Ocean Tides

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.

Introduction

1. Indispensable Information on the Theory of Tides

1.1 Forces Inducing Ocean Tides

1.2 Tidal Potential

1.3 Equations of Tidal Dynamics

1.4 Additional Potentials of Deformation

1.5 Boundary Conditions

1.6 References

2. Studies on the Equations of Tidal Dynamics

2.1 Formulation of the Problem

2.2 Basic Ideas and Definitions

2.3 Uniqueness Theorem

2.4 A Priori Estimates

2.5 Existence Theorem

2.6 On the Existence of a Periodic Solution of the Equations of Tidal Dynamics

2.7 Conjugate Equations of Tidal Dynamics

2.8 The Perturbation Theory

2.9 The Spectral Problem

2.10 References

3. Numerical Methods for the Solution of the Equations of Tidal Dynamics

3.1 Method of Boundary Values

3.2 Hn-Method

3.3 Modified Variant of the Hn-Method

3.4 The Method of Fractional Steps

3.5 A Modified Variant of the Method of Fractional Steps

3.6 References

4. Tides in the World Ocean

4.1 Empirical Cotidal Charts

4.2 Basic Features of the Spatial Distribution of Tides in the World Ocean

4.3 An Example of Numerical Modeling of Tides in the World Ocean

4.4 Some Other Calculations of Tides in the World Ocean

4.5 Numerical Experiments on Tidal Dynamics in the World Ocean

4.6 Estimation of the Rate of Tidal Energy Dissipation in the Open Ocean

4.7 References

5. The Bottom Boundary Layer in Tidal Flows

5.1 Some Definitions

5.2 Experimental Data

5.3 Theoretical Models of the Bottom Boundary Layer in Tidal Flows

5.4 On the Law of Drag in Tidal Flow

5.5 References

6. Vertical Structure of Internal Tidal Waves

6.1 Generation of Internal Tidal Waves

6.2 Qualitative Analysis of the Equations for Internal Waves

6.3 Vertical Structure of the Internal Tidal Waves in a Realistically Stratified Ocean

6.4 References

Bibliography

Appendix

Index