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Coupled Korteweg-de Vries equations describing, to high-order, resonant flow of a fluid over topography

Journal Article


Abstract


  • The near-resonant flow of a fluid over a localized topography is examined. The flow is considered in the weakly nonlinear long-wave limit and is governed by the forced Korteweg-de Vries (fKdV) equation at first order. It is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at second order. To resolve this incompatibility, a forced coupled KdV system, which allows left-moving waves, is derived to third order (two orders beyond the fKdV approximation). The second-order fKdV equation is reformulated as an asymptotically equivalent forced Benjamin-Bona-Mahony (fBBM) equation, as its numerical scheme has superior stability. First- and second-order predictions for the resonant flow of surface water waves are compared and the mass flux between the right- and left-moving waves is found. An analytical estimate for the mass flux between the right- and left-moving waves is also derived and good agreement with the numerical solution is obtained. © 1999 American Institute of Physics.

Publication Date


  • 1999

Citation


  • Marchant, T. R. (1999). Coupled Korteweg-de Vries equations describing, to high-order, resonant flow of a fluid over topography. Physics of Fluids, 11(7), 1797-1804. doi:10.1063/1.870044

Scopus Eid


  • 2-s2.0-2042499862

Start Page


  • 1797

End Page


  • 1804

Volume


  • 11

Issue


  • 7

Abstract


  • The near-resonant flow of a fluid over a localized topography is examined. The flow is considered in the weakly nonlinear long-wave limit and is governed by the forced Korteweg-de Vries (fKdV) equation at first order. It is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at second order. To resolve this incompatibility, a forced coupled KdV system, which allows left-moving waves, is derived to third order (two orders beyond the fKdV approximation). The second-order fKdV equation is reformulated as an asymptotically equivalent forced Benjamin-Bona-Mahony (fBBM) equation, as its numerical scheme has superior stability. First- and second-order predictions for the resonant flow of surface water waves are compared and the mass flux between the right- and left-moving waves is found. An analytical estimate for the mass flux between the right- and left-moving waves is also derived and good agreement with the numerical solution is obtained. © 1999 American Institute of Physics.

Publication Date


  • 1999

Citation


  • Marchant, T. R. (1999). Coupled Korteweg-de Vries equations describing, to high-order, resonant flow of a fluid over topography. Physics of Fluids, 11(7), 1797-1804. doi:10.1063/1.870044

Scopus Eid


  • 2-s2.0-2042499862

Start Page


  • 1797

End Page


  • 1804

Volume


  • 11

Issue


  • 7