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Dynamics of Benjamin–Ono Solitons in a Two-Layer Ocean with a Shear Flow

Author

Listed:
  • Pawan Negi

    (Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur 721302, India)

  • Trilochan Sahoo

    (Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur 721302, India)

  • Niharika Singh

    (School of Mathematics, Physics and Computing, University of Southern Queensland, Toowoomba, QLD 4350, Australia)

  • Yury Stepanyants

    (School of Mathematics, Physics and Computing, University of Southern Queensland, Toowoomba, QLD 4350, Australia
    Department of Applied Mathematics, Nizhny Novgorod State Technical University, 603950 Nizhny Novgorod, Russia)

Abstract

The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed ( U ) exceeds the speed of long linear waves ( c 1 ), then BO solitons experience “explosive-type” enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when U < c 1 , BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as A ∼ t − 1 / 2 or A ∼ t − 1 / 3 , depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters.

Suggested Citation

  • Pawan Negi & Trilochan Sahoo & Niharika Singh & Yury Stepanyants, 2023. "Dynamics of Benjamin–Ono Solitons in a Two-Layer Ocean with a Shear Flow," Mathematics, MDPI, vol. 11(15), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3399-:d:1210219
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