1. 0 DHEC – Office of Ocean and Coastal Resource Management Public Hearing Berkley Electric Cooperative Community Room Kiawah Island Sheet Pile Project Peter Mugglestone June 10 th, 2009

2. 1 Kiawah River Bend A satellite image showing the neck of the Spit and Beachwalker parking lot at the top right. The track visible from the lower end of the lot is used by emergency vehicles and the beach patrol

3. 2 2763’ Bulkhead/Revetment Proposal An overlay showing the position of the proposed 2783’ bulkhead/revetment (from submission drawings)

4. 3 2763’ Bulkhead/Revetment Proposal The position of the proposed bulkhead/revetment

5. 4 Kiawah Island Sheet Pile Project An overlay showing the position of the proposed crane way

6. 5 Kiawah Island Sheet Pile Project Position of the proposed crane way and position of the sheet pile bulkhead. (magenta – original submission; cyan – latest OCRM image)

7. 5 Fluid Dynamics that apply to the Kiawah River A brief summary of the Fluid Dynamics that apply to the Kiawah River

8. Fluids obey Newton’s 2 nd Law of Motion Isaac Newton (1687) The equations that describe the motion of fluids, including those in a river bed were developed by Claude Navier (1825) and made practical by George Stokes (1850). They are known as the Navier-Stokes Equations. 7 Time–dependent Fluid Mechanics 101 Philosophiæ Naturalis Principia Mathematica, Isaac Newton (1687) Equations for an incompressible fluid, Claude-Louis Navier (1822) Incompressible fluids and some cases of fluid motion, George Stokes (1842)

9. 8 Navier-Stokes Equations The top 3 equations relate acceleration, in each of the 3 directions, to pressure gradient, viscous forces and gravitational forces. The final equation is continuity (fluid is not created or destroyed)

10. 9 Navier-Stokes Equations This has significant implications: 1.The velocity, of a small packet of fluid, depends on the pressure and velocity of all surrounding fluid. 2.The velocity of a small packet of fluid near to a boundary, depends on that boundary and all other boundaries. It can be seen that each equation has terms that relate it to the properties of the fluid in the other two directions

11. 10 Navier-Stokes Equations 1.The only external influences on the flow of the fluid are due to the boundaries (the bed of the river, the banks of the river, the surface of the river [wind, waves and wakes], the inlet and the outlet.) 2.A change to any boundary will affect everything within the influence of the fluid. It follows that:

12. 11 Navier-Stokes Equations 1.A change, even a small one, to any boundary will affect all fluid flow both upstream and downstream. Hence, it further follows that:

13. 12 Navier-Stokes Equations 1.A small change to any boundary may have very large effects on the upstream or downstream flow. 2.We are not able to model the boundaries sufficiently accurately to predict the effect. 3.A bulkhead, revetment, change in the oyster beds, or, spartina cover can have significant effects. (Look at the areas around docks, or the places where boats have been dragged over the bank into the river) The fluid system is unstable:

14. 12 Meanders (expected from the Navier Stokes Equations) The fluid (i.e. the water in the river and any suspended material) will tend to meander. This snake-like pattern can be seen on most rivers and streams that do not have solid boundaries. The mechanism of a meander is that a perfectly straight river will be locally deflected slightly to the side by a natural event, e.g. a tree falling from the bank into the fluid stream. The curvature of the flow will generate forces near to the river bed that will tend to move particles from the outside of the bend to the inside. This increases the out-of- straightness of the flow and increases the effect. The fluid will be reflected from the opposite bank and flow in a snake-like manner that tends to get progressively worse.

15. 13 Reasonably Contained Meander It can be seen that the meander has increased until it broke through and partially straightened the flow. The effect will repeat (slightly differently each cycle). Here we see a region at the west end of Seabrook showing recent changes to the meander pattern and good containment of the flow field within the banks.

16. 14 Man-made Problems Here we see a region between the Kiawah River and Cassique golf course, where human changes to the system have likely caused a problem. By changing the inlet configuration, the meander has been modified, and the stream has shifted closer to one bank, causing erosion.

17. 15 Man-made Problems A region of the Kiawah River basin showing the path of the river pinned by the Kiawah Parkway bridge. This has exaggerated the meander and caused erosion of Mingo Point (lower right.) Changes of the marsh, due to the bridge, are evident.

18. 16 A Classic Man-made Problem This picture illustrates how the cut in the Spit has exaggerated the curvature of the meander and increased the rate of erosion at the river bend. The original path of the river, with smaller curvature, is clearly visible. Material has been added to the wide end of the Spit, but there has been more erosion at the neck.