Iterative source-range estimation in a sloping-bottom shallow-water waveguide using the generalized array invariant

2017 ◽  
Vol 141 (5) ◽  
pp. 3991-3991
Author(s):  
Chomgun Cho ◽  
Hee-Chun Song ◽  
Paul Hursky ◽  
Sergio Jesus
Keyword(s):  
Shallow Water ◽  
Range Estimation ◽  
Sloping Bottom

scholarly journals Near-coast tsunami waveguiding: phenomenon and simulations

2008 ◽  
Vol 8 (2) ◽  
pp. 175-185 ◽  
Author(s):  
E. van Groesen ◽  
D. Adytia ◽  
Keyword(s):  
Shallow Water ◽  
High Variability ◽  
Boussinesq Model ◽  
Tsunami Waves ◽  
Wave Amplification ◽  
Reality Show ◽  
Sloping Bottom

Abstract. In this paper we show that shallow, elongated parts in a sloping bottom toward the coast will act as a waveguide and lead to large enhanced wave amplification for tsunami waves. Since this is even the case for narrow shallow regions, near-coast tsunami waveguiding may contribute to an explanation that tsunami heights and coastal effects as observed in reality show such high variability along the coastline. For accurate simulations, the complicated flow near the waveguide has to be resolved accurately, and grids that are too coarse will greatly underestimate the effects. We will present some results of extensive simulations using shallow water and a linear dispersive Variational Boussinesq model.

scholarly journals The shallow water equations: conservation laws and symplectic geometry

1987 ◽  
Vol 10 (3) ◽  
pp. 557-562 ◽  
Author(s):  
Yilmaz Akyildiz
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Symplectic Form ◽  
Symplectic Geometry ◽  
Nonlinear Differential Equations ◽  
Shallow Water Waves ◽  
Hodograph Method ◽  
Sloping Bottom

We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin.

Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom

2018 ◽  
Vol 104 (5-6) ◽  
pp. 915-921 ◽  
Author(s):  
A. V. Aksenov ◽  
S. Yu. Dobrokhotov ◽  
K. P. Druzhkov
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
One Dimensional ◽  
Sloping Bottom

scholarly journals Mass Transport Velocity in Shallow-Water Waves Reflected in a Rotating Ocean with a Coastal Boundary

2007 ◽  
Vol 37 (10) ◽  
pp. 2429-2445 ◽  
Author(s):  
Frode Hoydalsvik
Keyword(s):  
Mass Transport ◽  
Shallow Water ◽  
Water Waves ◽  
Traditional Approach ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Transport Velocity ◽  
Uniform Solution ◽  
Mass Transport Velocity ◽  
Sloping Bottom

Abstract The mass transport velocity in shallow-water waves reflected at right angles from an infinite and straight coast is studied theoretically in a Lagrangian reference frame. The waves are weakly nonlinear and monochromatic, and propagate in a homogenous, viscous, and rotating ocean. Unlike the traditional approach where the domain is divided into thin boundary layers and a core region, the uniform solution is obtained here without constraints on the thickness of the bottom wave boundary layer. It is shown that the mass transport velocity is not only sensitive to topography, but depends heavily on the interplay between the vertical length scales. Similarities and differences between the cases of a constant depth, a linearly sloping bottom, and a wavy and linearly sloping bottom are discussed. The mass transport velocity can be divided into two main categories—that induced by waves with a frequency close to the inertial frequency, and that induced by waves with a much larger frequency. For waves significantly affected by rotation to first order, the cross-shore mass transport velocity is very small relative to the alongshore mass transport velocity, and the direction of the mass transport velocity is reversed relative to that in waves of much higher frequencies.

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