Marchuk / Kagan Ocean Tides

Mathematical Models and Numerical Experiments
1. Auflage 2014
ISBN: 978-1-4831-8978-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten, Web PDF

Ocean Tides: Mathematical Models and Numerical Experiments discusses the mathematical concepts involved in understanding the behavior of oceanic tides. The book utilizes mathematical models and equations to interpret physical peculiarities of tidal generation. The text first presents the essential information on the theory of tide, and then proceeds to tackling the studies on the equations of tidal dynamics. Next, the book covers the numerical methods for the solution of the equations of tidal dynamics. Chapter 4 deals with the tides in the World Ocean, while Chapter 5 talks about the bottom boundary layer in tidal flows. The last chapter tackles the vertical structure of internal tidal waves. The book will be of great interest to individuals whose profession involves the direct interaction with tides, such as mariners, marine biologists, and oceanographers.

Autoren/Hrsg.

Marchuk, G. I.

Kagan, B. A.

Inhaltsverzeichnis

1;Front Cover;1
2;Ocean Tides: Mathematical Models and Numerical Experiments;4
3;Copyright Page;5
4;Table of Contents;10
5;Foreword;6
6;Preface;8
7;Introduction;12
8;CHAPTER 1. Indispensable Information on the Theory of Tides;14
8.1;1.1 Forces Inducing Ocean Tides;14
8.2;1.2. Tidal Potential;24
8.3;1.3. Equations of Tidal Dynamics;36
8.4;1.4. Additional Potentials of Deformation;39
8.5;1.5. Boundary Conditions;44
8.6;1.6. References;47
9;CHAPTER 2. Studies on the Equations of Tidal Dynamics;49
9.1;2.1. Formulation of the Problem;49
9.2;2.2. Basic Notions and Definitions;53
9.3;2.3. Uniqueness Theorem;56
9.4;2.4. A priori Estimates;58
9.5;2.5. Existence Theorem;65
9.6;2.6. On the Existence of a Periodic Solutionof the Equations of Tidal Dynamics;72
9.7;2.7. Conjugate Equations of Tidal Dynamics;76
9.8;2.8. The Perturbation Theory;80
9.9;2.9. The Spectral Problem;84
9.10;2.10. References;88
10;CHAPTER 3. Numerical Methods for the Solutionof the Equations of Tidal Dynamics;89
10.1;3.1. Method of Boundary Values;89
10.2;3.2. HN-method;97
10.3;3.3. Modified Variant of the HN-method;102
10.4;3.4. The Method of Fractional Steps;108
10.5;3.5. A Modified Variant of the Method of Fractional Steps;120
10.6;3.6. References;121
11;CHAPTER 4. Tides in the World Ocean;123
11.1;4.1. Empirical Cotidal Charts;123
11.2;4.2. Basic Features of the Spatial Distributionof Tides in the World Ocean;134
11.3;4.3. An Example of Numerical Modellingof Tides in the World Ocean;141
11.4;4.4. Some Other Calculations of Tides in the World Ocean;156
11.5;4.5. Numerical Experiments on Tidal Dynamics in theWorld Ocean;168
11.6;4.6. Estimation of the Rate of Tidal Energy Dissipationin the open Ocean;184
11.7;4.7. References;188
12;CHAPTER 5. The Bottom Boundary Layerin Tidal Flows;190
12.1;5.1. Some Definitions;190
12.2;5.2. Experimental Data;197
12.3;5.3. Theoretical Models of the Bottom Boundary Layer in Tidal Flows;217
12.4;5.4. On the Resistance Law in Tidal Flow;246
12.5;5.5 References;259
13;CHAPTER 6. Vertical Structure of InternalTidal Waves;261
13.1;6.1. Generation of Internal Tidal Waves;261
13.2;6.2. Qualitative Analysis of the Equations for Internal Waves;269
13.3;6.3. Vertical Structure of Internal Tidal Waves in a RealisticallyStratified Ocean;275
13.4;6.4. References;283
14;Bibliography;286
15;Additional References;294
16;AppendixNotes added to the proofs;298
17;Index;304