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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
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 HIGH ORDER 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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