Waves in Geophysical Fluids

Course Bibliography

• M. Berti, R. Grande, A. Maspero, G. Staffilani. Rogue waves and large deviations for 2D gravity deep-water waves . arxiv preprint arxiv:2510.15159
• R. Bianchini, A.-L. Dalibard, L. Saint-Raymond. Near-Critical Reflection of Internal Waves . Analysis & PDE (2021).
• Brouzet, C. Internal Wave Attractors: From Geometrical Focusing to Nonlinear Energy Cascade and Mixing . Ph.D. dissertation, ENS de Lyon, 2016.
• J.Y. Chemin, B. Desjardins, I. Gallagher, E. Grenier. Mathematical Geophysics: An Introduction to Rotating Fluids and to the Navier-Stokes Equations . Oxford University Press (2006).
• C. Cheverry, I. Gallagher, T. Paul, L. Saint-Raymond. Trapping Rossby Waves by Wind Forcing , Duke J. Math. 161, 845–892 (2012).
• Y. Colin de Verdière, L. Saint-Raymond. Attractors for Two-Dimensional Waves with Homogeneous Hamiltonians of Degree 0 . Comm. Pure App. Math. 73 (2020), 421–462.
• Y. Colin de Verdière. Spectral theory of pseudo-differential operators of degree 0 and an application to forced linear waves . Analysis & PDE (2020).
• Y. Colin de Verdière, J. Vidal. On gravito-inertial surface waves .https://arxiv.org/pdf/2402.12992
• B. Cushman-Roisin, J.M. Beckers. Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects . Academic Press, 2006.
• A.--L. Dalibard, L. Saint-Raymond. Mathematical study of rotating fluids with resonant surface stress , J. Differential Equations 246, 2304–2354 (2009).
• A.--L. Dalibard, L. Saint-Raymond. “Mathematical Study of the beta-plane model for rotating fluids in a thin layer .” Journal de mathématiques pures et appliquées 94, 131–169 (2010).
• A.--L. Dalibard, L. Saint-Raymond. Mathematical Study of degenerate boundary layers: A large-scale ocean circulation problem . Memoirs of the AMS (2018).
• Y. Deng and Z. Hani. Full derivation of the wave kinetic equation , Invent. Math. 233 (2023), 543–724.
• B. Desjardins, D. Lannes, J.-C. Saut. Normal mode decomposition and dispersive and nonlinear mixing in stratified fluids . Water Waves (2022).
• T. Buckmaster, P. Germain, Z. Hani, and J. Shatah. Onset of the wave turbulence description of the long-time behavior of the nonlinear Schrödinger equation , Invent. Math. (2021), 1–69.
• Dyatlov, S.; Zworski, M. Microlocal analysis of forced waves. Pure Appl. Analysis 1 (2019) 359–384.
• G. E. Fal’kovich, A. V. Shafarenko. On the stability of Kolmogorov spectra of weak turbulence , Physica D: Nonlinear Phenomena 27 (3) (1987), 399–411.
• I. Gallagher, L. Saint-Raymond. Mathematical study of the beta-plane model: equatorial waves and convergence results . Mémoires de la SMF 107 (2006).
• I. Gallagher, L. Saint-Raymond. On the influence of the Earth’s rotation on geophysical flows .
• Handbook of Mathematical Fluid Dynamics (2007).
• S. Galtier. A Multiple Time Scale Approach for Anisotropic Inertial Wave Turbulence . J. Fluid Mech. 974, A24 (2023).
• A.E. Gill. Atmosphere-Ocean Dynamics , Elsevier Science, 1982.
• E. Grenier. Pseudo-differential energy estimates of singular perturbation . Comm. Pure Appl. Math., 50 (1997), 821–865.
• Gostiaux, L.; Dauxois, T.; Didelle, H.; Sommeria, J.; Viboud, S. Quantitative laboratory observations of internal wave reflection on ascending slopes . Physics of Fluids 18 (2006).
• M. Jézéquel, J. Wang. Stationary internal waves in a two-dimensional aquarium at low viscosity . arxiv (2026).
• R. Klein, U. Achatz, D. Bresch, O.M. Kino, P.K. Smolarkiewicz. Regime of validity of soundproof atmospheric flow models . J. Atmospheric Sciences (2010).
• S. Klainerman, A. Majda. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids . Comm. Pure Appl. Math. 34 (1981), 481–524?
• J.L. Lions. Singular Perturbations in Boundary Value Problems and Optimal Control. Vol. 323, Springer Verlag, 1973.
• Maas, L.R.M.; Benielli, D.; Sommeria, J.; Lam, F.-P. A. Observation of an internal wave attractor in a confined stably stratified fluid . Nature 388 (1997), 557.
• Maas, L.; Lam, F.-P. Geometric focusing of internal waves . J. Fluid Mech. 300 (1995), 1.
• S. Nazarenko. Wave Turbulence , Vol. 825, Springer Science & Business Media, 2011.
• A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency ,” Physica D: Nonlinear Phenomena 152–153 (May 2001), 520–550.
• Ogilvie, G. “Wave attractors and the asymptotic dissipation rate of tidal disturbances .” J. Fluid Mech. 543 (2005), 19–44.
• J. Pedlosky. Geophysical Fluid Dynamics . Springer Verlag, 1987.
• J. Pedlosky. Ocean Circulation Theory . Springer Verlag, 1996.
• Rodda, C., Savaro, C., Davis, G., Reneuve, J., Augier, P., Sommeria, J., et al. (2022). Experimental observations of internal wave turbulence transition in a stratified fluid . Physical Review Fluids, 7(9).
• Rodda, C., Savaro, C., Bouillaut, V., Augier, P., Sommeria, J., & Mordant, N. (2023). Strongly nonlinear wave turbulence in stratified water . In European Turbulence Conference 18.
• F. Rousset. Asymptotic behavior of geophysical fluids in highly rotating fluids . ZAMP (2006).
• Ralston, J.V. On Stationary Modes in Inviscid Rotating Fluids . J. Math. Anal. Appl. 44 (1973), 366–383.
• Rieutord, M.; Valdettaro, L. Viscous dissipation by tidally forced inertial modes in a rotating spherical shell . J. Fluid Mech. 643 (2010), 363–394.
• S. Schochet. Fast singular limits of hyperbolic PDEs . J. Differential Equations 114 (1994), 476–512.
• S. Schochet, X. Xu. Toward uniform existence and convergence theorems for three-scale systems of hyperbolic PDEs with general initial data . CPDE (2022).
• G.K. Vallis. Atmospheric and Oceanic Fluid Dynamics. Fundamentals and Large-Scale Circulation . 2nd ed. Cambridge University Press; 2017.
• J. Vanneste. “Balance and spontaneous wave generation in geophysical flows ,” Annual Review of Fluid Mechanics 45 (2013), 147–172.