Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

By Andrew J. Majda, Xiaoming Wang. 2006

421 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9e89ec5c82eaf4e76ba61f6128d0c455e40b1400

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Citations in the corpus

Small scale creation for solutions of the incompressible two dimensional Euler equation (2013, methodology): “Plausible conjectures can be made using methods of Statistical Mechanics, see for example [18, 21, 22, 16], in which one relies on conserved quantities and ergodicity-type (mixing) assumptions (rather than the actual dynamics).”
Challenges in Climate Science and Contemporary Applied Mathematics (2012, methodology): “This asymmetric functional on probability densities, P(p, q), has two attractive features [70, 81, 86] as a metric for model fidelity : (i) P(p, q) ≥ 0 with equality if and only if p = q; (ii) P(p, q) is invariant under general nonlinear changes of variables.”
Filtering Complex Turbulent Systems (2012, methodology): “It is widely used as a test model for algorithms for prediction, filtering, and low frequency climate response [96, 108].”
On the modelling of equatorial waves (2012, background): “Note also that we can not take advantage of the geostrophic balance that proved so useful at mid-latitudes [cf. Gallagher and SaintRaymond, 2007; Majda and Wang, 2006].”
On the Euler equations of incompressible fluids (2007, background): “Stochastic models also have applications to modeling based on information theoretical ideas in geophysics and atmospheric science ([106]).”
The dynamics of waves interacting with the Equatorial Undercurrent (2015, methodology): “…approximation, note that half of the Earth lies at latitudes of less than 30◦ and in these regions, when the spatial scale of an oceanatmosphere motion is of the order of 1000 km, then the use of the β-plane approximation is appropriate; see the discussions in Gill (1982) and Majda and Wang (2006).”
The physics of climate variability and climate change (2019, background): “from statistical mechanics and nonequilibrium thermodynamics have, therefore, to be considered (Bouchet and Sommeria, 2002; Farrell and Ioannou, 1996; Lucarini et al., 2014; Lucarini and Sarno, 2011; Majda and Wang, 2006; Robert and Sommeria, 1991; Trefethen et al., 1993), and will be discussed in S”
On the arrest of inverse energy cascade and the rhines scale (2006, background): “Such an interpretation applies to unforced flows considered by Rhines (1979) in great detail (see also Majda and Wang 2006, chapters 10–13).”
Ensemble Kalman methods for inverse problems (2012, background): “035 this solution is stable (see [26], Chapter 2 for details).”