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V.V.Bulatov, Yu.V.Vladimirov
Wave dynamics of stratified mediums.
Moscow: Nauka, 2012, 584 pp.
Annotation
The monograph is devoted to the research of
the processes of disturbance and propagation
of the internal gravity waves within the
vertically stratified horizontally non-uniform
and non-stationary mediums, to development of
the asymptotic methods being by the
generalization of the space-time ray-tracing
method (the method of the geometrical optics,
WKBJ method), to research of the critical
phenomena at generation and propagations of
the internal gravity waves, and also to
development of non-spectral methods of the
hydro physical fields measurements in the
ocean. The monograph is intended for the
specialists in the field of the mathematical
modeling, hydrodynamics, ocean dynamics.
CONTENTS
INTRODUCTION
CHAPTER 1 INTERNAL GRAVITY WAVES DYNAMICS
IN VERTICALLY STRATIFIED MEDIUMS
1.1 INTERNAL GRAVITY WAVES IN VERTICALLY
STRATIFIED MEDIUMS: BASIC EQUATIONS,
PROBLEM DEFINITION, INTEGRAL FORMS OF
SOLUTIONS
1.2 INTERNAL GRAVITY WAVES FAR FROM
DISTURBING SOURCES
1.3 INTERNAL GRAVITY WAVES NEAR
DISTURBING SOURCES
1.4 INTERNAL GRAVITY WAVES IN THE
NEIGBORHOOD OF MOVING SOURCES TRAJECTORIES
1.5 MODIFIED GREEN'S FUNCTION FOR THE
EQUATION OF INTERNAL GRAVITY WAVES IN A
STRATIFIED MEDIUM LAYER WITH FIXED
AVERAGE SHEAR FLOW
1.6 INTERNAL GRAVITY WAVES GENERATED BY
ARBITRARY MOVING DISTURBING SOURCES AND
CRITICAL MODES OF GENERATION
1.7 INTERNAL GRAVITY WAVES GENERATED BY
STATIONARY DISTURBING SOURCES
CHAPTER 2 MATHEMATICAL MODELING OF
INTERNAL GRAVITY WAVES GENERATED BY
NON-LOCAL DISTURBING SOURCES
2.1. NUMERICAL METHODS FOR SOLVING
FUNDAMENTAL VERTICAL SPECTRAL PROBLEMS
OF THE INTERNAL GRAVITY WAVES EQUATION:
CALCULATION OF EIGENFUNCTIONS AND
DISPERSION CURVES
2.2. MATHEMATICAL MODELING OF INTERNAL
GRAVITY WAVES GENERATED BY NON-LOCAL
DISTURBING SOURCES.
2.3. NON-LOCAL BOUNDARY CONDITIONS
FOR INTERNAL GRAVITY WAVES MATHEMATICAL
MODELING
2.4 INITIAL-BOUNDARY CONDITIONS FOR
MATHEMATICAL MODELING OF INTERNAL
GRAVITY WAVES FAR FROM DISTURBING SOURCES
CHAPTER 3 INTERNAL GRAVITY WAVES DYNAMICS
IN HORIZONTALLY NON-UNIFORM AND
NON-STATIONARY STRATIFIED MEDIUMS
3.1. BASIC CONCEPTS AND GENERALIZATION
OF THE GEOMETRIC OPTICS (WKBJ) METHOD
3.2. INTERNAL GRAVITY WAVES IN
STRATIFIED VARIABLE DEPTH MEDIUMS
3.3. INTERNAL GRAVITY WAVES IN
HORIZONTALLY INHOMOGENEOUS STRATIFIED
MEDIUMS
3.4. INTERNAL GRAVITY WAVES IN
NON-STATIONARY STRATIFIED MEDIUMS
3.5 THE UNIFORM ASYMPTOTIC FORM
OF INTERNAL GRAVITY WAVES IN STRATIFIED
MEDIUMS WITH VARIABLE DEPTH
3.6. HARMONIC INTERNAL GRAVITY WAVES
IN A STRATIFIED MEDIUMS WITH VARIABLE DEPTH:
EXACT SOLUTIONS AND ASYMPTOTIC REPRESENTATIONS
3.7. CONSTRUCTION OF ADVANCED APPROXIMATIONS
FOR INTERNAL GRAVITY WAVES ASYMPTOTICS IN
STRATIFIED MEDIUMS WITH VARIABLE DEPTH
CHAPTER 4 NON-SPECTRAL ALGORYTHMS FOR
PROCESSING FIELD DATA BASED ON MATHEMATICAL
MODELING OF INTERNAL GRAVITY WAVES DYNAMICS
4.1. BASIC CONCEPTS OF SPECTRAL AND
NON-SPECTRAL METHODS
FOR ANALYZING OF INTERNAL GRAVITY WAVES
MEASUREMENTS
4.2. ALGORITHMS AND RESULTS OF SPECTRAL
AND NON-SPECTRAL METHODS FOR ANALYZING
HYDROPHYSICAL FIELDS MEASUREMENTS
4.3 NON-SPECTRAL ALGORITHMS FOR PROCESSING
THE INTERNAL GRAVITY WAVES MEASUREMENTS
IN THE OCEAN
CHAPTER 5 SELECTED PROBLEMS OF THE LINEAR
AND NON-LINEAR INTERNAL GRAVITY WAVES THEORY
5.1. INTERNAL GRAVITY WAVES IN AN UNBOUNDED
EXPONENTIALLY STRATIFIED MEDIUM
5.2. INTERNAL GRAVITY WAVES IN STRATIFIED
MEDIUMS WITH VARIABLE AVERAGE SHEAR FLOWS
5.3. INTERNAL GRAVITY WAVES IN THE STRATIFIED
MEDIUMS WITH THE VAISALA-BRUNT VARIABLE FREQUENCY
5.4. INTERNAL GRAVITY WAVES IMPULSE PROPAGATION
IN AN INCOMPRESSIBLE STRATIFIED MEDIUM
5.5. ACOUSTIC-GRAVITY WAVES IMPULSES IN A
STRATIFIED COMPRESSIBLE MEDIUMS
5.6. EVALUATION OF SATISFIABILITY LIMITS FOR THE
INTERNAL GRAVITY WAVES LINEAR THEORY
REFERENCES
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