Ostrovsky Lev A.

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Ostrovsky
First Name
Lev A.
ORCID
0000-0003-2233-1305

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  • Article
    Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids
    (Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 2011-02-14) Ostrovsky, Lev A. ; Helfrich, Karl R.
    Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.
  • Technical Report
    Internal solitons in the ocean
    (Woods Hole Oceanographic Institution, 2006-01) Apel, J. R. ; Ostrovsky, Lev A. ; Stepanyants, Y. A. ; Lynch, James F.
    Nonlinear internal waves in the ocean are discussed (a) from the standpoint of soliton theory and (b) from the viewpoint of experimental measurements. First, theoretical models for internal solitary waves in the ocean are briefly described.Various nonlinear analytical solutions are treated, commencing with the well-known Boussinesq and Korteweg-deVries equations. Then certain generalizations are considered, including effects of cubic nonlinearity, Earth's rotation, cylindrical divergence, dissipation, shear flows, and others. Recent theoretical models for strongly nonlinear internal waves are outlined. Second, examples of experimental evidence for the existence of solitons in the upper ocean are presented; the data include radar and optical images and in situ measurements of waveforms, propagation speeds, and dispersion characteristics. Third, and finally, action of internal solitons on sound wave propagation is discussed. This review paper is intended for researchers from diverse backgrounds, including acousticians, who may not be familiar in detail with soliton theory. Thus, it includes an outline of the basics of soliton theory. At the same time, recent theoretical and observational results are described which can also make this review useful for mainstream oceanographers and theoreticians.
  • Article
    Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
    (European Geosciences Union, 2022-06-15) Helfrich, Karl R. ; Ostrovsky, Lev A.
    Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.
  • Article
    Some new aspects of the joint effect of rotation and topography on internal solitary waves.
    (American Meteorological Society, 2019-06-13) Ostrovsky, Lev A. ; Helfrich, Karl R.
    Using a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves in a two-layer ocean. The interplay between different singularities—terminal damping due to radiation and disappearing quadratic nonlinearity, and reaching an “internal beach” (e.g., zero lower-layer depth)—is discussed. Examples of the adiabatic evolution of a single solitary wave over a uniformly sloping bottom under realistic conditions are considered in more detail and compared with numerical solutions of the variable-coefficient, rotation-modified Korteweg–de Vries (rKdV) equation.