Energy equation for certain approximate models of long-wave hydrodynamics

Zinaida I. Fedotova; Gayaz S. Khakimzyanov; Denys Dutykh

doi:10.1515/rnam-2014-0013

Energy equation for certain approximate models of long-wave hydrodynamics

Zinaida I. Fedotova, Gayaz S. Khakimzyanov, Denys Dutykh

Mathematics

Academy of Sciences

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.

Original language	British English
Pages (from-to)	167-178
Number of pages	12
Journal	Russian Journal of Numerical Analysis and Mathematical Modelling
Volume	29
Issue number	3
DOIs	https://doi.org/10.1515/rnam-2014-0013
State	Published - 1 Jun 2014

Keywords

Conservative laws
ideal incompressible fluid
nonlinear dispersion equations
surface waves.

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10.1515/rnam-2014-0013

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title = "Energy equation for certain approximate models of long-wave hydrodynamics",

abstract = "A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.",

keywords = "Conservative laws, ideal incompressible fluid, nonlinear dispersion equations, surface waves.",

author = "Fedotova, {Zinaida I.} and Khakimzyanov, {Gayaz S.} and Denys Dutykh",

note = "Funding Information: Funding: The work was supported by the Russian Foundation for Basic Research (12–01–00721-a) and also by the program {\textquoteleft}Leading scientific schools of the Russian Federation{\textquoteright} (NSh–6293.2012.9).",

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doi = "10.1515/rnam-2014-0013",

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journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",

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T1 - Energy equation for certain approximate models of long-wave hydrodynamics

AU - Fedotova, Zinaida I.

AU - Khakimzyanov, Gayaz S.

AU - Dutykh, Denys

N1 - Funding Information: Funding: The work was supported by the Russian Foundation for Basic Research (12–01–00721-a) and also by the program ‘Leading scientific schools of the Russian Federation’ (NSh–6293.2012.9).

PY - 2014/6/1

Y1 - 2014/6/1

N2 - A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.

AB - A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.

KW - Conservative laws

KW - ideal incompressible fluid

KW - nonlinear dispersion equations

KW - surface waves.

UR - http://www.scopus.com/inward/record.url?scp=84902299205&partnerID=8YFLogxK

U2 - 10.1515/rnam-2014-0013

DO - 10.1515/rnam-2014-0013

M3 - Article

AN - SCOPUS:84902299205

SN - 0927-6467

VL - 29

SP - 167

EP - 178

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

IS - 3

ER -

Energy equation for certain approximate models of long-wave hydrodynamics

Abstract

Keywords

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