Dispersive Shallow Water Waves

Khakimzyanov, G. S.; Dutykh, Denys; Fedotova, Z. I.; Gusev, Oleg

doi:10.1007/978-3-030-46267-3

Cited by 11 publications

(4 citation statements)

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“…Additional interesting and new results about water waves can be found in the publications of [61][62][63][64][65]. The newest results about disperse shallow water waves can be found in the monograph of Khakimzyanov et al [66].…”

Section: Theory and Resultsmentioning

confidence: 92%

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

2022

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We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well.

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Section: Theory and Resultsmentioning

confidence: 92%

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

2022

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“…The increasing complexity in the hierarchy allows us to determine the applicability limits of various models and, thus, to find the best trade-off between the model complexity/accuracy depending on the situation being modelled. A similar research effort has been undertaken for free water wave propagation in [23] over globally flat and spherical geometries.…”

Section: = ======= ⇒mentioning

confidence: 99%

Long wave interaction with a partially immersed body. Part II: Numerical results

Khakimzyanov¹,

Dutykh²,

Gusev³

2022

Preprint

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In this manuscript we perform an extensive numerical study of the long wave interaction problem with a fixed partially immersed body into a fluid layer. The incident wave is assumed to be an isolated solitary wave. The body in this study is assumed to be fixed with a rectangular section which is not touching the bottom of the channel. The mathematical modelling of this problem is based on Part I [22] of this series and considered models include the Nonlinear Shallow Water Equations (NSWE), fully nonlinear weakly dispersive Serre-Green-Naghdi Equations (SGN equations) (completed with appropriate compatibility conditions on solid/fluid boundaries) and the free surface irrotational full Euler equations (FEE). We study the influence of the floating body elongation, immersion depth and incident wave amplitude on the wave field before and after the obstacle. The comparison of all three models predictions and the data of small-scale laboratory experiments is performed. Moreover, in the framework of the FEE model we investigate the anomalous wave run-up behind the floating body in the close presence of a vertical wall. We demonstrate the cases where the vertical wall creates extreme wave amplitudes behind the body, but also we show the cases where the wall attenuates wave amplitudes comparing to the wave field without a wall.

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“…In [5], the author derived the viscous Boussinesq model without the irrotationality assumption that is usually done for Euler equations. Other articles already took the vorticity into account, even for fully nonlinear Boussinesq equations (here, called Serre-Green-Naghdi or SGN) [6,7] but not yet viscosity.…”

Section: Introductionmentioning

confidence: 99%

“…In the inviscid case of a non-small surface wave, an SGN system was derived [9,10]. It was proven to extend the Boussinesq system [8] and to be well-posed [11] and is numerically more stable than the Boussinesq systems [7]. Here, we try to extend the SGN system to take viscosity into account.…”

Section: Introductionmentioning

confidence: 99%

Derivation of a Viscous Serre–Green–Naghdi Equation: An Impasse?

Dutykh

Meur

2021

Fluids

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In this article, we present the current status of the derivation of a viscous Serre–Green–Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier–Stokes equations. We consider a particular regime binding the Reynolds number and the shallowness parameter. The computations presented in this article are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prandtl-like equation that we claim to be irreducible. Further approximations are necessary to obtain a tractable model.

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Dispersive Shallow Water Waves

Cited by 11 publications

References 0 publications

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Long wave interaction with a partially immersed body. Part II: Numerical results

Derivation of a Viscous Serre–Green–Naghdi Equation: An Impasse?

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