimensions (1987).
A simple fractal structureFractal measurement is ideal for measuring turbulent flow, since the surfaces they measure are finely detailed. Linear measure for a basic curve could be used, if one could find a straight segment small enough to be laid next to another segment and account for the bend (1987). However, as previously stated, the whorls and eddies that appear in turbulence resolves into infinitely smaller whorls and eddies. In a completely theoretically circumstance, these eddies would be repeating themselves increasingly smaller scales ad infinitum. Fractals make measuring such a surface possible, because they mimic the self-repeating pattern in the dynamic system.
The Mississippi resists the bridle of the Eads Jetties. Hence, they are more vulnerable than ever to chaotic processes that arise from interfering in natural, environmental systems. The turbulent flow the jetties were built to control wears on the structure, dredging structure threatening holes in and along its walls and pushes relentlessly against its foundations. These forces have tested the the strength and efficacy of the Eads Jetties for over a century and continue to pose a convoluted engineering problem today.
Chaos and the Eads Jetties Today
The Eads Jetties still stand, although almost the entire west jetty and about a third of the east jetty have been buried under the large amount of sand along their upstream flanks, thus affecting their efficiency (PBS, 2000). Although the South Pass has closed to large, ocean bound ships in favor of the deeper and wider Southwest Pass, the Eads Jetties still maintains a midline scour in the channel, mitigates the formation of large sandbars on the mouth of the Mississippi, and prevents some of the erosion that would cause the deterioration of the pass (CWPPRA, 2012).
The Eads Jetties Today
However, massive changes in climate change, including the expansion of the dead zone in the Gulf, sea level rise, ocean acidification, and the increasing frequency of powerful storms will test the efficacy and integrity of these jetties. Extensive tests performed on jetties on the Bandar e-Imam Port in the Persian Gulf suggest that the 30 year old reinforced concrete had significantly deteriorated due to chloride erosion (Moradi-Marani, F et. al., 2010; Moradian, M., 2012). Though the materials used to build the jetties were high quality, the increasing frequency of hurricanes and tropical storms and increasing ocean salinity led to rapid corrosion (Moradian, M., 2012). The Eads Jetties, built on willow mattresses, wood pilings supporting an internal concrete structure and a large stone slope, are much older than those on the Bandar e- Imam Port. However, they are subject to a similar increase in storm activity, salinity, and erosion.
Furthermore, By keeping the South Pass open and maintaining the Eads Jetties, Louisiana could alleviate some of the boat traffic heading out to the Gulf. Furthermore, the pass still diverts some of the Mississippi’s flow. If the flow out of the South Pass, though less than that in the Southwest Pass, was captured by the larger distributary, the turbulent flow out of this channel could be too great. On the other hand, allowing the South Pass to close could encourage natural land building processes. This would be beneficial for southern Louisiana, which is projected to lose much of the low ground land within the next century. This would leave cities such as New Orleans, Baton Rouge, and other cities vulnerable to storms and flooding. However, the land building that would accrue from allowing the South Pass to close and the Eads Jetties to be buried could eventually develop into protective marshland.
All of this suggests that within the next century, if the Eads Jetties are not kept in better repair, they will either be completely obscured by sand or will be slowly eaten away, and that the chaotic processes that surrounding the Eads Jetties will only become more unpredictable, mysterious, and erratic.
References
Azarmsa, S. A., Esmaeili, M., & Khaniki, A. K. (2009). Impacts of jetty construction on the wave heights off the Kiashahr Lagoon. Aquatic Ecosystem Health & Management, 12, 358-363. doi:10.1080/14634980903354726
Barry, J. M. (2007). Rising tide: The great Mississippi flood of 1927 and how it changed America: Simon & Schuster.
Corthell, E. L. (1880). A history of the jetties at the mouth of the Mississippi Retrieved from http://babel.hathitrust.org/cgi/pt?id=nyp.33433066397740
CWPPRA. (2012). The Atchafalaya Basin. Basins. Retrieved April 20, 2014, from http://lacoast.gov/new/About/Basin_data/at/Default.aspx
De Gennaro, N., & Wright, R. (2007). Tidal siphon: Alternative to a jetty-hardened inlet. Journal of Waterway, Port, Coastal & Ocean Engineering, 133, 200-212. doi:10.1061/(ASCE)0733-950X(2007)133:3(200)
Erosion generated by wave-induced currents in the vicinity of a jetty: Case study of the relationship between the Adour River mouth and Anglet Beach, France, 24, aph 59-69, Journal of Coastal Research (Allen Press Publishing Services Inc. 2008).
Friedman, G. (2007). The ghost city. Retrieved from The Ghost City by George Friedman website: http://www.nybooks.com/articles/archives/2005/oct/06/the-ghost-city/
Gleick, J. (1987). Chaos: Making a new science: Open Road Media.
Hickson, R., & Rodolf, F. (2010). DESIGN AND CONSTRUCTION OF JETTIES. Coastal Engineering Proceedings, 1(1), 26. doi:10.9753/icce.v1.26
Hughes, S. (2000). Effect of offset jetties on tidal inlet flood flow. Shore & Beach, 68, 31-38.
Kelman, A. (2003). A referendum on the river: The Mississippi jetties controversy. Gulf South Historical Review, 19, 46-71.
McConnell, K., Allsop, W., Cruickshank, I., & Great Britain. Dept. of Trade and, I. (2004). Piers, jetties and related structures exposed to waves: Guidelines for hydraulic loadings: Thomas Telford.
McPhee, J. (1987). The control of nature: The Atchafalaya. The New Yorker. http://www.newyorker.com/archive/1987/02/23/1987_02_23_039_TNY_CARDS_000347146?currentPage=all
Moradi-Marani, F., Shekarchi, M., Dousti, A., & Mobasher, B. (2010). Investigation of corrosion damage and repair system in a concrete jetty structure. Journal of Performance of Constructed Facilities, 24, 294-301. doi:10.1061/(ASCE)CF.1943-5509.0000112
Moradian, M., Shekarchi, M., Aabdollah, M., & Alidadi, R. (2012). Assessment of long-term performance of a 50-year-old jetty in the south of Iran. Journal of Performance of Constructed Facilities, 26, 633-643. doi:10.1061/(ASCE)CF.1943-5509.0000275
Morris, C. (2012). The big muddy: An environmental history of the mississippi and its peoples from hernando de soto to hurricane katrina: Oxford University Press, USA.
PBS. (2000). The jetties today. The American Experience. Retrieved April 20, 2014, from http://www.pbs.org/wgbh/amex/eads/sfeature/sf_jetties.html
Tanaka, H., & Lee, H.-S. (2003). Influence of jetty construction on morphology and wave set-up at a river mouth. Coastal Engineering Journal, 45, 659-683.
Wada, A., & Tanaka, N. (2002). Advances in fluid modeling & turbulence measurements: Proceedings of the 8th international symposium on flow modeling and turbulence measurements: Tokyo, japan, 4-6 december 2001: World Scientific.
Check out the Coastal Wetlands Planning, Protection, and Restoration Act for more information on the formation of the terminus of the Mississippi!
http://lacoast.gov/new/About/
A more in depth look into chaos theory:
https://www.csuohio.edu/
sciences/dept/physics/physicsweb/
kaufman/yurkon/chaos.html
One photographer’s take on the southern Lousisiana coast:
http://neworleansphotoalliance.org/
grants/MPS_Fund/2012/Michel_Varisco/