Malaysian Journal of Mathematical Sciences, September 2019, Vol. 13, No. 3
Analytical and Numerical Studies of Resonant Wave Run-up on a Plane Beach
Erwina, N., Erianto, E. S. and Pudjaprasetya, S. R.
Corresponding Email: nerwina@math.itb.ac.id
Received date: 27 December 2017
Accepted date: 16 March 2019
Abstract:
Wave run up is the vertical extent of wave up rushed on a beach. In the case of monochromatic wave run-up, it was a common belief that
the leading wave will reach the maximum run-up. However, this is not always the case, when the incident wave is of normal mode frequency,
resonance phenomena might appear. In this article, the normal mode frequency of a semi-enclosed basin on a plane beach is derived using
the variable separation technique. Simulation results demonstrate that when the incoming wave frequency is close to the normal mode frequency, the largest run-up height is not the leading wave, but the second, third or fourth waves, which indicates the occurrence of resonance phenomena. Sensitivity analysis was applied to show the dependence of the maximum run-up height to the beach slope, as well as the incident wave frequency. Further, a simulation using a real bathymetry was conducted to examine whether the resonance phenomenon appears in the actual tsunami events.
Keywords: The Staggered Conservative Scheme, Wave Run-up, Resonance
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