Skip to main content
Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 97
  • Cited by
    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,


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.


'… 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

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content items to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed