Oceanic and Atmospheric Fluid Dynamics/Гидродинамика океана и атмосферы

Издание на английском языке
The book is an introduction to fluid dynamics with an emphasis on oceanography and meteorology, based on the author's many years of teaching experience. It covers the basic concepts of hydrodynamics and their applications to ocean and atmospheric dynamics, offering a simple and compact presentation of the material. The author pays attention to the connections between the topics, providing intuitive explanations and quantitative aspects that connect mathematical results with real data. The book consists of two parts: the first introduces the basics of hydrodynamics, and the second examines specific oceanographic and meteorological topics, including the influence of Corrolius and various types of currents. In addition to the main text, there are appendices that help deepen understanding. In general, the book is intended for undergraduates, postgraduates, and researchers seeking to gain solid knowledge in the field of ocean and atmospheric physics.

Contents
Part I Fluid Dynamics in Inertial Reference Frames
1 Introduction
1.1 Fluids
1.2 The Fluid as a Continuous System
1.3 Fluid Dynamics in Inertial and Rotating Reference Frames
Bibliography
2 Forces in Fluid Dynamics
2.1 Volume Forces, Gravity
2.2 Surface Forces: The Pressure
2.3 Pressure Gradient Force
2.4 Surface Forces: Viscosity in Newtonian Fluids.
Recommended Readings
3 Elements of Fluid Statics.
3.1 Mechanical Equilibrium, Hydrostatic Pressure
3.2 The Hydrostatic Paradox, the Communicating Vessels
3.3 Archimedes’ Principle, Reduced Gravity
Recommended Readings
4 Elements of Fluid Kinematics
4.1 Lagrangian Derivative
4.2 Continuity Equation
4.3 Two-Dimensional and Incompressible Flows
4.4 Vorticity
4.5 Irrotational and Incompressible Flows
4.6 Circulation, Vorticity Tubes
Recommended Readings
5 The Equations of Fluid Dynamics
5.1 Derivation of the Governing Equations
5.2 Euler’s Equations
5.3 Navier-Stokes Equations
5.4 Initial and Boundary Conditions
5.5 Complete Set of Equations for an Incompressible Fluid
5.6 Energy Flux, Viscous Dissipation
5.7 Bernoulli’s Theorem and Its Applications
5.8 Dynamics of Vorticity
5.9 Balance of Forces and Energy in Poiseuille Flow
Recommended Reading
6 Turbulence and Turbulent Viscosity
6.1 Phenomenology of Turbulence
6.2 Transition to Turbulence, Reynolds Number
6.3 Equations for the Average Fields
6.4 Reynolds Stress, Turbulent Viscosity
Bibliography
7 Low-Reynolds Number Flows
7.1 Approximate Governing Equations for Low-Reynolds Number Flows
7.2 Flow Induced by a Sphere at Low Reynolds Number
7.3 Meteorological and Oceanographic Applications
Bibliography
8 High-Reynolds Number Flows.
8.1 The Boundary Layer: Structure and Separation
8.2 Transition of an Internal Flow from Potential to Viscous
8.3 Irrotationality in Perfect Fluids, Kelvin’s Theorem
8.4 External Flows: Lift and Drag
8.5 Elementary and Composite Potential External Flows
8.6 Magnus Effect, Kutta-Zukovskij Theorem
Bibliography
9 Surface Gravity Waves: General Aspects
9.1 Linear Surface Gravity Waves
9.2 Derivation of the Velocity Field and the Dispersion Relation
9.3 Deep and Shallow Water Waves
9.4 Group Velocity
9.5 Phenomenology of Surface Waves
9.6 Tsunami Waves
9.7 Nonlinear Effects: Stokes and Cnoidal Waves
9.8 Nonlinear Effects: Korteweg-de Vries Equation, Solitons
Bibliography
10 Surface Gravity Waves: Energy and Statistics
10.1 Wave Energy, Power Spectral Density
10.2 Phillips and Miles Generation Mechanisms
10.3 Statistics of Sea Level and Wave Heights
Bibliography
11 Internal Gravity Waves
11.1 Linear Internal Gravity Waves
11.2 Internal Gravity Waves in a Two-Layer Fluid
11.3 Phenomenology and Generation of Internal Gravity Waves, Internal Solitons
11.4 Nonlinear Effects: Kadomtsev-Petviashvili Equation
Bibliography
Part II Fluid Dynamics in Rotating Reference Frames
12 Coriolis Force, Geostrophic Motions
12.1 Coriolis Force
12.2 Coriolis Parameter
12.3 Rossby and Ekman Numbers
12.4 Geostrophic Motions
Recommended Readings
13 Two-Dimensionality in Rotating Fluids
13.1 Taylor-Proudman Theorem, Taylor Columns
13.2 Mixing in Two-Dimensional Flows
13.3 Vorticity in Rotating Reference Frames
13.4 The Various Approximations
Bibliography
14 The Thermal Wind
14.1 The Thermal Wind Relationship
14.2 The Thermal Wind in the Atmosphere
14.3 The Thermal Wind in the Ocean: The Relative Currents
Bibliography
15 Ageostrophic Winds in Atmospheric Boundary Layers
15.1 The Planetary Boundary Layer
15.2 Ageostrophic Winds in a Convective Planetary Boundary Layer
15.3 Ageostrophic Winds in a Stably Stratified Planetary Boundary Layer
15.4 Winds in the Surface Layer
Bibliography
16 Ageostrophic Currents in Oceanic Boundary Layers.
16.1 Oceanic Surface Ekman Layer
16.2 Inertia Currents
16.3 Oceanic Bottom Ekman Layer
16.4 Generation of Geostrophic Currents from Ageostrophic Flows.
16.5 Elementary Current System in a Coastal Ocean
Bibliography
17 The Shallow-Water Approximation
17.1 The Shallow-Water Equations
17.2 Integrated Continuity Equation in Shallow-Water
17.3 The Two-Layer Model
17.4 The Reduced-Gravity Model
17.5 An Example of Intrinsic and Chaotic Variability of a Reduced-Gravity Flow
Bibliography
18 Potential Vorticity and Its Applications
18.1 Evolution Equation of Potential Vorticity in Shallow Water
18.2 Conservation of Potential Vorticity.
18.3 Zonality of Prevailing Winds, Topographic Effects
18.4 The Restoring Mechanism of Rossby Waves
Bibliography
19 Quasigeostrophic Approximation, Rossby Waves
19.1 Quasigeostrophic Approximation
19.2 Rossby Waves
19.3 Dispersion Relation for Barotropic Waves
19.4 Dispersion Relation for Baroclinic Waves
19.5 Rossby Waves in the Atmosphere and in the Ocean
Bibliography
20 Atmospheric and Oceanic Vortices, Wind-Driven Ocean Circulation
20.1 Atmospheric Dynamics on the Synoptic Scale
20.2 Mesoscale and Sub-basin Oceanic Vortices
20.3 Wind-Driven Ocean Circulation, the Sverdrup Balance
20.4 Western Boundary Currents
20.5 Laboratory Simulations
Bibliography
Appendix A: Gauss’s and Stokes’ Theorems
Appendix B: The Stress Tensor
Appendix C: Relative Motion of the Fluid Near a Point
Appendix D: Kelvin’s Theorem
Appendix E: The Special Theory of Relativity and Relativistic
Fluid Dynamics
Bibliography