The statistical mechanics of meandering

2014 We present a simple mathematical model to describe the statistical properties of the meandering of narrow streams on clean and smooth substrates. The model is shown to contain three different regimes, depending on the flow rate : (i) at low rates, the stream path is a timeindependent random walk ; (ii) for intermediate flow rates, static meanders appear. The onset of meandering is found to be closely analogous to the physics of continuous phase transitions ; (iii) at high flow rates, the meanders start to slide downhill. The problem of the depinning of meanders can be mapped onto the problem of domain-wall depinning in disordered magnets. Using this correspondence, we can compute the critical flow rate for the onset of meander sliding. J. Phys. France 51 (1990) 829-845 1er MAI 1990, Classification Physics Abstracts 05.40 46.30 68.42