The linear model for wave generation of a bump
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A channel with a bump over at bottom will a ect the pro- le of the water surface that ows over it. This phenomenon can be modeled by the nondimensional Boussinesq equation. The governing equation used is expressed in variable of speed, elevation, the height of bump and Froude number. Here, we will investigate the dependance of wave formed by a bump on Froude number and dimension of the bump. In this paper, we focus only on the case of supercritical ow or Froude number greater than 1. We will derive the analytical solution for the free surface prole over a bump. From the analytical solution, we conclude that a bump generate waves with 1 peak and 2 dales. The formed peak does not propagate anywhere, but the two dales propagate to the direction of the ow with di erent speed and amplitude. For- ward Time Backward Space (FTBS) method is implemented to solve the equation numerically. The obtained numerical results con rm the analytical solution well.
Abstract
A channel with a bump over at bottom will a ect the pro- le of the water surface that ows over it. This phenomenon can be modeled by the nondimensional Boussinesq equation. The governing equation used is expressed in variable of speed, elevation, the height of bump and Froude number. Here, we will investigate the dependance of wave formed by a bump on Froude number and dimension of the bump. In this paper, we focus only on the case of supercritical ow or Froude number greater than 1. We will derive the analytical solution for the free surface prole over a bump. From the analytical solution, we conclude that a bump generate waves with 1 peak and 2 dales. The formed peak does not propagate anywhere, but the two dales propagate to the direction of the ow with di erent speed and amplitude. For- ward Time Backward Space (FTBS) method is implemented to solve the equation numerically. The obtained numerical results con rm the analytical solution well.
참고문헌 (1)
- L. H. Wiryanto, "A Boussinesq-type Model for Waves Generated by Flow Over A Bump", Appl. Math. Sci, 8, pp.5293~5302 (2014)