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Author = "Canuto, C., M.Y. Hussaini, A. Quarteroni, & T.A. Zang"
Title = "Spectral Methods in Fluid Dynamics"
Publisher = "Springer-Verlag, N.Y."
Year = "1987"
Pages = "557"
LOC = "QA 377 S676 1987"
ISBN = "3-540-17371-4"
Table of contents:
1. Introduction 1,
1.1 Historical background 1,
1.2 Some examples of spectral methods 3,
1.2.1 A Fourier Galerkin method for the wave equation 3,
1.2.2 A Chebyshev collocation method for the heat equation 7,
1.2.3 A Legendre tau method for the Poisson equation 10,
1.2.4 Basic aspects of Galerkin, tau and collocation
methods 12,
1.3 The equations of fluid dynamics 13,
1.3.1 Compressible Navier-Stokes 13,
1.3.2 Compressible Euler 15,
1.3.3 Compressible potential 16,
1.3.4 Incompressible flow 17,
1.3.5 Boundary layer 18,
1.4 Spectral accuracy for a 2-D fluid calculation 19,
1.5 3-D applications in fluids 25,
2. Spectral approximation 31,
2.1 The Fourier system 32,
2.1.1 The continuous Fourier expansion 32,
2.1.2 The discrete Fourier expansion 38,
2.1.3 Differentiation 42,
2.1.4 The Gibbs phenomenon 44,
2.2 Orthogonal polynomials in (-1,1) 53,
2.2.1 Sturm-Liouville problems 53,
2.2.2 Orthogonal systems of polynomials 54,
2.2.3 Gauss-type quadratures and discrete polynomial
transforms 55,
2.3 Legendre polynomials 60,
2.3.1 Basic formulas 60,
2.3.2 Differentiation 62,
2.4 Chebyshev polynomials 65,
2.4.1 Basic formulas 65,
2.4.2 Differentiation 68,
2.5 Generalizations 70,
2.5.1 Jacobi polynomials 70,
2.5.2 Mapping 71,
2.5.3 Semi-infinite intervals 72,
2.5.4 Infinite intervals 74,
3. Fundamentals of spectral methods for PDEs 76,
3.1 Spectral projection of the Burgers equation 76,
3.1.1 Fourier Galerkin 77,
3.1.2 Fourier collocation 78,
3.1.3 Chebyshev tau 79,
3.1.4 Chebyshev collocation 81,
3.2 Convolution sums 82,
3.2.1 Pseudospectral transform methods 83,
3.2.2 Aliasing removal by padding or truncation 84,
3.2.3 Aliasing removal by phase shifts 85,
3.2.4 Convolution sums in Chebyshev methods 86,
3.2.5 Relation between collocation and pseudospectral
methods 86,
3.3 Boundary conditions 87,
3.4 Coordinate singularities 90,
3.4.1 Polar coordinates 90,
3.4.2 Spherical polar coordinates 91,
3.5 Two-dimensional mapping 92,
4. Temporal discretization 94,
4.1 Introduction 94,
4.2 The eigenvalues of basic spectral operators 96,
4.2.1 The first-derivative operator 96,
4.2.2 The second-derivative operator 98,
4.3 Some standard schemes 101,
4.3.1 Multistep schemes 101,
4.3.2 Runge-Kutta methods 107,
4.4 Special purpose schemes 110,
4.4.1 High resolution temporal schemes 110,
4.4.2 Special integration techniques 112,
4.4.3 Lerat schemes 113,
4.5 Conservation forms 114,
4.6 Aliasing 118,
5. Solution techniques for implicit spectral equations 124,
5.1 Direct methods 125,
5.1.1 Fourier approximation 125,
5.1.2 Chebyshev tau approximation 129,
5.1.3 Schur-decomposition and matrix-diagonalization 133,
5.2 Fundamentals of iterative methods 137,
5.2.1 Richardson iteration 137,
5.2.2 Preconditioning 139,
5.2.3 Non-periodic problems 144,
5.2.4 Finite-element preconditioning 148,
5.3 Conventional iterative methods 149,
5.3.1 Descent methods for symmetric, positive-definite
systems 149,
5.3.2 Descent methods for non-symmetric problems 155,
5.3.3 Chebyshev acceleration 157,
5.4 Multidimensional preconditioning 159,
5.4.1 Finite-difference solvers 159,
5.4.2 Modified finite-difference preconditioners 160,
5.5 Spectral multigrid methods 166,
5.5.1 Model problem discussion 166,
5.5.2 Two-dimensional problems 168,
5.5.3 Interpolation operators 170,
5.5.4 Coarse-grid operators 172,
5.5.5 Relaxation schemes 172,
5.6 A semi-implicit method for the Navier-Stokes equations 174,
6. Simple incompressible flows 183,
6.1 Burgers equation 183,
6.2 Shear flow past a circle 186,
6.3 Boundary-layer flows 188,
6.4 Linear stability 193,
7. Some algorithms for unsteady Navier-Stokes equations 201,
7.1 Introduction 201,
7.2 Homogeneous flows 203,
7.2.1 A spectral Galerkin solution technique 203,
7.2.2 Treatment of the nonlinear terms 204,
7.2.3 Refinements 207,
7.2.4 Pseudospectral and collocation methods 208,
7.3 Inhomogeneous flows 212,
7.3.1 Coupled methods 213,
7.3.2 Splitting methods 222,
7.3.3 Galerkin methods 226,
7.3.4 Other confined flows 228,
7.3.5 Unbounded flows 230,
7.3.6 Aliasing in transition calculations 231,
7.4 Flows with multiple inhomogeneous directions 233,
7.4.1 Choice of mesh 234,
7.4.2 Coupled methods 236,
7.4.3 Splitting methods 237,
7.4.4 Other methods 238,
7.5 Mixed spectral/finite-difference methods 238,
8. Compressible flow 240,
8.1 Introduction 240,
8.2 Boundary conditions for hyperbolic problems 242,
8.3 Basic results for scalar nonsmooth problems 246,
8.4 Homogeneous turbulence 252,
8.5 Shock-capturing 255,
8.6 Shock-fitting 266,
8.7 Reacting flows 273,
9. Global approximation results 275,
9.1 Fourier approximation 275,
9.2 Sturm-Liouville expansions 281,
9.3 Discrete norms 286,
9.4 Legendre approximations 287,
9.5 Chebyshev approximations 294,
9.6 Other polynomial approximations 305,
9.7 Approximation results in several dimensions 307,
10. Theory of stability and convergence for spectral methods 315,
10.1 The three examples revisited 315,
10.2 Towards a general theory 323,
10.3 General formulation of spectral approximations to
linear steady problems 325,
10.4 Galerkin, collocation and tau methods 329,
10.5 General formulation of spectral approximations to
linear evolution equations 353,
10.6 The error equation 371,
11. Steady, smooth problems 375,
11.1 The Poisson equation 375,
11.2 Advection-diffusion equation 383,
11.3 Navier-Stokes equations 392,
11.4 The eigenvalues of some spectral operators 407,
12. Transient, smooth problems 415,
12.1 Linear hyperbolic equations 415,
12.2 Heat equation 430,
12.3 Advection-diffusion equation 440,
13. Domain decomposition methods 444,
13.1 Introduction 444,
13.2 Patching methods 447,
13.2.1 Notation 447,
13.2.2 Discretization 448,
13.2.3 Solution techniques 454,
13.2.4 Examples 456,
13.3 Variational methods 459,
13.3.1 Formulation 459,
13.3.2 The spectral-element method 461,
13.4 The alternating Schwartz method 466,
13.5 Mathematical aspects of domain decomposition methods 470,
13.5.1 Patching methods 470,
13.5.2 Equivalence beween patching and variational
methods 471,
13.6 Some stability and convergence results 473,
13.6.1 Patching methods 473,
13.6.2 Variational methods 475,
Appendices 477,
References 529,
Index 551 " }
Author = "Chapin, Henry and F. G. Walton Smith"
Title = "The Ocean River"
Publisher = "Charles Scribner's Sons"
Year = "1952"
Table of contents:
1. Oceanus 1,
2. Fire, rock and sea 13,
3. River of life 38,
4. Atlantic legend 57,
5. The Mediterranean looks west 74,
6. Charting the river 96,
7. The nature of the stream 120,
8. The engine of the air 148,
9. The age of fishes 173,
10. The treasure revealed 200,
11. The hand of the giant 228,
12. The codfish frontier 251,
13. Sail and the stream 276,
14. The Atlantic and Western man 296,
Bibliography 308,
Index 309 " }
Author = "Chapman, S. and R. S. Lindzen"
Title = "Atmospheric Tides, Thermal and Gravitational"
Publisher = "Gordon and Breach"
Pages = "200"
Year = "1970"
Table of contents:
NYA
Author = "Clancy, Edward P."
Title = "The Tides: Pulse of the Earth"
Publisher = "Doubleday"
Year = "1968"
Table of contents:
I. Introduction 3,
II. Isaac Newton and the equilibrium theory of the tides 11,
III. Tidal behavior as predicted by the equlibrium theory 32,
IV. Dynamical theory 57,
V. Measuring and predicting the tides 75,
VI. Tides and tidal currents in small areas 88,
VII. The tides as we see them 112,
VIII. Power from the tides 133,
IX. Tides in the earth 158,
X. Tides in the atmosphere 185,
XI. Tides and the planetary system 196 " }
Author = "Coker, R. E."
Title = "This Great and Wide Sea: An Introduction to
Oceanography and Marine Biology"
Publisher = "Univ. of N. Carolina Press"
Year = "1947"
Table of contents:
I. History and geography,
1. Discovery of the seas 11,
2. Beginnings of oceanography 17,
3. Pioneers in oceanography 19,
4. Oceanography in America 40,
5. Sea and land 57,
II. Chemistry and physics,
6. The sea as a solution 77,
7. Some physical properties of sea water 94,
8. Deposits at the bottom of the sea 112,
9. Sea water in motion: general plans of circulation 120,
10. Sea water in motion: water moved by the winds 138,
11. Sea water in motion: tides and other movements 146,
12. The sea and the sun 160,
III. Life in the sea,
13. Life in the sea: general conditions 177,
14. Pasturage of the sea 197,
15. Drifting life: the plankton 208,
16. Composition of the plankton 219,
17. Life on the bottom: the benthos 240,
18. Life at large: the nekton 255,
19. More about life at large: the nekton 281,
Selected bibliography 301,
Index 305 " }
Author = "Craik, A. D. D."
Title = "Wave Interactions and Fluid Flows"
Publisher = "Cambridge Univ. Press"
Year = "1985"
Pages = "322"
LOC = "TA 357 C73 1985"
Table of contents:
Sec. 1. Introduction 1,
1 Introduction 1,
Sec. 2. Linear wave interactions 10,
2 Flows with piecewise-constant density and velocity 10,
3 Flows with constant density and continuous velocity
profile 21,
4 Flows with density stratification and piecewise-constant
velocity 27,
5 Flows with continuous profiles of density and velocity 35,
6 Models of mode coupling 45,
7 Eigenvalue spectra and localized disturbances 59,
Sec. 3. Introduction to nonlinear theory 65,
8 Introduction to nonlinear theory 65,
Sec. 4. Waves and mean flows 75,
9 Spatially-periodic waves in channel flows 75,
10 Spatially-periodic waves on deformable boundaries 81,
11 Modulated wave-packets 87,
12 Generalized Lagrangian mean (GLM) formulation 105,
13 Spatially-periodic mean flows 113,
Sec. 5. Three-wave resonances 123,
14 Conservative wave interactions 123,
15 Solutions of the conservative interaction equations 136,
16 Linearly damped waves 151,
17 Non-conservative wave interactions 161,
Sec. 6. Evolution of a nonlinear wave-train 172,
18 Heuristic derivation of the evolution equations 172,
19 Weakly nonlinear waves in inviscid fluids 176,
20 Weakly nonlinear waves in shear flows 188,
21 Properties of the evolution equations 199,
22 Waves of larger amplitude 212,
Sec. 7. Cubic three- and four-wave interactions 231,
23 Conservative four-wave interactions 231,
24 Mode interactions in Taylor-Couette flow 244,
25 Rayleigh-Benard convection 258,
26 Wave interactions in planar shear flows 272,
Sec. 8. Strong interactions, local instabilities and
turbulence: a postscript 282,
27 Strong interactions, local instabilities and
turbulence: a postscript 282,
References 289,
Index 319 " }
Author = "Csanady, G. T."
Title = "Circulation in the Coastal Ocean"
Publisher = "D. Reidel, Boston"
Year = "1982"
Pages = "279"
ISBN = "90-277-1400-2"
LOC = "GC228.5 C74 1982"
Table of contents:
1. Fundamental equations and their simplification 1,
1.0 Introduction 1,
1.1 The equation of continuity 2,
1.2 Momentum balance 3,
1.3 Hydrostatic approximation 5,
1.4 The density field 8,
1.5 Quasi-horizontal motions 10,
1.6 Surface and bottom stress 10,
1.7 Interior stresses 10,
1.8 Linearization of the equations 14,
1.9 Shallow water equations 15,
1.10 Potential vorticity equation 17,
1.11 Some elementary conceptual models 19,
2. Inertial response to wind 25,
2.0 Introduction 25,
2.1 Wind setup close to coasts 25,
2.2 Setup in a basin of arbitrary size 29,
2.3 Seiches in narrow basins 34,
2.4 Evolution of setup along a straight open coast 39,
2.5 Longshore wind and sea level 42,
2.6 Wind acting for a limited period 47,
2.7 Pressure field-induced and frictional interior velocities 49,
2.8 Response of a closed basin to sudden wind 55,
2.9 The Kelvin wave 61,
3. The behavior of a stratified sea 64,
3.0 General remarks 64,
3.1 Perturbation theory 67,
3.2 Normal mode equations 68,
3.3 Stratification model 71,
3.4 Model of forcing 73,
3.5 Response of continuously stratified model to forcing 74,
3.6 The two-layer model 83,
3.7 Impulsive longshore wind 89,
3.8 Cross-shore wind 91,
3.9 Two-layer closed basin 92,
3.10 Surfacing of the pycnocline 99,
4. The subtle effects of topography 105,
4.0 Introduction 105,
4.1 Wind setup over variable depth 105,
4.2 Windward and leeward shores 112,
4.3 Seiches in variable depth basins 115,
4.4 Variable depth and earth rotation 116,
4.5 Vorticity waves 124,
4.6 Stratified fluid over realistic topography 133,
5. Transient coastal currents 143,
5.0 Introduction 143,
5.1 Longshore velocity and transport 144,
5.2 Coastal sea level 150,
5.3 Upwelling, downwelling and coastal jets 151,
5.4 Propagation of flow events 157,
5.5 Climatology of coastal currents 168,
6. Thermohaline circulation 174,
6.0 Introduction 174,
6.1 Frictional adjustment 175,
6.2 Interior velocities 177,
6.3 Simplified parameterization of interior and bottom stress 185,
6.4 Steady circulation near a straight coast 186,
6.5 Inclinded plane beach model 193,
6.6 Deep ocean influence 203,
6.7 Periodic cross-shore wind 205,
6.8 Circulation in a circular basin with a parabolic
depth profile 208,
7. Thermohaline circulation 211,
7.0 Introduction 211,
7.1 Frontal adjustment 214,
7.2 Gravitational convection 220,
7.3 The "nearly homogeneous" fluid idealization 223,
7.4 Mean circulation on a nearly homogeneous shelf 232,
7.5 Surface elevation distribution 234,
8. Observed quasi-steady flow patterns in shallow seas 238,
8.0 Introduction 238,
8.1 Mean circulation in the Mid-Atlantic Bight 239,
8.2 Storm currents over Atlantic type shelves 242,
8.3 Evidence of moored instruments 258,
8.4 Mean circulation in Lake Ontario 262,
8.5 Mean circulation over the Oregon shelf 264,
References 267,
Index of names 275,
Index of subjects 278 " }
Author = "Daley, Roger"
Title = "Atmospheric Data Analysis"
Publisher = "Cambridge Univ. Press"
Year = "1991"
Pages = "457"
LOC = "QC 880 O35 1991"
ISBN = "0-521-38215-7"
Table of contents:
1. Introduction 1,
1.1 Atmospheric characteristics 2,
1.2 The ultimate problem in meteorology 6,
1.3 The observing system 8,
1.4 Subjective analysis 17,
1.5 Objective analysis: first attempts 19,
1.6 The data assimilation cycle 24,
1.7 Spatial analysis 29,
2. Function fitting 32,
2.1 Local polynomial fitting 32,
2.2 Least squares estimation 34,
2.3 The Gram matrix 41,
2.4 Underfitting, overfitting, and other problems 45,
2.5 The a posteriori analysis weights 49,
2.6 Multivariate function fitting 52,
2.7 Constrained minimization: penalty functions 58,
3. The method of successive corrections 64,
3.1 Basic formulation for a single correction 65,
3.2 The iteration cycle 69,
3.3 Spectral response: infinite continuous networks 71,
3.4 Spectral response: finite discrete networks 78,
3.5 Convergence properties 86,
3.6 Barnes' algorithm 90,
3.7 Iteration to the optimal solution 93,
4. Statistical interpolation: univariate 98,
4.1 Minimum variance estimation 99,
4.2 The statistical interpolation algorithm 101,
4.3 Background error covariances and correlations 107,
4.4 A continuous analogue 118,
4.5 Filtering and interpolation properties 125,
4.6 One, two, and multiple observation problems 131,
4.7 The vertical question 136,
4.8 Correlated observation error 137,
4.9 Misspecification of the background and observation
error 143,
5. Statistical interpolation: multivariate 150,
5.1 The multivariate algorithm 150,
5.2 Statistics of a homogeneous two-dimensional windfield 155,
5.3 The geopotential/wind covariances 164,
5.4 Multivariate filtering properties 169,
5.5 Multivariate versus univariate analysis 175,
5.6 A generalized algorithm 180,
6. The initialization problem 186,
6.1 Characterization of the synoptic and planetary scale
motion in the atmosphere 186,
6.2 Filtered models and initialized primitive equation
models 188,
6.3 The benefits of initialization 190,
6.4 A linearized shallow water model 194,
6.5 Initialization of the linearized shallow water model 200,
6.6 Geostrophic adjustment 202,
6.7 A brief history of initialization 208,
7. Quasi-geostrophic constraints 212,
7.1 The Hinkelmann-Phillips model 212,
7.2 Initialization of the Hinkelmann-Phillips model 215,
7.3 Scale analysis of the primitive equations 219,
7.4 Quasi-geostrophic initialization of the primitive
equations 223,
7.5 The linear balance equation 227,
7.6 The nonlinear balance equation 230,
7.7 The quasi-geostrophic omega equation 236,
7.8 The quasi-geostrophic potential vorticity equation 238,
7.9 The limitations of quasi-geostrophic initialization 240,
8. Variational procedures 242,
8.1 The stationary value of a function 243,
8.2 The stationary value of a definite integral 246,
8.3 Application to atmospheric analysis problems 251,
8.4 Weak constraint formulations 255,
8.5 Inequality constraints 257,
8.6 Four-dimensional variational analysis: Thompson's
scheme 258,
9. Normal mode initialization: theory 263,
9.1 The linearized baroclinic primitive equations 263,
9.2 The vertical structure equation 267,
9.3 The horizontal structure equation 270,
9.4 Horizontal structure functions (Hough modes) 274,
9.5 Normal mode form of the model equations 281,
9.6 The Machenhauer balance condition 284,
9.7 The Baer-Tribbia scheme 288,
10. Normal mode initialization: applications 292,
10.1 Some results from normal mode initialization
experiments 292,
10.2 Separation of slow and fast time scales 297,
10.3 The slow manifold 301,
10.4 Normal mode and quasi-geostrophic initialization 306,
10.5 Variational normal mode initialization 308,
10.6 Initialization for limited area models 314,
10.7 Convergence properties and diabatic initialization 316,
11. Dynamic initialization 322,
11.1 Damping time integration procedures 322,
11.2 Application to simple models 326,
11.3 Experiments with sophisticated models 329,
12. Continuous data assimilation 333,
12.1 The basic philosophy 333,
12.2 Damping time integration schemes 338,
12.3 Identical twin configurations: convergence of
solutions 339,
12.4 The effect of nonlinearities 345,
12.5 The effect of observation error 348,
12.6 Real data experiments: the rejection problem 353,
12.7 The geostrophic wind correction 355,
12.8 Dynamic relaxation 357,
12.9 Data assimilation on the slow manifold 360,
13. Future directions 363,
13.1 Descent methods 364,
13.2 Four-dimensional variational analysis 369,
13.3 The Kalman-Bucy filter 376,
13.4 Initialization by Laplace transform 384,
13.5 The bounded derivative initialization method 390,
13.6 Initialization of the hydrological cycle 391,
13.7 Mesocale data assimilation 394,
13.8 Data assimilation in the oceans 399,
13.9 New challenges 402,
Appendices 407,
References 439,
Index 455 " }
Author = "Deacon, Margaret"
Title = "Scientists and the Sea (1650-1900): A
Study of Marine Science"
Publisher = "Academic Press"
Year = "1971"
Pages = "445"
LOC = "GC 29 D3.8 1971"
ISBN = "0-12-207850-0"
Table of contents:
I. The background the the seventeenth century movement
1. The ancient world
2. The Middle Ages
3. The Renaissance
II. Marine science in the seventeenth century
4. The seventeenth century movement towards a science
of the sea
5. Theories and observations of tides
6. Marine science in the works of Robert Boyle
7. The currents in the Strait of Gibraltar
8. Robert Hooke and the vanishing harvest
III. An age of philosophy and curious navigation
9. Reawakening interest in the sea, 1700-1800
10. Widening horizons: The last quarter of the eighteenth century
11. Marine science in the early nineteenth century: A period
of growth
IV. The unsatisfied ocean
12. Wild-meeting oceans: The study of tides
13. The threshold of the deep ocean
14. The magnificent generalization
15. The voyage of the H.M.S. Challenger
16. Edinburgh and the growth of oceanography at the end
of the nineteenth century
Author = "Debnath, Lokenath"
Title = "Nonlinear Water Waves"
Publisher = "Academic Press, Inc."
Year = "1994"
Pages = "544"
LOC = "QA 927 D33 1994"
ISBN = "0-12-208437-3"
Table of contents:
1. Basic equations of motion of inviscid and viscous fluids 1,
1.1 Introduction 1,
1.2 The equation of continuity 2,
1.3 Equations of motion of an inviscid fluid 4,
1.4 Boundary conditions 6,
1.5 The energy equation and energy flux 9,
1.6 Variational principle for water waves 10,
1.7 General properties of irrotational fluid flows 12,
1.8 Irrotational flows with dipole far fields and added mass 16,
1.9 Equations of motion in a viscous fluid and some simple
exact solutions 22,
1.10 Energy dissipation in an incompressible viscous fluid 31,
2. The theory of surface waves on water 35,
2.1 Introduction 35,
2.2 Surface gravity waves on water of uniform finite depth 35,
2.3 Surface gravity waves on deep water 40,
2.4 Capillary-gravity waves on water 42,
2.5 The steady-state wave problem and the radiation condition 44,
2.6 Steady waves on a running stream 47,
2.7 Group velocity and its physical interpretation 51,
2.8 Nonlinear effects and Stokes waves 62,
2.9 Mass transport in water waves 74,
3. Transient wave motions in an inviscid fluid 81,
3.1 Introduction 81,
3.2 The two-dimensional Cauchy-Poisson problem 83,
3.3 The axisymmetric Cauchy-Poisson problem 89,
3.4 Two-dimensional surface waves in water due to an
oscillatory surface pressure 92,
3.5 The axisymmetric surface waves in deep water due to
an oscillatory surface pressure 103,
3.6 Lighthill's general theory of water waves due to
oscillating sources 106,
3.7 Surface waves on a running stream of water of arbitrary,
but uniform, depth 115,
3.8 Nonlinear theory of water waves by a moving pressure
distribution at resonant conditions 128,
4. Nonlinear shallow water waves and solitons 141,
4.1 Introduction 141,
4.2 The nonlinear shallow water equations 142,
4.3 Linear and nonlinear water waves on a sloping beach 148,
4.4 The Boussinesq and Korteweg-de Vries (KdV) equations 155,
4.5 The history of the soliton 157,
4.6 Solutions of the KdV equations, solitary and cnoidal
waves 161,
4.7 Conservation laws and nonlinear transformations 168,
4.8 A continuous (or Lie) group for the KdV equation,
similarity and rational solutions 171,
4.9 The inverse scattering transform (IST) method 174,
4.10 B{\'a}cklund transformations and a nonlinear
superposition principle 188,
4.11 The Lagrangian and Hamiltonian structures 195,
4.12 The Lax formulation and its KdV hierarchy 198,
4.13 Hirota's bilinear operator method for multisoliton
solutions 203,
5. Ship waves and wave resistance 209,
5.1 Introduction 209,
5.2 The Kelvin ship wave pattern 213,
5.3 Ship wave profile and its amplitude 223,
5.4 Wave resistance of ships 224,
5.5 Hydrodynamic forces on a body in terms of Kochin's
H-function 233,
5.6 Wave resistance due to an arbitrary motion of a pressure
area in deep water 239,
5.7 Wave resistance of a ship moving in a circular path 251,
5.8 Wave resistance in a uniformly moving submerged source
model 261,
5.9 Nonlinear analysis of the Kelvin ship-wave systems 263,
6. Nonlinear diffraction of water waves 271,
6.1 Introduction 271,
6.2 Morison's equation 272,
6.3 Basic equations of water waves in cylindrical polar
coordinates and boundary conditions 275,
6.4 Linear diffraction theory and Morison's coefficient 279,
6.5 Nonlinear wave forces on offshore structures and
nonlinear modification of the Morison equation 282,
6.6 Linearized diffraction of short water waves by a long
thin body 294,
6.7 Nonlinear diffraction of steady Stokes waves by a thin
wedge 298,
7. The theory of nonlinear dispersive waves 303,
7.1 Introduction 303,
7.2 Linear dispersive waves 304,
7.3 Initial value problems and asymptotic solutions 308,
7.4 Nonlinear dispersive waves 311,
7.5 Nonlinear dispersive wvaes and Whitham's equations 314,
7.6 Whitham's averaged variational principle and its
applications to water waves 317,
7.7 Lighthill's theory of nonlinear dispersive wave
systems 328,
7.8 The nonlinear Schr{\"o}dinger equation and solitary
waves 343,
7.9 Higher-order nonlinear Schr{\"o}dinger equations 370,
7.10 The nonlinear Schr{\"o}dinger equation in a dispersive
and dissipative fluid medium 382,
7.11 Averaged pseudo-variational principle, nonlinear
dispersive and dissipative wave trains 389,
8. Nonlinear instability of dispersive waves with applications
to water waves 397,
8.1 Introduction 397,
8.2 One-dimensional nonlinear wave equation and breaking
of water waves 400,
8.3 The Whitham instability theory and its applications to
water waves 413,
8.4 The Benjamin-Feir instability of water waves 418,
8.5 The Phillips theory of resonant interactions among
surface gravity waves 429,
8.6 Zakharov's integral equation for nonlinear deep water
waves 445,
8.7 The Rayleigh-Taylor linear instability problem in two
inviscid fluids 469,
8.8 The Rayleigh-Taylor nonlinear instability problem 472,
8.9 The Kelvin-Helmholtz linear instability problem in
two inviscid streams 477,
8.10 The Kelvin-Helmholtz nonlinear instability problem 481,
Bibliography 489,
Index 535" }
Author = "Defant, Albert"
Title = "Physical Oceanography: Vol. I"
Publisher = "MacMillan, N.Y."
Year = "1961"
Pages = "729"
LOC = "551.46 D313P V1 1961"
Table of contents:
PART I: ,
I. The ocean 1,
A. The horizontal extent and the structure of the ocean 1,
B. The three-dimensional structure of the ocean 10,
II. The sea-water and its physical and chemical properties 32,
III. Temperatures in the ocean, the 3-D temperature
distribution and its variation in time 88,
IV. The salinity of the ocean, its variation in oceanic
space and in time 154,
V. The density of water masses in the ocean, vertical
and horizontal density distribution and its stability 185,
VI. The [TS]-relationship and its connection with mixing
processes and large water masses 202,
VII. Evaporation from the surface of the sea and the water
budget of the earth 219,
VIII. Ice in the sea 243,
PART II - Dynamical oceanography ,
IX. The geophysical structure of the sea 299,
X. Forces and their relationship to the structure of the
ocean 312,
XI. The ocean at rest (statics of the ocean) 337,
XII. The representation of oceanic movements and kinematics 342,
XIII. General theory of ocean currents in a homogeneous sea 382,
XIV. Water bodies and stationary current conditions at
boundary surfaces 451,
XV. Ocean currents in a non-homogeneous ocean 476,
XVI. Currents in a strait 513,
XVII. Effect of wind on the mass field and on the density
current 544,
XVIII. Basic principles of the general oceanic circulation 556,
XIX. The tropospheric circulation 592,
XX. The stratospheric circulation 661,
XXI. The main features of the general oceanic circulation and
their physical exploration 694,
Bibliography 708,
Author index 721,
Subject index 725 " }
Title = Physical Oceanography: Vol. II
Author = Defant, Albert
Publisher = MacMillan, N.Y.
Year = 1961
Pages = 598
LOC = 551.46 D313P V2 1961
Table of contents:
PART I - Surface and long waves: ,
I. General remarks on waves 1,
1. Introduction 1,
2. Classification of waves 2,
3. Group velocity 12,
II. Theory of short and long waves 16,
1. Waves with harmonic wave profile (Stokes' waves) 16,
2. Further development of the Stokes wave theory 22,
3. Gerstner's rotational waves 26,
4. Short-crested waves 29,
III. Observations and measurements of ocean waves 31,
1. Testing of the theory by laboratory experiments 31,
2. Observation and measurement of ocean waves 33,
3. Comparison between theory and observations 40,
4. Stereophotogrammetric survey of the sea surface 46,
5. Apparent and real characteristics of waves, the complexity
of wind-generated waves 50,
6. The energy spectrum and the spectral analysis of
recordings of ocean waves 52,
7. Statistical relations between the different apparent
wave characteristics and their interpretation 57,
8. Scales of sea motion and wind 60,
9. The mathematical formulation of the actual ocean wave
pattern 63,
IV. Generation, growth and propagation of waves 66,
1. Observations of the generation of waves 66,
2. Propagation of a wave disturbance through a region
previously undisturbed 68,
3. Theories of the generation and the growth of waves 74,
4. Theory of the growing of significant waves by wind 87,
5. Observations on the growth of waves 93,
6. Growing of spectral components of the wind-generated sea 97,
7. Swell, observations and theory 99,
V. Shallow water wave transformation through external factors 109,
1. Shallow water waves; theory and observations 109,
2. The solitary wave of Scott Russell 116,
3. Changes in form of waves by exterior causes 120,
4. Surf on flat and steep coasts 123,
5. Calming effect of oil on waves 139,
VI. Long waves in canals and standing waves in entirely or
partly closed basins 142,
1. Long waves in canals 142,
2. Standing waves in closed basins 154,
3. The character of the oscillation of connected systems 175,
4. Observed standing waves in lakes, bays and adjacent seas 182,
5. Influence of the earth's rotation on tidal waves and
seiches 202,
6. Generation and growth of the oscillations of the sea and
lake surface 219,
7. Dislocation and explosion waves 237,
PART II - Tides and tidal currents ,
VII. Principle features of tidal phenomena 245,
VIII. The tide-generating forces 254,
IX. Theory of the tides 272,
X. The harmonic analysis of tidal observations 299,
XI. Tides and tidal currents in the proximity of land 320,
XII. Tides in the Mediterranean and adjeacent seas.
Observations and discussion 364,
XIII. Tides in estuaries 457,
XIV. Tides of the oceans 475,
XV. The tides in relation to geophysical and cosmic problems 504,
XVI. Internal waves 517,
Bibliography 571 " }
Editor = "Desaubies, Y. and A. Taranatola and J. Zinn-Justin"
Author = "Dietrich, Gunter"
Author = "Drazin, P., and W. Reid"
Author = "Dutton, John A."
Title = "Oceanographic and Geophysical Tomography"
Publisher = "North-Holland"
Pages = "463"
Year = "1990"
Note = "NATO Advanced Study Institute, Session L, Les Houches
{\'E}cole D'{\'e}t{\'e} de Physique Th{\'e}oretique"
LOC = "QE 501.3 E26 1988"
ISBN = "0-444-88779-2"
Table of contents:
1. Probabilistic foundation of inverse theory - A. Tarantola 1,
2. A short course on theoretical seismology - P. G. Richards 29,
3. Asymptotic theory of normal modes and surface waves -
B. Romanowicz 135,
4. Ocean acoustic tomography - Y. Desaubies 159,
5. Using data with models: Ill-posed adn time-dependent
ill-posed problems - C. Wunsch 203,
6. Seismic numerical modeling - D. Kosloff and D. Kessler 249,
7. Ocean seismo-acoustic modeling: Numerical methods -
F. B. Jensen 313,
8. A unifying view of inversion - P. Mora 345,
9. Inversion of low-frequency electromagnetic data -
T. Madden 375,
10. Inverse methods in ocean bottom acoustics - G. Frisk 409,
11. Some practical aspects of ocean acoustic tomography -
Bruce Cornuelle 439" }
Title = "General Oceanography: An Introduction"
Publisher = "John Wiley and Sons"
Year = "1963"
LOC = "63-17346"
Table of contents:
I. Geomorphology of the ocean bottom 1,
A. Topography of the ocean bottom 1,
1. Land and water distribution 1,
2. Boundaries and names of the oceans 1,
3. Oceanic areas 3,
4. The development of sounding methods: knowledge of
bottom relief 3,
5. Statistics of depth distribution 6,
6. Major topographical features of the ocean bottom 8,
7. Bottom topography of the various oceans 13,
B. Sediments of the ocean bottom 15,
1. Relation between marine sediments, bottom topography,
and oceanographic conditions 15,
2. Origin of the sediments 15,
3. Grain size distribution of the sediments 17,
4. Chemical composition of sediments 20,
5. Geographic distribution of sediment types 22,
6. Sediment stratification and sedimentation velocity 23,
C. Formation of the morphological forms 24,
1. Methods of investigating the morphology of the
ocean bottom 24,
2. Deep-sea trenches 26,
3. Deep-sea basins 27,
4. Margins of the deep-sea basins 30,
5. The continental slope 30,
6. The shelf 33,
7. The formation of the oceans 36,
II. Physical and chemical properties of ocean water 38,
1. Unique characteristics 38,
2. Salinity 48,
3. Pressure 51,
4. Density 52,
5. Compressibility 54,
6. Heat expansion and density maximum 55,
7. Viscosity and surface tension 57,
8. Heat conduction, specific heat, and heat of evaporation 60,
9. Adiabatic temperature changes 61,
10. Physical properties of sea water as a salt solution 63,
11. Austausch and mixing 64,
12. Acoustical properties 67,
13. Optical properties 73,
14. Electrical conductivity 83,
15. Physical properties of sea ice 83,
16. Trace elements in sea water 85,
17. Gases in sea water 86,
18. Organic substances in ocean water 88,
19. Suspended substances and living organisms in sea water 90,
III. Oceanographic instruments and observational methods 95,
A. Problems and requirements 95,
1. Observations at sea 95,
2. Fundamental requirements of observational techniques 96,
B. Conditions for observations 97,
1. Important auxiliary tools 97,
2. Research vessels 98,
3. Position determination 101,
4. Winches 102,
5. Water samplers 104,
6. Bottom sampler 107,
7. Laboratories on board ship 109,
C. Instruments and observational procedures 110,
1. Observations of variations in sea level 110,
2. Observations of surface waves 117,
3. Observation of water depth 120,
4. Temperature measurements 124,
5. Density determinations 129,
6. Salinity determinations 131,
7. Current measurements 135,
8. Measurement of the suspended material content 146,
9. Measurement of the content of dissolved substances 148,
IV. Heat budget of the world ocean 152,
1. Heat budget equation 152,
2. Radiation 154,
3. Heat exchange between ocean and atmosphere by direct
heat transfer 159,
4. Evaporation, condensation, and their determination 161,
5. Heat transfer from evaporation 164,
6. Total heat transfer between ocean and atmosphere 165,
7. Heat distribution in the ocean 169,
V. Oceanic distribution of temperature, salinity, density
and ice 172,
A. Temperature distribution 172,
1. Daily variation 172,
2. Annual variations 172,
3. Long-range variations 176,
4. Distribution of surface temperature 180,
5. Vertical temperature distribution 182,
B. The salinity distribution 186,
1. The oceanic water budget 186,
2. The distribution of surface salinity 190,
3. Vertical salinity distribution 192,
4. Variations in salinity 192,
C. Density distribution and characteristic water masses
in the ocean 196,
1. Density distribution 196,
2. The temperature-salinity relationship 197,
3. Formation of characteristic water masses 198,
4. Characteristic oceanic water masses 201,
D. Ice in the ocean 202,
1. Ice formation and types of ice 202,
2. Ice coverage of the ocean 205,
3. Ice patrols 206,
VI. The budget of substances in the ocean 214,
A. Ocean geochemistry 214,
B. Biochemistry of the ocean 229,
1. General biochemical fundamentals 229,
2. The energy production of organisms 241,
3. Production in the ocean 247,
4. The mechanism of plankton metabolism 258,
5. The carbon dioxide-calcium carbonate system 266,
6. Regional distribution of nutrients and oxygen 273,
7. Marine chemistry and fishing 276,
VII. The theory of ocean currents 291,
A. Statics 292,
1. Field of gravity 292,
2. Field of mas 294,
3. Field of pressure 295,
4. Determination of the relative field of pressure 299,
5. Representation of the relative field of pressure 300,
6. Stability of water stratification 301,
B. Kinematics 305,
1. Representation of the field of motion 305,
2. Current fields and continuity condition 309,
3. Application of the continuity condition to sea
water properties 311,
C. Dynamics 313,
1. Survey of acting forces 313,
2. The deflecting force of the earth's rotation 314,
3. Hydrodynamic equations of motion 317,
4. Stationary frictionless currents in a homogeneous
ocean 319,
5. Stationary frictionless currents in a two-layer
ocean 321,
6. Frictionless currents of stationary eddies in a
two-layer ocean 325,
7. Stationary frictionless currents in a continuously
stratified ocean 328,
8. Friction and turbulence 335,
9. Stationary currents in a homogeneous ocean caused by
friction and wind (drift currents) 340,
10. Stationary currents and bottom friction in a
homogeneous ocean 344,
11. Stationary currents and mixing 345,
12. Thermodynamics of ocean currents 349,
13. Recent developments in the theory of ocean currents 352,
VIII. Surface and internal waves 359,
A. Nature of water waves 359,
1. Fundamental problems in wave theory 359,
2. Wave classification and definition 360,
B. Surface waves 361,
1. Particle motion and the shape of waves 361,
2. Wave generation 367,
3. Wave spreading 369,
4. Growth of waves in sea 371,
5. Wave decay and swell 380,
6. Wave transformation; surf 382,
C. Internal waves 384,
1. Appearance of internal waves 384,
2. Short internal waves 386,
3. Long internal waves 388,
IX. Long waves and tidal waves 394,
A. Long waves 394,
1. Undisturbed long waves 394,
2. Transformation of long waves by reflection 398,
3. Long waves modified by the Coriolis force 405,
4. Long waves modified by friction 410,
B. Tide-producing forces 414,
1. Introduction to oceanic tidal phenomena 414,
2. The system of tide-producing forces 420,
3. Derivation of the tidal potential 425,
4. Harmonic development of the tidal potential 425,
C. Representation of tides 431,
1. Harmonic representation of tides and tidal currents 431,
2. Harmonic analysis of tide observations 433,
3. The harmonic method of tide prediction 436,
4. Tide characteristics 439,
D. Theory of ocean tides 441,
1. Theoretical problems of ocean tides 441,
2. Equilibrium theory of tides 443,
3. Classic hydrodynamic theories 444,
4. Geophysical theories 447,
E. Tidal phenomena in the world ocean 457,
1. Tides 457,
2. Tidal currents 462,
X. Regional oceanography 475,
A. Deep-sea circulation in the oceans 476,
1. Water masses of the cold-water sphere 476,
2. Polar bottom water 477,
3. Subpolar intermediate water 480,
4. Deep water 481,
5. Antarctic water masses 484,
6. Water masses of the warm-water sphere 487,
7. Circulation gyres of the water masses in the
Atlantic Ocean 493,
8. Deep water of the mediterranean and marginal seas 496,
B. Hydrographic regions ofthe world ocean 507,
1. Criteria for the regional classification 507,
2. Currents of the trade wind regions 511
3. Trade wind current regions with components directed
toward the equator 511,
4. Regions of trade wind currents with currents moving
westward 514,
5. Regions of the trade wind currents with components
directed toward the poles 518,
6. Regions of equatorial currents 518,
7. Regions of monsoon currents 524,
8. Regions of the horse latitudes 527,
9. Regions of the jet stream 529,
10. Regions of the west wind drift 537,
11. Polar regions 543,
12. Shelf areas 547,
Bibliography 550,
List of sources of figures and charts 567,
Author index 571,
Subject index 577 " }
Title = "Hydrodynamic Stability"
Publisher = "Cambridge Univ. Press"
Year = "1981"
Title = "The Ceaseless Wind: An Introcution to the Theory of
Atmospheric Motion"
Publisher = "Dover"
Year = "1986"
Pages = "617"
LOC = "QC 880.4 A8 D87 1986"
ISBN = "0-486-65096-0"
Table of contents:
1. To touch the wind 1,
2. Some basic physical and mathematical concepts of
atmospheric science 16,
3. Introduction to atmospheric thermodynamics 35,
4. The vertical structure of the atmosphere 60,
5. Vector and tensor analysis and the fundamental
kinematics of fluid flow 96,
6. The equations of motion in inertial coordinates 169,
7. Meteorological equations of motion 220,
8. Water in the air 256,
9. Air in motion: models of the winds 289,
10. The rotational component of the wind: vorticity and
circulation 332,
11. Atmospheric energetics: global thermodynamics to
turbulence 399,
12. Atmospheric wave motion 452,
13. Approximate equations of motion for small-scale flow 488,
14. The quasi-geostrophic theory for large-scale flow 512,
15. Atmospheric modeling and metamodeling 554,
Appendix 1 - The first law of thermodynamics 585,
Appendix 2 - International system of units/mathematical
symbols 588,
Appendix 3 - Useful formulas, identities and constants 592,
Index 599,
Index to Chapter 15 615 " }
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
S. Baum
Dept. of Oceanography
Texas A&M University
baum@astra.tamu.edu