Numerical study of vegetation damping effects on solitary wave run-up using the nonlinear shallow water equations

2013 ◽  
Vol 75 ◽  
pp. 21-28 ◽  
Author(s):  
Jun Tang ◽  
Derek Causon ◽  
Clive Mingham ◽  
Ling Qian
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Study ◽  
Nonlinear Shallow Water Equations ◽  
Damping Effects ◽  
Run Up

Nonlinear landslide tsunami run-up

2011 ◽  
Vol 691 ◽  
pp. 440-460 ◽  
Author(s):  
M. Sinan Özeren ◽  
Nazmi Postacioglu
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Shallow Water Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Submarine Landslides ◽  
Partial Derivatives ◽  
Nonlinear Shallow Water Equations ◽  
Run Up

AbstractInhomogeneous nonlinear shallow-water equations are studied using the Carrier–Greenspan approach and the resulting equations are solved analytically. The Carrier–Greenspan transformations are commonly used hodograph transformations that transform the nonlinear shallow-water equations into a set of linear equations in which partial derivatives with respect to two auxiliary variables appear. Yet, when the resulting initial-value problem is treated analytically through the use of Green’s functions, the partial derivatives of the Green’s functions have non-integrable singularities. This has forced researchers to numerically differentiate the convolutions of the Green’s functions. In this work we remedy this problem by differentiating the initial condition rather than the Green’s function itself; we also perform a change of variables that renders the entire problem more easily treatable. This particular Green’s function approach is especially useful to treat sources that are extended in time; we therefore apply it to model the run-down and run-up of the tsunami waves triggered by submarine landslides. Another advantage of the method presented is that the parametrization of the landslide using sources is done within the integral algorithm that is used for the rest of the problem instead of treating the landslide-generated wave as a separate incident wave. The method proves to be more accurate than the techniques based on Bessel function expansions if the sources are very localized.

scholarly journals Long Wave Run-Up Resonance in a Multi-Reflection System

2020 ◽  
Vol 10 (18) ◽  
pp. 6172
Author(s):  
Shanshan Xu ◽  
Frédéric Dias
Keyword(s):  
Boundary Condition ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Incoming Wave ◽  
Wave Trapping ◽  
Relaxation Zone ◽  
Long Wave ◽  
Nonlinear Shallow Water Equations ◽  
Run Up ◽  
Sloping Beach

Wave reflection and wave trapping can lead to long wave run-up resonance. After reviewing the theory of run-up resonance in the framework of the linear shallow water equations, we perform numerical simulations of periodic waves incident on a linearly sloping beach in the framework of the nonlinear shallow water equations. Three different types of boundary conditions are tested: fully reflective boundary, relaxation zone, and influx transparent boundary. The effect of the boundary condition on wave run-up is investigated. For the fully reflective boundary condition, it is found that resonant regimes do exist for certain values of the frequency of the incoming wave, which is consistent with theoretical results. The influx transparent boundary condition does not lead to run-up resonance. Finally, by decomposing the left- and right-going waves into a multi-reflection system, we find that the relaxation zone can lead to run-up resonance depending on the length of the relaxation zone.

Numerical Investigation of Wave Period Influence on Long Wave Run-Up on Slope With Rigid Vegetation

2016 ◽  
Author(s):  
Jun Tang ◽  
Yongming Shen
Keyword(s):  
Shallow Water Equations ◽  
Water Wave ◽  
Wave Period ◽  
Coastal Vegetation ◽  
Coastal Structures ◽  
Rigid Vegetation ◽  
Comparison With Experiment ◽  
Long Wave ◽  
Nonlinear Shallow Water Equations ◽  
Run Up

Coastal vegetation can not only provide shade to coastal structures but also reduce wave run-up. Study of long water wave climb on vegetation beach is fundamental to understanding that how wave run-up may be reduced by planted vegetation along coastline. The present study investigates wave period influence on long wave run-up on a partially-vegetated plane slope via numerical simulation. The numerical model is based on an implementation of Morison’s formulation for rigid structures induced inertia and drag stresses in the nonlinear shallow water equations. The numerical scheme is validated by comparison with experiment results. The model is then applied to investigate long wave with diverse periods propagating and run-up on a partially-vegetated 1:20 plane slope, and the sensitivity of run-up to wave period is investigated based on the numerical results.

A Numerical Study on the Reflection of a Solitary Wave in Shallow Water

1982 ◽  
Vol 51 (3) ◽  
pp. 1018-1023 ◽  
Author(s):  
Mitsuaki Funakoshi ◽  
Masayuki Oikawa
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Numerical Study

A shock solution for the nonlinear shallow water equations

2010 ◽  
Vol 658 ◽  
pp. 166-187 ◽  
Author(s):  
MATTEO ANTUONO
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Theoretical Analysis ◽  
Asymptotic Behaviour ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Boundary Data ◽  
Depth Analysis ◽  
Nonlinear Shallow Water Equations ◽  
Shock Solution

A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the main quantities along and behind the bore. The theoretical analysis is then applied to the specific case in which the water at the front of the shock wave is still. A comparison with the Shen & Meyer (J. Fluid Mech., vol. 16, 1963, p. 113) solution reveals that such a solution can be regarded as a specific case of the more general solution proposed here. The results obtained can be regarded as a useful benchmark for numerical solvers based on the NSWEs.

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