scholarly journals Energy Partition of Equatorial Waves Excited by Various Initial Imbalances in the Linearized Shallow-Water Equation System on the Equatorial Beta Plane

2002 ◽  
Vol 53 (1) ◽  
pp. 29-46
Author(s):  
Masanori Yoshizaki
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Equation System ◽  
Equatorial Waves ◽  
Energy Partition ◽  
Beta Plane

A Class of Exact Solution of (3+1)-Dimensional Generalized Shallow Water Equation System

2015 ◽  
Vol 16 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Jian-Guo Liu ◽  
Zhi-Fang Zeng ◽  
Yan He ◽  
Guo-Ping Ai
Keyword(s):  
Shallow Water ◽  
Nonlinear Models ◽  
Shallow Water Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Equation System ◽  
Wave Solutions ◽  
Spurious Oscillation ◽  
Localized Excitations ◽  
Undetermined Function

AbstractShallow water wave equation has increasing use in many applications for its success in eliminating spurious oscillation, and has been widely studied. In this paper, we investigate (3+1)-dimensional generalized shallow water equation system. Based on the $(G'/G)$-expansion method and the variable separation method, we choose $\xi (x,y,z,t) = f(y + cz) + ax + h(t)$ and suppose that ${a_i}(i = 1,2, \ldots,m)$ is an undetermined function about $x,y,z,t$ instead of a constant in eq. (3), which are different from those in previous literatures. With the aid of symbolic computation, we obtain a family of exact solutions of the (3+1)-dimensional generalized shallow water equation system in forms of the hyperbolic functions and the trigonometric functions. When the parameters take special values, in addition to traveling wave solutions, we also get the nontraveling wave solutions by using our method; these obtained solutions possess abundant structures. The figures corresponding to these solutions are illustrated to show the particular localized excitations and the interactions between two solitary waves. The $(G'/G)$-expansion method is a very general and powerful tool that will lead to further insights and improvements of the nonlinear models.

scholarly journals A mathematical formulation for estimating maximum run-up height of 2018 Palu tsunami

2020 ◽  
Author(s):  
Ikha Magdalena ◽  
Antonio Hugo Respati Dewabrata ◽  
Alvedian Mauditra Aulia Matin ◽  
Adeline Clarissa ◽  
Muhammad Alif Aqsha
Keyword(s):  
Shallow Water ◽  
Cross Section ◽  
Incident Wave ◽  
Shallow Water Equation ◽  
Mathematical Formulation ◽  
Equation System ◽  
Type Transformation ◽  
Linear Equation System ◽  
Nonlinear Shallow Water Equations ◽  
Run Up

Abstract. Run-up is defined as sea wave up-rush on a beach. Run-up height is affected by many factors, including the shape of the bay. As an archipelagic country, Indonesia consists of thousands of islands with bays of diverse profiles, including Palu Bay, which is a well-known example of a bay with a drastically-increasing wave run-up height. In the case of the 2018 Palu tsunami, scientists found that the incident wave was amplified by the shape of the bay. The amplifying wave played a large role in the significant increase of run-up height. The run-up in question caused severe inundation, which led to a high number of casualties and damages. Therefore a mathematical model will be constructed to investigate the wave run-up. The bay's geometry will be approximated using three linearly-inclined channel types: one of parabolic cross-section, one of triangular cross-section, and a plane beach. We use the generalized nonlinear shallow water equations, which is then solved analytically using a hodograph-type transformation. As a result, the nonlinear shallow water equation system can be reduced to a one-dimensional linear equation system. Assuming the incident wave is sinusoidal, we can obtain a simple formula for calculating maximum run-up height on the shoreline.

scholarly journals Data‐Driven Learning of Reduced‐Order Dynamics for a Parametrized Shallow Water Equation

PAMM ◽  
2021 ◽  
Vol 20 (S1) ◽  
Author(s):  
Süleyman Yıldız ◽  
Pawan Goyal ◽  
Peter Benner ◽  
Bülent Karasözen
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Data Driven ◽  
Reduced Order

Stream Computation of Shallow Water Equation Solver for FPGA-based 1D Tsunami Simulation

2016 ◽  
Vol 43 (4) ◽  
pp. 82-87 ◽  
Author(s):  
Kentaro Sano ◽  
Fumiya Kono ◽  
Naohito Nakasato ◽  
Alexander Vazhenin ◽  
Stanislav Sedukhin
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Tsunami Simulation
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