TRAVELING WAVES EXHIBITING SPATIOTEMPORAL CHAOS ON THE SURFACE OF A VERTICALLY FALLING THIN-FILM


SEFIK B., UNAL G.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, cilt.32, sa.5, ss.721-742, 1994 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Konu: 5
  • Basım Tarihi: 1994
  • Doi Numarası: 10.1016/0020-7225(94)90056-6
  • Dergi Adı: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Sayfa Sayıları: ss.721-742

Özet

Nonlinear wave motion on the surface of a vertically falling thin viscous film has been examined by considering the Kuramoto-Sivashinsky (K-S) equation for Reynolds number Re approximately 1. We have considered a dynamical system with solutions known as travelling waves. The third- and fourth-order normal form analysis has been carried out near the fixed point located at the origin to capture the travelling wave solutions. Our analysis reveals that the fixed point bifurcates to a limit cycle via Hopf bifurcation. Then secondary Hopf bifurcation occurs yielding quasi-periodic solutions. Solitary waves with a different number of humps and hydraulic jump solutions are found analytically for a certain degree of approximation. The route which leads to deterministic chaos has been investigated by making use of Melnikov's theory. This analysis is based on the fourth-order normal form equations. The results revealed that the homoclinic bifurcation has occurred before the onset of chaos. Poincare section obtained by numerical calculations, were used to verify this picture. We have also observed that one of the Lyapunov characteristic exponents is positive.