Center for Complex and Nonlinear Science

A stream of fluid flowing down a partially wetting inclined plane usually meanders, unless the volume flow rate is maintained at a highly constant value. However, fluctuations in the flow rate are inevitable in naturally occurring flows. Previous studies have conjectured that for some surfaces the meandering of a stream is an inherent instability. In this paper we show that on an acrylic plate we can eliminate the meandering by reducing perturbations entering the flow.By re-introducing controlled fluctuations, we show that they are indeed responsible for the onset of the meandering. We derive a theoretical model for the stream shape from first principles, which includes stream dynamics and forcing by external noise. While the deviation h(x) from a straight linear stream h(x) = 0 shows considerable variability as a function of downstream distance x, when an ensemble average is computed, averaging power spectrum S(k) as a function of wavenumber k for several different times t we obtain the power-law scaling S(k) ~ k**{5/2}. In addition, the growth of the area A(x) swept by the stream at the distance x grows as A(x) ~ x**{1.75}. These experimental results are in excellent agreement with our theory, as well as with recent results on turbulent flows in rivers and on landsurface evolutions.