%AAA @article{abarbanel-brown-etal:1993, Author = "Abarbanel, H. D. I. and R. Brown and J. J. Siderowich and L. S. Tsimring", Title = "The analysis of observed chaotic data in physical systems", Journal = "Rev. Mod. Phys.", Volume = "65", Year = "1993", Pages = "1331--1392", Abstract = "Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical importance from such measurements. They discuss methods for (1) separating the signal of physical interest from contamination (``noise reduction''), (2) constructing an appropriate state space or phase space for the data in which the full structure of the strange attractor associated with the chaotic observations is unfolded, (3) evaluating invariant properties of the dynamics such as dimensions, Lyapunov exponents, and topological characteristics, and (4) model making, local and global, for prediction and other goals. They briefly touch on the effects of linearly filtering data before analyzing it as a chaotic time series. The emphasis throughout the review is on the tools one now has for the realistic study of measured data in laboratory and field settings. It is the goal of this review to bring these tools into general use among physicists who study classical and semiclassical systems. Much of the progress in studying chaotic systems has rested on computational tools with some underlying rigrous mathematics. Heuristic and intuitive analysis tools guided by the mathematics and realizable on existing computers constitute the core of this review.", Note = " \begin{enumerate} \item Introduction, \begin{enumerate} \item Observed chaos, \item Outline of the review, \end{enumerate} \item Signals, dynamical systems, and chaos, \item Analyzing measured signals--linear and nonlinear, \begin{enumerate} \item Signal separation, \item Finding the space, \item Classification and identification, \item Modeling--linear and nonlinear, \item Signal synthesis, \end{enumerate} \item Reconstructing phase space or state space, \begin{enumerate} \item Choosing time delays, \item Average mutual information, \item Choosing the embedding dimension, \item T and d_E, \end{enumerate} \item Invariants of the dynamics, \begin{enumerate} \item Density estimation, \item Dimensions, \item A seque--from geometry to dynamics, \item Lyapunov spectrum, \item Global exponents, \item Ideal case: Known dynamics, \item Real world: Observations, \item Local exponents from known dynamics and from observations, \item Topological invariants, \end{enumerate} \item Nonlinear model building: Prediction in chaos, \begin{enumerate} \item The dimension of models, \item Local modeling, \item Global modeling, \item In between local and global modeling, \end{enumerate} \item Signal separation--'noise reduction', \begin{enumerate} \item Knowing the dynamics: manifold decomposition, \item Knowing a signal: probabilistic cleaning, \item Knowing very little, \end{enumerate} \item Linearly filtered signals, \item Control and synchronization of chaotic systems, \begin{enumerate} \item Controlling chaos, \item Synchronization and chaotic driving, \end{enumerate} \item Spatio-temporal chaos, \item Conclusions, \begin{enumerate} \item Summary, \item Cloudy crystal ball gazing \end{enumerate} \end{enumerate}" } @article{abraham.f:1986, Author = "Abraham, Farid F.", Title = "Computational statistical mechanics: Methodology, applications and supercomputing", Journal = "Advances in Physics", Volume = "35", Year = "1986", Pages = "1--111", Note = " \begin{enumerate} \item Complexity is reality: gaining an understanding through computer simulation \item Methodology of computational statistical mechanics \begin{enumerate} \item Statistical mechanics concepts relevant for simulation \item Non-dynamical methods \item Dynamical methods \item The other important ingredients for doing a simulation \end{enumerate} \item Applications of computational statistical mechanics \begin{enumerate} \item Dynamics of two-dimensional condensation \item Two-dimensional melting of simple atomic systems \item Melting of quasi two-dimensional solid films \item The incommensurate phase of krypton on graphite \item The silicon crystal-melt interface and roughening \end{enumerate} \item Super computing in science \begin{enumerate} \item Super problems for super computers \item Supercomputers for super problems \end{enumerate} \end{enumerate}" } @article{airy:1842, Author = "Airy, G. B.", Title = "Tides and waves", Journal = "Encyclopedia Metropol., London", Year = "1842", Pages = "241--396" } @article{allen-barth-etal:1990, Author = "Allen, J. S. and J. A. Barth and P. A. Newberger", Title = "On intermediate models for barotropic continental shelf and slope flow fields. Part I: Formulation and comparison of exact solutions", Journal = "J. of Phys. Oceanogr.", Volume = "20", Year = "1990", Pages = "1017--1042", Note = " \begin{enumerate} \item Introduction \item Formulation \begin{enumerate} \item Shallow-water equations - SWE \item Quasi-geostrophic equations - QG \end{enumerate} \item Intermediate models \begin{enumerate} \item Intermediate model - IM \item Geostrophic vorticity - GV \item Geostrophic momentum - GM \item Salmon's equation - HP \item Balance equations - BE \item Linear balance equations - LBE \item Linear balance equations (potential vorticity conserving) - LQBE \item Hybrid balance equations - HBE \item Balance equations (based on momentum equations) - BEM \item Near balance equations - NBE \item Slow equations - SE \item Modified slow equations - MSE \end{enumerate} \item Limiting cases \begin{enumerate} \item Quasi-geostrophic limit \item Linear ageostrophic coastally-trapped waves \end{enumerate} \item Exact solutions of the shallow-water equations \item Exact solutions of the intermediate models \begin{enumerate} \item Intermediate model - IM \item Geostrophic vorticity - GV \item Geostrophic momentum - GM \item Salmon's equations - HP \item Balance equations - BE,HBE,BEM,NBE \item Linear balance equations - LBE,LQBE \item Quasi-geostrophic - QG \item Modified slow equations - MSE \end{enumerate} \item Comparison of exact solutions \item Summary of results \end{enumerate}" } @article{allen.j:1980, Author = "Allen, J. S.", Journal = "Models of wind-driven currents on the continental shelf", Journal = "ARFM", Volume = "12", Year = "1980", Pages = "389--433", Note = " \begin{enumerate} \item Introduction \item Observations \item Formulation \item Analytical models \item Numerical models \item Future work \end{enumerate}" } @article{ames-lee:1987, Author = "Ames, William F., and Ding Lee", Title = "Current developments in the numerical treatment of ocean acoustic propagation", Journal = "Applied Numerical Mathematics", Volume = "3", Year = "1987", Pages = "25--47", Note = " \begin{enumerate} \item Introduction, \item History of parabolic equation approximation, \item History of the first solution to the parabolic wave equation, \item A parade of parabolic wave equations, \item Improved parabolic wave solutions, \item The wide angle wave equation, \item Related unsolved remaining problems \end{enumerate}" } @article{anderson.d-willebrand:1992, Author = "Anderson, David L. T. and Jurgen Willebrand", Title = "Recent advances in modelling the ocean circulation and its effects on climate", Journal = "Rep. Prog. Phys.", Volume = "55", Year = "1992", Pages = "1--37", Note = " \begin{enumerate} \item Introduction \item Numerical circulation models \begin{enumerate} \item Governing equations \item Surface boundary conditions \item Parametrization of subgrid-scale processes \item Numerical implementation \end{enumerate} \item Observing the ocean circulation \begin{enumerate} \item Instruments and techniques \item The use of data with models \end{enumerate} \item Wind-driven circulation and the role of eddies \item Short-term climate variability \begin{enumerate} \item A description of ENSO \item Modelling ENSO \item Predicting ENSO \end{enumerate} \item Thermohaline circulation and long-term variability \item Concluding remarks \end{enumerate}" } @article{apel:1980, Author = "Apel, John R.", Title = "Satellite sensing of ocean surface dynamics", Journal = "Ann. Rev. of Earth and Planetary Sciences", Volume = "8", Year = "1980", Pages = "303--342", Note = " \begin{enumerate} \item Introduction \item Planetary scale phenomena \begin{enumerate} \item The Gulf Stream system \item Equatorial current systems \end{enumerate} \item Intermediate scale phenomena \begin{enumerate} \item Coastal eddies \item Upwelling \item Coastal and estuarine fronts \end{enumerate} \item Small-scale motions \begin{enumerate} \item Internal waves \item Surface waves \end{enumerate} \item Concluding remarks \end{enumerate} @incollection{arakawa:1986, Author = "Arakawa, Akio", Title = "Finite-difference methods in climate modeling", Booktitle = "Physically-Based Modelling and Simulation of Climate and Climatic Change", Editor = "M. E. Schlesinger", Year = "1986", Pages = "79-168", TOC = " 1. Introduction, 2. The governing equations, 3. Generalized vertical coordinate, 4. Comments on the upper and lower boundary conditions, 5. Vertical grid structure and resolution, I: Vertical wave propagation and computational mode, 6. Conservative vertical difference schemes, 7. Vertical grid structure and resolution, II: Quasi-geostrophic model, 8. Horizontal coordinates, 9. Geostrophic adjustment in the continuous case, 10. Geostrophic adjustment in discrete cases, 11. Conservative space finite-difference schemes for the two-dimensional advection equations with nondivergent current, 12. Conservative and bounded space finite-difference schemes for the general two-dimensional advection equation, 13. Finite-difference schemes for the nonlinear momentum equation" } Aref, Hassan, "The numerical experiment in fluid mechanics," J. Fluid Mech., Vol. 173, 1986, pp. 15-41. 1. Introduction 2. On the evolution of computing machines 3. Modi operandi 4. On algorithms 5. Simulation vs. animation 6. Outlook @article{argyris-faust-etal:1993, Author = "Argyris, John and Gunter Faust and Maria Haase", Title = "Routes to chaos and turbulence. A computational introduction", Journal = PhilTransA, Volume = "344", Year = "1993", Pages = "207--234", Keyword = "nonlinear dynamics, chaos, turbulence, numerical methods" } Note = " 1. Survey of the problem, 2. Routes to chaos, a. Landau's route to chaos, b. Ruelle-Takens scenario, c. The period doubling cascade: Feigenbaum's route to chaos, d. Quasi-periodic transition, e. A route to chaos via intermittency, 3. Remark to the concept of universality, 4. Conclusions and what next?" } @article{arking:1991, Author = "Arking, Albert", Title = "The radiative effects of clouds and their impact on climate", Journal = "Bull. Amer. Meterolog. Soc.", Volume = "71", Year = "1991", Pages = "795--813", TOC = " 1. Introduction, 2. Effect of clouds on earth radiation budget parameters, a. Early studies of sensitivity to cloud amount, b. Narrow-band satellite observations, c. Broad-band satellite observations, d. Comparison of the satellite-based estimates of cloud effect, 3. Sensitivity of cloud radiative effects to other cloud parameters and the environment, a. The environment, b. Macrophysical structure - sensitivity to cloud type, c. Microphysical structure - effects of aerosols on cloud properties, 4. Cloud feedback in climate models, a. Cloud feedback in response to doubled atmospheric CO2, b. Liquid water content and cloud microphysics feedback, c. Intercomparison of cloud cover feedback in GCMs, 5. Conclusion" } Arnold, V.I., A.B. Givental, "Symplectic geometry," In _Dynamical Systems IV_, V. I. Arnold, S. P. Novikov, eds., Springer-Verlag, N.Y., 1990, pp. 1--136. Chapter 1. Linear symplectic geometry 1. Symplectic space 2. Linear Hamiltonian systems 3. Families of quadratic Hamiltonians 4. The symplectic group Chapter 2. Symplectic manifolds 1. Local symplectic geometry 2. Examples of symplectic manifolds 3. The Poisson bracket 4. Langrangian submanifolds and fibrations Chapter 3. Symplectic geometry and mechanics 1. Variational principles 2. Completely integrable systems 3. Hamiltonian systems with symmetries Chapter 4. Contact geometry 1. Contact manifolds 2. Symplectificatoin and contact Hamiltonians 3. The method of characteristics Chapter 5. Langrangian and Legendre singularities 1. Lagrangian and Legendre mappings 2. The classification of critical points of functions 3. Singularities of wave fronts and caustics Chapter 6. Langrangian and Legendre cobordisms 1. The Maslov index 2. Cobordisms 3. Characteristic numbers Arnold, V.I., B.A. Khesin, "Topological methods in hydrodynamics," Ann. Rev. Fluid Mech., Vol. 24, 1992, pp. 145-166. Introduction 1. Invariants of motion for fluid flows 1.1 Hydrodynamics and Riemannian manifolds 1.2 Generalized superconductivity and barotropic fluid equations 2. Ergodic interpretation of hydrodynamics invariants 2.1 Main definitions for the three-dimensional case 2.2 Linking numbers in magnetohydrodynamics 2.3 Estimates of energy and helicity of vector fields 2.4 Ergodic meaning of multidimensional invariants 3. Differential geometry of diffeomorphism groups 3.1 Finiteness of the diameter for the group of volume-preserving diffeomorphisms 3.2 Infinite diameter of the symplectomorphism group 3.3 Curvatures of diffeomorphism groups BBB @incollection{backus:1971, Author = "Backus, George", Title = "Inference from inadequate and inaccurate data", Booktitle = "Mathematical Problems in the Geophysical Sciences: 2. Inverse Problems, Dynamo Theory, and Tides", Editor = "William H. Reid", Publisher = "American Mathematical Soc., Providence, R. I.", Year = "1971", Pages = "1--105", Note = " \begin{enumerate} \item Introduction \begin{enumerate} \item A qualitative variety of scientific inference \item Problems of nonlinearity \end{enumerate} \item Linear inference \begin{enumerate} \item Mathematical preliminaries \item Bounded linear inference on a Hilbert space \item Linear quelling \end{enumerate} \item Localized nonlinear infernece \begin{enumerate} \item Nonlinear quelling \item Differentiable nonlinear inference on Hilbert spaces \end{enumerate} \item Nonlocalized nonlinear inference \begin{enumerate} \item Formulation of the problem \item Examples from geophysics \end{enumerate} \end{enumerate}" } Baines, P. G., and P. A. Davies, "Laboratory studies of topographic effects in rotating and/or stratified fluids," In "Orographic effects in planetary flows," GARP Publ. Ser. No. 23, Geneva, WMO, 1980, pp. 233-299. @article{barnett-hasselmann:1979, Author = "Barnett, T. P. and K Hasselmann", Title = "Techniques of linear prediction, with application to oceanic and atmospheric fields in the tropical Pacific", Journal = "RGSP", Volume = "17", Year = "1979", Pages = "949--968" } Battjes, Jurjen A., Rodney J. Sobey, and M. J. F. Stive, "Nearshore circulation," In _The Sea, Vol. 9, Part A: Ocean Engineering Science_, John Wiley & Sons, N.Y., 1990, pp. 467-493. 1. Introduction 2. Types and scales of motion 3. Nearshore wave field a. Qualitative discussion b. Quantitative discussion 4. Vertical circulation 5. Horizontal circulation 6. Three-dimensional circulation 7. Summary and conclusions @Article{bell:1994, Author = "Bell, Gordon", Title = "Scalable, parallel computers: Alternatives, issues, and challenges", Journal = "Int. J. of Parallel Computing", Volume = "22", Year = "1994", Pages = "3--46", Note = " 1. Introduction, 2. Computer space taxonomy and scalable computers, 2.1 Single instruction streams, 2.2 Multiple instruction streams: Multicomputers, 2.3 Multiple instruction systems: Multiprocessors, 2.4 The alternatives and trade-off, 3. Evolution of smPs, networks, and smCs to smPs, 3.1 Multiprocessor evolution: Supercomputers, mainframes, and minicomputers, 3.2 Workstation evolution, 3.3 Experimental scalable multicomputers for parallel processing, 4. Applications parallelism, benchmarks, and computer characteristics, 4.1 Benchmarks and real application performance (RAP), 4.2 Metrics and balance for scalable computers, 5. Future scalable, distributed general purpose computers, 5.1 The computing nodes, 6. Summary" } Bendjoya, Ph., and E. Slezak, "Wavelet analysis and applications to some dynamical systems," Celestial Mech. and Dynam. Astronomy, Vol. 56, 1993, pp. 231-262. 1. Introduction 2. The available tools 2.1 The Fourier transform 2.2 The window Fourier transform 2.3 The wavelet transform 3. Wavelets and the solution of differential equations 3.1 Interpolation bases 3.2 Application to the regularized Burgers equation 4. Fractals and turbulence 4.1 Fractals 4.2 The fully developed turbulence 5. The wavelet cluster analysis 5.1 Conclusion Benjamin, T. Brooke, "Impulse, flow force and variational principles," IMA Journal of Applied Mathematics, Vol. 32, 1984, pp. 3-68. 1. Introduction 2. Systems of differential equations with one space variable 3. Pseudo-differential equations in Hamiltonian form 4. Systems with several space variables 5. Dynamics of vorticity 6. Water waves 7. Clebsch transformations Benton, E. R., and A. Clark, Jr., "Spin-up," Ann. Rev. of Fluid Mech., Vol. 6, 1974, pp. 257-280. @article{berger:1988, Author = "Berger, A.", Title = "Milankovitch theory and climate", Journal = "Rev. of Geophys.", Volume = "26", Year = "1988", Pages = "624--657", TOC = " 1. Introduction, 2. Paleoclimates and Quaternary glacial-interglacial cycles, 3. Astronomical theory of paleoclimates: a historical point of view, 4. Earth's orbital parameters, 5. Spectra of geological records, 6. Astronomical insolation, 7. Paleoclimate modeling, 8. Conclusions" } Berkooz, Gal, Philip Holmes, and John L. Lumley, "The proper orthogonal decomposition in the analysis of turbulent flows," Ann. Rev. Fluid Mech., Vol. 25, 1993, pp. 539-575. 1. Introduction 1.1 The problems of turbulence 1.2 Experiments, simulations, analysis and understanding 1.3 The proper orthogonal decomposition 2. Fundamentals of the proper orthogonal decomposition 2.1 The eigenvalue problem 2.2 The span of the empirical basis 2.3 Optimality 2.4 Symmetries and homogeneity 2.5 The nature of attractors 2.6 Computational schemes and further results 3. POD in data description and analysis 3.1 Wall-bounded flows 3.2 Free shear flows 3.3 Convection 3.4 Mathematical models 4. POD in dynamical modeling 4.1 Direction simulations using POD 4.2 Models based on the POD 5. Relation to other techniqes 5.1 Linear stochastic estimation 5.2 Conditional sampling 5.3 Pattern-recognition techniques 6. Discussion Berlage, H. P., "The Southern Oscillation and world weather," K. Ned. Meteorol. Inst., Meded. Verh., Vol. 88, 1966, pp. 1-152. Besnard, Didier, Francis H. Harlow, Norman L. Johnson, Rick Rauenzahn, and Jonathan Wolfe, "Instabilities and turbulence," Los Alamos Science, 1987, pp. 145-174. 1. What is turbulence? a. Molecular systems b. Turbulent eddies and mean flow 2. Turbulence energy: sources and sinks a. Turbulence sinks 3. Transport modeling of turbulence a. Ensemble averages b. Reynolds stress transport equation c. Advection, mean-flow source, and rotation d. Triple correlation e. Driving force f. Diffusion and decay 4. Simpler transport models and examples of their application 5. Current research a. Two-phase flow b. Density gradients c. Supersonic turbulence 6. Concluding remarks @inproceedings{beyn:1991, Author = "Beyn, Wolf--J\"urgen", Title = "Numerical methods for dynamical systems", Booktitle = "Advances in Numerical Analysis - Vol. 1: Nonlinear Partial Differential Equations and Dynamical Systems", Editor = "Will Light", Publisher = "Clarendon Press, Oxford", Year = "1991", Pages = "175--236", ISBN = "0-19-853438-8", LOC = "QA 297 A38 1991 V.1", Note = " 1. Basic phenomena and numerical problems, 2. The direct computation of stationary points, periodic orbits and more general invariant manifolds, 3. Singular points in one--parameter systems, 4. Two--parameter problems, 5. The longtime behavior of integration methods" } Author = "Birkhoff, Garrett", Title = "Sound waves in fluids", Journal = "Applied Numerical Mathematics", Volume = "3", Year = "1987", Pages: "3--24", Comments: " 1. Introduction, A. Geometrical acoustics, 2. Fermat and Huygens, 2.1 Stratified media, 3. Fresnel's model, 3.1 Acoustic applications, 4. Hamilton-Jacobi equations, 4.1 Riemannian manifolds, 5. Eikonal function, B. Wave equations, 6. General remarks, 6.1 Fourier analysis in time, 6.2 Normal modes, 6.3 Plane waves, 7. Similarity solutions, 7.1 Mathematical models versus physical reality, 8. Reduced wave equation, 8.1 Simple waves, 9. Kirchoff's formulas, 9.1 Acoustic analogy, 10. Inhomogeneous elastic fluids, C. Numerical experiments, 11. Introduction, 12. One-dimensional sound waves, 13. Inhomogeneous fluids, 14. Testing 'ray theory', 15. Inhomogeneous fluids " Bjerknes, V. W., and W. Sandstrom, "Dynamic meteorology and hydrography. Part 1: statics," Carnegie Inst., Publ. No. 88, 1910, pp. 1-146. Blumberg, Alan F., and Li-Yaew Oey, "Modeling circulation and mixing in estuaries and coastal oceans," Advances in Geophysics, Vol. 28A, 1985, pp. 525-547. 1. Introduction 2. Some problems 3. Models and model results and interpretations a. Two-dimensional vertically integrated models b. Two-dimensional models with vertical structure c. Three-dimensional models 4. Future directions and concluding remarks @incollection{borgman:1972, Author = "Borgman, Leon E.", Title = "Statistical models for ocean waves and wave forces", Booktitle = "Advances in Hydroscience", Editor = "Ven Te Chow", Volume = "8", Year = "1972", Pages = "139--181", TOC = " I. Introduction, II. A variety of statistical models for ocean waves, A. A preliminary deterministic model, B. The sea surface as a stationary, second-order stochastic process, C. The Gaussian model for the ocean wave surface, D. The narrow-band model for wave heights, E. Some general comments, III. Statistical properties of wave forces on piling, A. Force relationshps for the general Gaussian model, B. Forces for waves with a narrow-band spectrum, IV. Estimation of force formula coefficients, A. Deterministic fitting methods, B. Statistical fitting methods, V. Some final comments" } Borgman, Leon E., "Irregular ocean waves: kinematics and forces," In _The Sea, Vol. 9, Part A: Ocean Engineering Science_, John Wiley & Sons, N.Y., 1990, pp. 121-168. 1. Introduction 2. A summary of formulas for linear wave theory a. A general coordinate system b. Basic wave properties c. Wave properties in complex form d. Irregular waves by superposition e. Irregular waves in frequency domain f. The fast Fourier transform algorithm g. Wave properties in the FFT format 3. The complex-valued amplitude matrix a. Characterization of irregular waves b. The Ochi-Hubble spectra formula c. The wrapped normal spreading function d. Random simulations of irregular waves e. Conditional simulation of irregular waves f. The multivariate normal probability density g. The conditional normal density h. A basic conditional simulation method i. Conditional simulation of complex wave amplitudes j. Frequency domain conditioning k. Time domain conditioning 4. Techniques for compliant structures a. Stretching b. Software c. Statistics of random wave geometry d. Wave group simulation @incollection{bourke:1986, Author = "Bourke, William", Title = "Spectral methods in global climate and weather prediction models", Booktitle = "Physically-Based Modelling and Simulation of Climate and Climatic Change", Editor = "M. E. Schlesinger", Year = "1986", Pages = "169--220", TOC = " 1. Introduction, 2. Basic mathematics of spherical harmonics, 3. Alternative spherical basis functions, 4. Spectral model algebra, a. Nondivergent vorticity equation, b. Quadratic invariants, c. Transform method, 5. Multi-level spectral model, a. Prognostic equations, b. Prognostic equations in spectral form, c. Transform grid operations, 6. Model linearizations, a. Normal modes, b. Semi-implicit time differencing, 7. Spectral model computer coding, a. BMRC model code, b. ECMWF model code, 8. Applications of global spectral models, a. Numerical weather prediction, b. General circulation simulations, 9. Conclusions" } Bourke, W., B. McAvaney, K. Puri, and R. Thurling, "Global modelling of atmospheric flow by spectral methods," In _Methods in Computational Physics_, Vol. 17, Chang, ed., 1977, pp. 267-324. @article{bowler-kenway:1987, Author = "Bowler, K. C. and R. D. Kenway", Title = "Physics on parallel computers. Part 1: The new technology", Journal = "Contemp. Phys.", Volume = "28", Year = "1987", Pages = "573--598", Note = " 1. Computational science, 1.1 Introduction, 1.2 New science, 1.3 The scale of the enterprise, 2. Parallelism, 2.1 The concept, 2.2 Types of parallelism, 3. Parallelism in computer architectures, 3.1 Introduction, 3.2 Parallel architectures, 3.3 Software for parallel computers, 3.4 Cost-effectiveness, 4. Parallel algorithms, 4.1 Introduction, 4.2 Event parallelism, 4.3 Geometric parallelism, 4.4 Algorithmic parallelism, 5. Concluding remarks" } @article{boyd:1990, Author = "Boyd, John P.", Title = "New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly nonlocal solitary waves, and numerical boundary value algorithms", Journal = "Adv. in Appl. Mechanics", Volume = "27", Year = "1990", Pages = "1--82", TOC = " I. Introduction, II. Polycnoidal waves, A. Definition and overview, B. Variational principle, C. Nonlinear Fourier transform, D. Theta functions, E. The phase variable boundary value problem and the Stokes series, F. Polycnoidal waves in two space dimensions, III. Periodic (``cnoidal'') waves as exact imbricate series of solitons, A. Background: Constructing periodic solutions from soliton trains, B. Imbricate series and the Poisson summation formula, C. Generalizations and open problems, IV. Numerical boundary value algorithms for direct computation of solitons, A. Introduction, B. A catalogue of direct computations of solitons, C. The Newton/Pseudospectral/Continuation polyalgorithm: A closer look, D. The nonlinear Richardson (``Newton flow'') iteration and other artificial time methods, E. Suggestions and guidelines, V. Weakly nonlocal solitary waves, A. Introduction, B. Far field analysis, C. Perturbation theory, D. Numerical methods: Ignorance, the radiation basis, and cnoidal matching, E. Physical illustrations: Rossby waves, Higgs bosons, and the slow manifold, F. Summary: The generalization of the concept of a ``solitary wave''" } Boyd, J. P., "Nonlinear equatorial waves," In _Nonlinear Topics in Ocean Physics_, A. R. Osborne, ed., North-Holland, 1991, pp. 51-97. 1. Introduction 2. Solitary and cnoidal waves 3. The improbable solitary wave and the soliton paradox 4. The unsolitary solitary wave: the strong overlap between the cosine and soliton regimes 5. Secularity: one-dimensional evolution equations for three-dimensional waves 6. The nonlinearity taxonomy of equatorial waves 7. Nonlinear equatorial Kelvin waves: wave-breaking and the formation of fronts 8. Nonlinear equatorial Kelvin waves in mean currents: Korteweg-de- Vries solitons 9. Long Rossby waves: derivation of the Korteweg-de Vries equation 10. Phenomenology of the Korteweg-de Vries equation 11. Equatorial modons 12. Rossby solitary waves in numerical models 13. Strong dispersion and envelope solitions: the nonlinear Schrodinger equation 14. Resonant triads 15. Continuous stratification 16. Summary and open problems Boyd, J. P., "Weakly nonlocal solitary waves," In _Nonlinear Topics in Ocean Physics_, A. R. Osborne, ed., North-Holland, 1991, pp. 527-555. 1. Introduction 2. Far-field analysis 3. The exponential smallness of the far-field oscillation 4. The glory and the failure of perturbation theory for weakly nonlocal solitary waves 5. Numerical algorithms for nonlocal solitons: ignorance, the radiation basis and cnoidal matching 6. The far-field phase parameters 7. Example one: equatorial Rossby solitons with n >= 3 8. Example two: the psi**4 breather 9. Example three: the "slow manifold" of numerical weather prediction 10. Summary and open problems @article{bretherton:1982, Author = "Bretherton, Francis P.", Title = "Ocean climate modeling", Journal = "Prog. Oceanog.", Volume = "11", Year = "1982", Pages = "93-129", TOC = " 1. Introduction, 2. An oceanographer's model of the atmosphere, 3. The mixed layer and the seasonal thermocline, 4. Equatorial time dependent motions, 5. The general circulation, 6. The future" } Bretherton, Francis P. "The general linearised theory of wave propagation," - 1. Concepts 2. Wave kinematics 3. Internal gravity waves 4. Slowly varying wave trains (geometrical optics) 5. Wave energy and wave action 6. Radiation stress, wave energy, and the mean flow @article{bricker-rice:1993, Author = "Bricker, Owen P. and Karen C. Rice", Title = "Acid rain", Journal = "Ann. Rev. Earth Planet. Sci.", Volume = "21", Year = "1993", Pages = "151--174", TOC = " 1. Introduction, 2. Atmospheric deposition, 3. Watershed processes, 4. Acid rain effects, a. Surface waters, b. Groundwaters, c. Forests, d. Materials, 5. Remediation, 6. Summary" } Brink, K. H., "Coastal-trapped waves and wind-driven currents over the continental shelf," Ann. Rev. Fluid Mech., Vol. 23, 1991, pp. 389-412. 1. Introduction 2. Coastal-trapped-wave models 3. Stochastic models of wind-driven currents 4. Critique 5. Conclusions Bryan, Kirk, "Models of the world ocean," Dyn. of Atmos. and Oceans, Vol. 3, 1979, pp. 327-338. 1. Introduction 2. Two-layer global models 3. Multi-level models 4. A model of water mass formation and poleward heat transport @article{bryan:1982, Author = "Bryan, Kirk", Title = "Poleward heat transport by the oceans: Observations and models", Journal = "Ann. Rev. Earth Planet. Sci.", Volume = "10", Year = "1982", Pages = "15--38" } Bryan, Kirk, "Modeling ocean circulation," Advances in Geophysics, - , 1985, pp. 433-459. 1. Introduction 2. The model 3. Zonally averaged transports of mass, heat and potential vorticity 4. Pycnocline structure 5. Transient response 6. Tritium simulations 7. Summary Bryan, Kirk, "Potential vorticity in models of the ocean circulation," Q. J. R. Meteorol. Soc., Vol. 113, 1987, pp. 413-734. 1. Introduction 2. Potential vorticity as a diagnostic field variable 3. Theories for the potential vorticity distribution in the thermocline 4. Observed potential vorticity fields 5. Numerical experiments based on the primitive equations and isopycnal coordinates 6. An eddy-resolving, primitive equation model 7. Budget of potential vorticity 8. Mesoscale eddies and poleward heat transport 9. Discussion Buzyna, G. and G. Veronis, "Spin-up of a stratified fluid: theory and experiment," J. Fluid Mech., Vol. 50, 1971, pp. 579-608.