A Simple Physical Model of River Meandering

Aims: Rivers often are twisting (meandering). There is no a simple physical model, which would explain the cause of formation of meanders and would describe their main (general) features, abstracting from the peculiarities of the real rivers. The resent work is devoted to creation and discussion of such model.
Study Design: We describe general features of river meandering in the framework of a simple physical model based on the law of constancy of the total stream velocity and action of gravity.
Place and Duration of Study: Institute of Materials, Khabarovsk, Russia; Institute of Applied Mathematics, Khabarovsk, Russia; 2013-2014.
Methodology: We consider a water stream flowing with a constant average velocity along a valley having slopes of constant inclination.
Results: We have found that the stream deviations at different obstacles can play a role of the reason of meandering. The sinousity of a stream depends on the ratio of the slope and valley steep angles; and its mean value is about 1.5 in accordance with observed geography data.
Conclusion: General features of river meandering may be understood in the framework of a simple physical model based on influence of gravity and the law of constancy of the total stream velocity. We have found that the stream deviations at different obstacles can play a main causal role for meandering. The sinousity S of a stream depends on the ratio of the slope and valley steep angles β/α and is equal to 1.507 for β/α=1 and the deviation angle δ=90º. For other cases the value of S lies between 1 and 2 for δ≤90º and has a maximal limit of 2.4 for δ≤90º at δ=123.4º.