Meandering acrosss the digital divide III: Pedagogy of a meandering stream

My teaching was clearly rooted on the other side of the digital divide from here and now. In it I developed a fairly consistent program for using meandering streams as a means of teaching how geology goes about answering its basic question (how did the Earth get to be the way it is?) by bringing to bear the non-historical sciences, in this case physics.

I started with an in-class problem. The students got a piece of paper with a meander loop drawn on it, and a data set with depth and water velocity. As I recall now I stole the data from something of Strahler’s. Actual stream gauge measurements. That required some explanation of measurement and operationalism. The students plotted the depth profile and the velocity profile across the meander loop. Needless to say, there was a close correlation: deeper water on the outside of the curve, running faster where deeper. Generalizing from this, I showed them how to draw the thalweg down the length of the stream shown on the map, completing the three-dimensional view of the  inter-relationship of process and form.
The next step was to, hypothetically, dump a load of mixed size sediment into the river at the thalweg on the cross-section and follow it downstream, using the stream competency diagram (particle size vs stream velocity). I had to resort to drawing my own version, even if there was one in the text. With it by interpolating velocity at max at the thalweg to zero at the bank, the students could figure out where to look for the sediment: on the next point bar downstream on the same side of the thalweg it started from and sorted out by size.
In the interests of saving time during the term, I dropped the in-class problem aspect and just lectured my way through these ideas. That doesn’t work nearly as well, but I needed to save the time for my other problems that I thought were more fundamental to geology- eight in all. The mysteries of log-scaled graphs, interpolation, and diagrams that show process but are too easily conflated with form just took too long to unravel.

After I felt that I had the students mind thoroughly into the stream, I went back to the cross-section and started talking about the actual point to point velocity and how that could be measured. I re-introduced the turbulence, showing where it maxed out on the outer part of the curve, below the surface, not at the bottom, sometimes with some helical flow. Then, with the bald assertion that the velocity plotted in the competency diagram was a surrogate measurement for the degree of turbulence, which we did not know how to measure, I further asserted-teachers in a classroom can get away with crap like that!-that if the stream was eroding, the point at which the erosion occurred was where the turbulence was maximum where, in turn, velocity changed the most in the shortest distance. That is, below the water surface, on the outside of the  curve, not at the bottom. Sediment removed from that point would leave the unconsolidated material above it un-supported, and it would collapse into the stream. All this stuff would be carried downstream to the next loop and depositied on the point bar, sorted out according to size. Frequently there were students who had swum in rivers, knew where the beach was and where the swimming hole was, and could testify about walking into the water over increasingly coarse sand, pebbles, etc.

The net result of these processes operating was the migration of the asymmetric profile sideways, leading to the side-cutting action of the stream and the accentuation of the meander loop, etc. By introducing some speed-up and slow-down of velocity around the loop, down-valley migration can be accounted for. Oxbow lakes, clay plugs resisting erosion(back to the competency diagram): it fits together beautifully. Occasionally you can see the click on the face of the student when all the various pieces of the puzzle fall into place.

All of this leads easily to saying that once the form of a meander is established, the process that occupies the form will re-create the form continually. The only remaining question was what caused the stream to wiggle in the first place.
I then went through the familiar examples from Leopold’s work of melt water streams on glaciers, the Gulf Stream, the jet stream in the atmosphere, even adding my own favorite examples, streams flowing across beaches, like at Alamere Falls. I could say at that point that meandering seemed to be an inherent property of fluids in turbulent flow, so we have to await a further understanding of turbulent flow from the people who are responsible for that sort of thing, the physicists.

Uncomfortably, the above development implies that all streams should meander. So that required some work on the conditions that rule in non-meandering streams: braided streams (variability of sediment load and discharge) and riffle and pool streams in canyons (flowing water can’t cut sideways into bedrock- the cutting tools are all in the bottom. They are doing the best they can.).

Meanwhile, geologically speaking we could say that the observational evidence indicates that we need refer to nothing beyond the current on-going process to explain the existing form. The independent variables in a stream system are the discharge and sediment load, which are both determined basically by climate. The internal dynamics of the process adjust the form to meet the needs of uniform dissipation of energy. While the process can approximate balance or equilibrium or steady state at the local time scale, so long as there is land above water, the planet Earth is not gravitationally in a stable configuration, and will continue to change at the global time scale. The internal energy residual and generated within the Earth is now, and has for nearly 5 billion years, acted to counter the force of gravity, fueling the continuing and shifting interactions at the surface of the Earth that we call geologic history.

Having spent the last four decades in front of a classroom, dealing with the structured ignorance of the students, I am a little intimidated by the staggering amount of new knowledge the scientific community has compiled while my back was turned, facing away from learning and toward teaching. To be a little more precise, I have been learning, but the thing I have been learning about is hidden behind that phrase “the structured ignorance of the students” and how that clashes with the fundamentals of science. In this process, I have been forced to re-learn those fundamentals again, but trying now to look at them from the point of view of someone who is, consciously or unconsciously, committed to a radically different frame of reference. But that’s not this story!

Alamere Falls 2006

The last Alamere: no beach, no stream


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