Variational Mechanics Formulation for Stream Meander Mechanics under Stable State End Conditions

A mechanical analog formulation for distributed vibrating systems is used to derive a relationship between the fundamental meander frequency (cycling/s) and stream flow parameters mass per unit length and stream length. Cycling frequency is estimated from the number of peak–peak lateral migrations divided by the travel time of a bank-full 2-year return flow flood wave and implemented in an arcpy/python routine in the ArcGIS-pro environment. The peak–peak meander cycling of a sample of first- and second-order and higher streams in the Brazos River basin were analyzed for traction force generated by the associated bank-full flows. The bank-full celerity was determined from historical 2-year return flows obtained from the United States Geological Survey gauging points in the Central Texas region. Bed and bank normal and shear stresses due to flow traction force were estimated for submeter depths and compared against measured values from undrained and drained shear tests. Estimated traction forces in the studied first-order streams primarily caused surficial erosion rather than structural failure. On the other hand, traction forces in second-order and higher streams were high enough to contribute to structural failure of stream banks. Pore-water pressures that reduce the shear strength of soils are likely to contribute to added bed and bank failure modes of second- and higher-order streams. It was found that second-order and higher streams had evolved to shallower slopes compared to their initial meander onset stages.