Internal Gravity Waves in Horizontally
Inhomogeneous Ocean
Vitaly V. Bulatov and Yury V. Vladimirov
Introduction
The dynamics of wave motion in the ocean is currently of great interest because
they are important in geophysics and oceanology. As a rule, theoretical analysis of
these phenomena is based on the asymptotic methods, because the study of
unperturbed hydrodynamic equations leads to asymptotic expansions (ansatzs,
which is a German term for a type of solutions). These expansions permit solving
the problems of perturbed equations, which can be used to describe the effects of
nonlinearity, inhomogeneity, and non-stationary behavior of the real ocean. To
obtain a detailed description of a wide range of physical phenomena related to wave
dynamics of the stratified horizontally inhomogeneous unsteady ocean, it is necessary to start from the sufficiently developed mathematical models, which are
usually quite complicated, nonlinear, and multi-parametric. They can be investigated completely only using efficient numerical methods. However, there are several cases, in which a preliminary qualitative concept of the phenomena under study
can be obtained on the basis of simper asymptotic models and analytic methods for
studying these models. These models then enter a set of “blocks” used to construct
the complete pattern of wave dynamics, which permits discovering the correlation
between different wave phenomena and their relationship. Sometimes, despite the
seeming simplicity of the model assumptions, a successive choice of the solution
form allows one to obtain physically interesting results [1, 2, 5, 14].
The propagation of internal gravity waves (IGW) in the ocean is strongly
affected by the horizontal inhomogeneity and unsteady behavior of the basic
V. V. Bulatov ( ✉ ) ⋅ Y. V. Vladimirov
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
e-mail: internalwave@mail.ru
Y. V. Vladimirov
e-mail: vladimyura@yandex.ru
© 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_10
109
Inhomogeneous Ocean
Vitaly V. Bulatov and Yury V. Vladimirov
Introduction
The dynamics of wave motion in the ocean is currently of great interest because
they are important in geophysics and oceanology. As a rule, theoretical analysis of
these phenomena is based on the asymptotic methods, because the study of
unperturbed hydrodynamic equations leads to asymptotic expansions (ansatzs,
which is a German term for a type of solutions). These expansions permit solving
the problems of perturbed equations, which can be used to describe the effects of
nonlinearity, inhomogeneity, and non-stationary behavior of the real ocean. To
obtain a detailed description of a wide range of physical phenomena related to wave
dynamics of the stratified horizontally inhomogeneous unsteady ocean, it is necessary to start from the sufficiently developed mathematical models, which are
usually quite complicated, nonlinear, and multi-parametric. They can be investigated completely only using efficient numerical methods. However, there are several cases, in which a preliminary qualitative concept of the phenomena under study
can be obtained on the basis of simper asymptotic models and analytic methods for
studying these models. These models then enter a set of “blocks” used to construct
the complete pattern of wave dynamics, which permits discovering the correlation
between different wave phenomena and their relationship. Sometimes, despite the
seeming simplicity of the model assumptions, a successive choice of the solution
form allows one to obtain physically interesting results [1, 2, 5, 14].
The propagation of internal gravity waves (IGW) in the ocean is strongly
affected by the horizontal inhomogeneity and unsteady behavior of the basic
V. V. Bulatov ( ✉ ) ⋅ Y. V. Vladimirov
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
e-mail: internalwave@mail.ru
Y. V. Vladimirov
e-mail: vladimyura@yandex.ru
© 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_10
109