Coupling between Shallow Water Equation and k-ω Model for Simulating Solitary Wave Run-Up

Simulating discontinuous phenomena such as shock waves and wave breaking during wave propagation and run-up has been a challenging task for wave modeller. This requires a robust, accurate, and efficient numerical implementation. In this paper, we propose a two-dimensional numerical model for simulating wave propagation and run-up in shallow areas. We implemented numerically the 2-dimensional Shallow Water Equations (SWE) on a staggered grid by applying the momentum conserving approximation in the advection terms. The numerical model is named MCS-2d. For simulations of wet–dry phenomena and wave run-up, a method called thin layer is used, which is essentially a calculation of the momentum deactivated in dry areas, i.e., locations where the water thickness is less than the specified threshold value. Efficiency and robustness of the scheme are demonstrated by simulations of various benchmark shallow flow tests, including those with complex bathymetry and wave run-up. The accuracy of the scheme in the calculation of the moving shoreline was validated using the analytical solutions of Thacker 1981, N-wave by Carrier et al., 2003, and solitary wave in a sloping bay by Zelt 1986. Laboratory benchmarking was performed by simulation of a solitary wave run-up on a conical island, as well as a simulation of the Monai Valley case. Here, the embedded-influxing method is used to generate an appropriate wave influx for these simulations. Simulation results were compared favorably to the analytical and experimental data. Good agreement was reached with regard to wave signals and the calculation of moving shoreline. These observations suggest that the MCS method is appropriate for simulations of varying shallow water flow.

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Stability of solitary waves for a generalized higher-order Shallow water equation

Filomat ◽

10.2298/fil1405007d ◽

2014 ◽

Vol 28 (5) ◽

pp. 1007-1017 ◽

Cited By ~ 1

Author(s):

Nurhan Dündar ◽

Necat Polat

Keyword(s):

Solitary Wave ◽

Shallow Water ◽

Solitary Waves ◽

Shallow Water Equation ◽

Higher Order ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

Existence And Stability ◽

Stability Of Solitary Waves

In this work, we consider solitary wave solutions of a generalized higher-order shallow water equation. We investigate the existence and stability of solitary waves of the equation.

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BED STRESS INVESTIGATION UNDER BREAKING SOLITARY WAVE RUNUP

Coastal Engineering Proceedings ◽

10.9753/icce.v33.currents.23 ◽

2012 ◽

Vol 1 (33) ◽

pp. 23

Author(s):

Mohammad Bagus Adityawan ◽

Hitoshi Tanaka ◽

Pengzhi Lin

Keyword(s):

Boundary Layer ◽

Solitary Wave ◽

Shallow Water Equation ◽

Empirical Method ◽

Wave Runup ◽

Short Period ◽

Bed Stress ◽

Stress Estimation ◽

Run Up ◽

Upper Boundary

The bed stress under breaking solitary wave runup was investigated in this study using the Simultaneous Coupling Method (SCM). The SCM couples the shallow water equation (SWE) with k-w model. The depth averaged velocity from SWE is applied as the upper boundary condition in k-w model for bed stress assessment from the boundary layer. It was found that the boundary layer approach provides more accurate bed stress estimation than the empirical method, which leads to a more accurate prediction of runup and wave profile. The accumulation of bed stress in during solitary wave runup was evaluated. The bed stress on the direction leaving the shoreline will have more impact in the overall process. However, during a short period of run up process, bed stress toward the shoreline may have significant effect as well.

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Identifikasi Pendekatan Shallow Water Equation Dalam Simulasi 2D Gelombang Tsunami di Pantai Keburuhan Purworejo

Majalah Ilmiah Bahari Jogja ◽

10.33489/mibj.v18i1.233 ◽

2020 ◽

Vol 18 (1) ◽

pp. 127-152

Author(s):

Benny Hartanto ◽

Ningrum Astriawati

Keyword(s):

Shallow Water ◽

Shallow Water Equation ◽

Run Up ◽

Tsunami Model

Kabupaten Purworejo merupakan salah satu dari lima daerah yang terkena dampak run-up tsunami Jawa 17 Juli 2006. Berdasarkan hasil Rapid Survey oleh BPDP dan BPPT, sepanjang Pantai Keburuhan merupakan lokasi terjadinya run-up tsunami di Kabupaten Purworejo di koordinat 109.912 LS -7.85 BT sebesar 1,7 meter. Tujuan dari penelitian ini adalah memperkirakan waktu tempuh tsunami, distribusi tinggi gelombang tsunami dan daerah jangkauan tsunami akibat dampak gempa tsunami Jawa 17 Juli 2006 di Pantai Keburuhan, Purworejo. Metode yang digunakan adalah metode deskriptif analitis dengan pendekatan kuantitatif. Data yang digunakan pada penelitian ini adalah titik tinggi, batimetri, parameter gempa, peramalan pasang surut wilayah perairan Pantai Keburuhan, data citra Geo Eye 1, dan kelerengan pantai. Pemodelan tsunami menggunakan perangkat lunak COMCOT v1.7 dengan kejadian gempa Jawa 17 Juli 2006. Berdasarkan pengolahan data, diketahui bahwa kecepatan gelombang maksimal sebesar 3.8788 m/s. Pada menit ke- 40, amplitudo awal gelombang tsunami sebesar 1.644 meter telah mencapai Pantai Keburuhan. Daerah jangkauan tsunami terluas dan jarak jangkauan maksimum terjauh terjadi di Pantai Keburuhan adalah 1,23 km2 dan 1,4 km. Berdasarkan hasil verifikasi dengan nilai RSR sebesar 0,26. Hasil validasi simulasi tsunami menggunakan COMCOT v1.7 diketahui bahwa tinggi run-up tsunami model sudah cukup sesuai dengan data run-up yang terjadi saat kejadian, dengan nilai RSR sebesar 0,29 dan CF sebesar 1,63.

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