The Mathematics of a Meander
Indian Creek is a tributary of the Blue River which feeds into the Missouri River. While this creek meanders towards the Missouri, it offers us a unique chance to observe bank erosion from two different perspectives! While there are many basins and rivers in the area, rivers that are too wide, have too little flow, or are too fast may make it more difficult to observe the phenomena described herein. Please take a few minutes to walk to GZ and to observe some of the features of the riverbank here and answer some questions. Please note that as an Earthcache this geocache does not have any container; in order to log this cache as "found" please send the CO answers to the answers at the bottom of this page. You may send these answers via the message center or via email.
It's all about Energy
As a river meadners from its origin to the sea, they serve as a transport mechanism for not only water but all the particulates and sediment deposit that are picked up in the water and eroded from the banks of the river. These bodies of water don't move in a straight
line. Meanders are produced when water in the stream channel erodes the sediments of an outer bend of a streambank and deposits this and other sediment on subsequent inner bends downstream. This process reinforces the riffle-pool structure of a stream.
Erosion in a stable stream can be minimal from year to year, but as a meander moves outward and becomes more looped, flows intensify on the outer bends. Meander patterns follow a remarkably predictable geometry described by wavelength, radius of curvature, and channel bank-full width – the height on the bank where, at higher flows, water begins to tip onto the floodplain (see figure below). No matter the size of the stream, the wavelength is approximately 11 times the channel width and, invariably, between 10 and 14 times the width. The radius of curvature of the central portion of the channel’s bend averages about 1/5 of the wavelength. Channels throughout the world follow this meander geometry so closely that the form of a large river resembles that of small streams.
Examining the Erosion
Riverbank erosion tends to fall into two primary categories: point bars and cut banks. Erosion around meanders or bends in the creek occur because
currents move faster along the outside of the curve than they do along the inside, which causes sedimentation to deposit on the inside banks forming large flat areas of silty deposits known as point bars and to erode the outside edge of the curve often forming cliff known as cut banks. In nature trees often serve to stabalize the erosion of the banks as their root systems tightly compact soil which slows the erosion process. In very specific situations this type of erosion can form an Oxbow Lake.
Here at Indian Creek, we are able to see some of the external factors that determine the course of the meadner. As you stand at ground zero, you'll notice that you're standing on a hard limestone outcropping. As you glance across the creek take a moment to examine the substrate that makes up the bank on the far side (hint: you'll need this observation later to answers some questions!).
If a substrate on one side of a river is harder than that of the other bank, it will typically act as a bumper on the side of a bowling lane - it will redirect the water as it takes significantly longer to erode. This will help increase the velocity on that side of the river, which in turn leads to deposition on the far side. In an area where you have two banks made of the same material, you will get a straighter section of the waterway, wheras when you have bank stabilizing forces on one side of the bank and not the other, you'll see meanders develop.
LOGGING REQUIREMENTS:
To log this Earthcache: Read the geology lesson above. Answer all three questions posted below. Answers can be sent via e-mail or messenger contacts on my Geocaching profile within a reasonable time. Group answers are fine, just list the members of your party with your answers. Do not post the answers to the questions in your logs.
QUESTION 1. GZ is on the banks of a meander. Face south and look at at the creek bank. Examine the far side of the meander. Is this an example of cut bank erosion or a point bar? Is this an outer bend or an inner bend?
QUESTION 2. Continue looking to the South and look at the creek bank. Examine the near side of the bank. Is this an example of cut bank erosion or a point bar? Is this an outer bend or an inner bend?
QUESTION 3. Compare and contrast the far bank of the creek with the bank you're standing on. In your own words how has the substrate impacted this meander?
QUESTION 4. What are some other factors (naturally occurring or man-made) that may prevent erosion and reduce the size of a meandner? Look up and down the creek - do you see any examples here?
Additional Logging Requirement: Post a photo that readily indicates that you (and anyone else logging the find) are at the location. This photo should be of you (face not required) or a personal item. Please ensure you do not include the observable river bank in any of your photos.
References:
- https://www.ausableriver.org/blog/why-do-streams-meander
- https://www.sciencedirect.com/topics/earth-and-planetary-sciences/bank-erosion