Internal Solitary Waves in a Layered Weakly
Stratified Flow
Nikolay Makarenko, Janna Maltseva, Roman Tarakanov
and Kseniya Ivanova
Introduction
Internal waves play a significant role in the energy transformation and mass transport
in the oceanic stratified flows [9]. In many cases, large-amplitude waves are generated due to the interaction of internal tides with irregular bottom topography near
underwater ridges [16]. Our contribution has been inspired by recent field observations [24] related to extremely long series of internal waves and Kelvin–Helmholtz
billows in the equatorial Romanche Fracture Zone of the Mid-Atlantic Ridge. We
consider a theoretical model intended to describe internal solitary waves in a twolayer fluid flow with the density depending exponentially on the thickness of both
layers. This model generalizes the non-linear models early suggested by [2, 15, 19]
for a system with constant densities in both layers, as well as the latest “2.5-layer”
models considered by [11–13, 25]. The method of derivation involves the analysis
of the non-linear Dubreil-Jacotin—Long equation that results from the stationary
Euler equations of stratified fluid. Long-wave scaling procedure uses a small Boussinesq parameter which characterizes gentle slope of the density profile in the layers
and small density jump at their interface. This asymptotic procedure combines the
approaches, applied formerly to pure two-fluid system, with perturbation technique
N. Makarenko ( ✉ ) ⋅ J. Maltseva
Lavrentyev Institute of Hydrodynamics, Novosibirsk State University,
Novosibirsk 630090, Russia
e-mail: makarenko@hydro.nsc.ru
J. Maltseva
e-mail: maltseva@hydro.nsc.ru
R. Tarakanov
Shirshov Institute of Oceanology, Moscow 117997, Russia
e-mail: rtarakanov@gmail.com
K. Ivanova
Aix-Marseille Universite, Marseille 06, France
e-mail: ivanova.kseniya15@gmail.com
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_7
55
Stratified Flow
Nikolay Makarenko, Janna Maltseva, Roman Tarakanov
and Kseniya Ivanova
Introduction
Internal waves play a significant role in the energy transformation and mass transport
in the oceanic stratified flows [9]. In many cases, large-amplitude waves are generated due to the interaction of internal tides with irregular bottom topography near
underwater ridges [16]. Our contribution has been inspired by recent field observations [24] related to extremely long series of internal waves and Kelvin–Helmholtz
billows in the equatorial Romanche Fracture Zone of the Mid-Atlantic Ridge. We
consider a theoretical model intended to describe internal solitary waves in a twolayer fluid flow with the density depending exponentially on the thickness of both
layers. This model generalizes the non-linear models early suggested by [2, 15, 19]
for a system with constant densities in both layers, as well as the latest “2.5-layer”
models considered by [11–13, 25]. The method of derivation involves the analysis
of the non-linear Dubreil-Jacotin—Long equation that results from the stationary
Euler equations of stratified fluid. Long-wave scaling procedure uses a small Boussinesq parameter which characterizes gentle slope of the density profile in the layers
and small density jump at their interface. This asymptotic procedure combines the
approaches, applied formerly to pure two-fluid system, with perturbation technique
N. Makarenko ( ✉ ) ⋅ J. Maltseva
Lavrentyev Institute of Hydrodynamics, Novosibirsk State University,
Novosibirsk 630090, Russia
e-mail: makarenko@hydro.nsc.ru
J. Maltseva
e-mail: maltseva@hydro.nsc.ru
R. Tarakanov
Shirshov Institute of Oceanology, Moscow 117997, Russia
e-mail: rtarakanov@gmail.com
K. Ivanova
Aix-Marseille Universite, Marseille 06, France
e-mail: ivanova.kseniya15@gmail.com
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_7
55