Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface
- 14 January 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 40 (2), 307-314
- https://doi.org/10.1017/s0022112070000186
Abstract
Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.Keywords
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