

V.V.Bulatov, Yu.V.Vladimirov
Internal gravity waves:
theory and applications.
Moscow, Nauka, 2007, pp.304
Annotation
The monography is devoted to the research
of the processes of disturbance and
propagation of the internal gravity waves
within the vertically stratified
horizontally nonuniform and nonstationary
mediums, to development of the asymptotic
methods being by the generalization of the
spacetime raytracing method (the method
of the geometrical optics), to research of
the critical phenomena at generation and
propagations of the internal gravity waves,
and also to development of nonspectral
methods of the analysis of the fullscale
measurements of the internal gravity waves
in the ocean.
The monography is intended for the
specialists in the field of hydrodynamics,
oceanology and the mathematical modeling
of geophysical processes.
The bibliography 409, figures 60.
CONTENTS
Introduction
Chapter 1.
General problems of the linear theory of the
internal gravity waves.
1.1. Basic equations.
1.2. Planar internal gravity waves in the
exponentially stratified medium.
1.3. Steadystate internal gravity waves and
the problem of reflection from the planar
boundaries.
1.4. Green function of the equation of the
internal gravity waves in the exponentially
stratified medium.
1.5. The internal gravity waves in the
stratified layer of the finite depth.
1.6. The internal gravity waves in the
stratified mediums with the average shift
flows.
Chapter 2.
Internal gravity waves from the local
and nonlocal sources of disturbances
in the stratified mediums.
2.1 Local sources of disturbances of the
internal gravity waves in the stratified
mediums: formulation of the problem and
the integral forms of solutions.
2.2 Asymptotic behavior of the solutions
far from the local and nonlocal disturbing
sources.
2.3 Asymptotic forms of the solutions in
the vicinity of the trajectories of movement
of the disturbances sources.
2.4 Far and intermediaterange asymptotic
forms of the fields of the internal gravity
waves in the deep ocean.
2.5 Asymptotic representations of the
solutions near to the sources of disturbances.
2.6 Internal gravity waves from the
nonlocal sources of disturbances
(threedimensional case).
Chapter 3.
Nonharmonic wave trains of the internal
gravity waves in the heterogeneous and
nonstationary stratified mediums.
3.1. Basic concepts of the method of the
geometric optics.
3.2.. Uniform asymptotics of the far field
of the internal gravity waves in the layer
of the stratified medium with the smoothly
varying bottom.
3.3. Local asymptotics of the far field
of the internal gravity waves in the layer
of the stratified medium with smoothly
varying bottom.
3.4. Uniform asymptotics of the fart field
of the internal gravity waves in the
stratified heterogeneous in the horizontal
direction mediums.
3.5. Local asymptotics of the far field
of the internal gravity waves in the
stratified heterogeneous in the horizontal
direction medium.
3.6 Local asymptotics of the far field of
the internal gravity waves in the stratified
nonstationary medium.
Chapter 4.
Critical modes of generation of the internal
gravity waves.
4.1. Internal gravity waves at the
arbitrary nonstationary movement of the
source.
4.2. Critical modes of generation of the
internal gravity waves.
4.3 Internal gravity waves near to the
sources of disturbances at the critical
modes of generation.
Chapter 5.
Nonspectral methods of analysis of the
insitu measurements of the internal
gravity waves.
5.1. Main ideas and methods of the
spectral analysis of the internal gravity
waves.
5.2. Nonspectral methods of the
analysis of the measurements of the
internal gravity waves in the Western
Sahara shelf region.
5.3 Nonspectral and the spectral
researches of propagation of the tidal
internal gravity waves on the example
of the experiment  "Mezopolygon"
(the tropical part of the Eastern Atlantic).
5.4 Single out of the wavetrains of the
internal gravity waves on the background
of the heavy interferences in compliance
with the results of the insitu
measurements in the Black sea.
Appendix A.
Numerical methods of solution of the
fundamental vertical spectral problems
Appendix B.
Green modified function for the equation
of the internal gravity waves in the
stratum of the stratified medium with
the constant average flow.
Conclusion.
References.
