Meandering of a stream flowing down a partially wetting inclined plane

Vakhtang Putkaradze
Colorado State University

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. Previous studies have
conjectured that for some surfaces the meandering of a stream is an inherent instability.
In our experiment, we eliminate meandering on several partially wetting substrates 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, which includes stream dynamics and forcing
by external noise. The deviation h(x) from a straight linear stream h(x) = 0 shows
considerable variability as a function of downstream distance x. However, for an ensemble
average of stream shapes acquired at different times, the power spectrum S(k) as a
function of wavenumber k manifests a power-law scaling S(k)\sim k^5/2$. Moreover, the
growth of the area A(x) swept by the stream at the distance x grows as A(x) \sim x^1.75.
This data provide curious coincidence with river morphology data (Hack's law).

Presentation (PDF File)

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