PENGARUH ANGIN TERHADAP GELOMBANG PERMUKAAN BERTIPE MENGGULUNG (ROLL WAVES) PADA BIDANG MIRING

• Main Author: Fauzi, Rifky
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46312
• Institution: Institut Teknologi Bandung

This study discusses the formation of roll waves on a fluid flow down an inclined plane. This wave type has the characteristics of being periodic, propagating at a constant speed, and steep wavefronts. Roll waves are modeled using Shallow Water Equation (SWE), which is modified so that it involves the effect of viscosity and the effect of wind. Analysis of roll waves is examined using two approaches, the study of the stability of the equilibrium solution of the SWE and dynamic property of the traveling wave SWE. In the study of instability, roll waves can occur if the Froude number of the flow exceeds a threshold number. This number depends on viscosity, wind velocity, and wavenumber. In the case that the relative viscosity is zero and wind effect is ignored, the threshold number is four, which is the condition when a perturbation will develop into roll waves, as recorded in (Dressler, 1949). Both wind and viscosity have clear effects on the development of roll waves. Froude number is larger if the wind direction is the same with the flow as well as if the viscosity is smaller, whereas if the other way around, the Froude number will be smaller. The Adam-Bashforth-Moulton (ABM) numerical method is used to solve SWE. The analytically derived Froude numbers are then confirmed using this scheme. The scheme is used to simulate the evolution and propagation of monochromatic waves to develop roll waves. In general, the greater wind velocity will have a stronger effect on the amplitude and steepness of the waves. A study of the dynamic property of the traveling wave SWE reveals that roll waves depends on viscosity and the direction of the wind. Several conditions for unstable situation yielding as roll waves solution is found here. Roll waves are obtained from limit cycle of the dynamical system derived from the SWE in traveling wave variable, which is obtained numerically using Runge-Kutta method. The results show that wavelength, amplitude, and steepness of the roll waves depend not only on the physical parameters but also on the speed of the wave. In general, the formation of roll waves that results from this study is consistent with the study of the instability of the equilibrium solution.