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Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
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  • Cited by 97
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Wu, Wei and McFarquhar, Greg M. 2018. Statistical Theory on the Functional Form of Cloud Particle Size Distributions. Journal of the Atmospheric Sciences, Vol. 75, Issue. 8, p. 2801.

    Qi, Di and Majda, Andrew J. 2018. Rigorous Statistical Bounds in Uncertainty Quantification for One-Layer Turbulent Geophysical Flows. Journal of Nonlinear Science,

    Chada, Neil K Iglesias, Marco A Roininen, Lassi and Stuart, Andrew M 2018. Parameterizations for ensemble Kalman inversion. Inverse Problems, Vol. 34, Issue. 5, p. 055009.

    Dubinkina, Svetlana 2018. Relevance of conservative numerical schemes for an Ensemble Kalman Filter. Quarterly Journal of the Royal Meteorological Society, Vol. 144, Issue. 711, p. 468.

    San, Omer and Maulik, Romit 2018. Extreme learning machine for reduced order modeling of turbulent geophysical flows. Physical Review E, Vol. 97, Issue. 4,

    David, Tomos W Zanna, Laure and Marshall, David P 2018. Eddy-mixing entropy and its maximization in forced-dissipative geostrophic turbulence. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, Issue. 7, p. 073206.

    Okamoto, Hisashi 2018. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. p. 729.

    Boyd, John P. 2018. Dynamics of the Equatorial Ocean. p. 405.

    Majda, Andrew J. and Qi, Di 2017. Effective control of complex turbulent dynamical systems through statistical functionals. Proceedings of the National Academy of Sciences, Vol. 114, Issue. 22, p. 5571.

    Gibbon, John D and Holm, Darryl D 2017. Bounds on solutions of the rotating, stratified, incompressible, non-hydrostatic, three-dimensional Boussinesq equations. Nonlinearity, Vol. 30, Issue. 6, p. R1.

    Šverák, Vladimír 2017. Vector-Valued Partial Differential Equations and Applications. Vol. 2179, Issue. , p. 195.

    Spineanu, F and Vlad, M 2017. On the late phase of relaxation of two-dimensional fluids: turbulence of unitons. New Journal of Physics, Vol. 19, Issue. 2, p. 025004.

    Venaille, A. Gostiaux, L. and Sommeria, J. 2017. A statistical mechanics approach to mixing in stratified fluids. Journal of Fluid Mechanics, Vol. 810, Issue. , p. 554.

    Myerscough, Keith W. Frank, Jason and Leimkuhler, Benedict 2017. Observation-based correction of dynamical models using thermostats. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 473, Issue. 2197, p. 20160730.

    Natale, Andrea and Cotter, Colin J. 2017. Scale-selective dissipation in energy-conserving finite-element schemes for two-dimensional turbulence. Quarterly Journal of the Royal Meteorological Society, Vol. 143, Issue. 705, p. 1734.

    Yasuda, Yuki Bouchet, Freddy and Venaille, Antoine 2017. A New Interpretation of Vortex-Split Sudden Stratospheric Warmings in Terms of Equilibrium Statistical Mechanics. Journal of the Atmospheric Sciences, Vol. 74, Issue. 12, p. 3915.

    Chen, Nan and Majda, Andrew J. 2017. Beating the curse of dimension with accurate statistics for the Fokker–Planck equation in complex turbulent systems. Proceedings of the National Academy of Sciences, Vol. 114, Issue. 49, p. 12864.

    Majda, Andrew J. and Tong, Xin T. 2016. Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion. Journal of Nonlinear Science, Vol. 26, Issue. 5, p. 1483.

    Turkington, Bruce Chen, Qian-Yong and Thalabard, Simon 2016. Coarse-graining two-dimensional turbulence via dynamical optimization. Nonlinearity, Vol. 29, Issue. 10, p. 2961.

    Tong, Xin T. and Majda, Andrew J. 2016. Moment bounds and geometric ergodicity of diffusions with random switching and unbounded transition rates. Research in the Mathematical Sciences, Vol. 3, Issue. 1,

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Book description

The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.

Reviews

'… this book is a valuable contribution to the fascinating intersection of applied mathematics and geophysical fluid dynamics. … The authors are adept at illuminating and motivating rigorous mathematical analysis, qualitative models and physical intuition through exceptionally lucid exposition and a rich collection of examples.'

Source: Mathematical Reviews

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