Necessary conditions for the stability of simple loops

Many self-formed flow networks in nature are loopy, and these loops can occur because of adaptation to fluctuating hydrologic boundary conditions.  However, the relationship between fluctuations and loop stability has not been thoroughly tested at the scale of a single loop. We use linear stability analysis to assess whether a three node loop will be stable under various boundary conditions. Loops are stable when the difference between fluctuating states exceeds a well-defined criterion, and form tree-like structures otherwise.  The magnitude by which this criterion is exceeded also predicts the asymmetry of link conductivities in the loop. The averaging method, and nonlinearities in conductivity-discharge relationship also affect the outcome. These tools may provide new insight into emergent loops in natural systems such as river deltas.

Zoom link: https://us02web.zoom.us/j/82881783943?pwd=TUp3OGNvZ3R5akpXclZESmx2aGVkUT09

Meeting ID: 828 8178 3943
Passcode: 435791