gfd_in_dedalus

A collection of computer simulations of GFD models using the Dedalus solver.

https://github.com/empyreal092/gfd_in_dedalus

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A collection of computer simulations of GFD models using the Dedalus solver.

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  • Host: GitHub
  • Owner: Empyreal092
  • Language: Jupyter Notebook
  • Default Branch: main
  • Homepage:
  • Size: 51.9 MB
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Created almost 3 years ago · Last pushed about 2 years ago
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README.md

GFD in Dedalus

This is a collection of computer simulations of Geophysical Fluid Dynamics (GFD) models using the Dedalus version 3 solver. The typed-up note is here, and the codes are in the folders organized by problems solved.

The examples in this note expand on the examples provided by the Dedalus documentation. We also implement some common functions used in GFD studies. Now we list all the models in the note:

  • Barotropic vorticity model
    • Implement CFL-based adaptive timestep for models where velocities are based on streamfunctions.
    • Include function for calculating spectra for doubly periodic fields.
    • Solve the Stommel and Munk model on the circle. The only curvilinear example in the note.
  • 2D QG-Near Inertial Wave (QG-NIW) model
  • The Quasi-Geostrophic (QG) model
    • Baroclinically unstable two-layer QG
    • Rossby wave in linear QG
  • Baroclinic modes of arbitrary stratification
  • Linear instability of 3DQG
    • Greatly expands on the eigenproblem example provided by the Dedalus documentation. In particular, we show how to obtain eigenvectors for a particular field.

Please contact us if you find any mistakes. Please consider contributing to this note.

Owner

  • Name: Ryan Shìjié Dù
  • Login: Empyreal092
  • Kind: user
  • Company: CAOS, Courant Institute, NYU

Ph.D. student in Atmosphere Ocean Science and Mathematics at CAOS, Courant Institute

Citation (citation.bib)

@article{Vallis_16,
  title = {Geophysical Fluid Dynamics: Whence, Whither and Why?},
  shorttitle = {Geophysical Fluid Dynamics},
  author = {Vallis, Geoffrey K.},
  date = {2016-08},
  journaltitle = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume = {472},
  number = {2192},
  pages = {20160140},
  publisher = {{Royal Society}},
  doi = {10.1098/rspa.2016.0140}
}

@article{RochaEtAl_18,
  title = {Stimulated Generation: Extraction of Energy from Balanced Flow by near-Inertial Waves},
  shorttitle = {Stimulated Generation},
  author = {Rocha, Cesar B. and Wagner, Gregory L. and Young, William R.},
  date = {2018-07},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {847},
  pages = {417--451},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2018.308},
  langid = {english}
}

@article{Vallis_96a,
  title = {Potential Vorticity Inversion and Balanced Equations of Motion for Rotating and Stratified Flows},
  author = {Vallis, Geoffrey K.},
  date = {1996},
  journaltitle = {Quarterly Journal of the Royal Meteorological Society},
  volume = {122},
  number = {529},
  pages = {291--322},
  issn = {1477-870X},
  doi = {10.1002/qj.49712252912},
  langid = {english}
}

@article{WagnerYoung_15,
  title = {Available Potential Vorticity and Wave-Averaged Quasi-Geostrophic Flow},
  author = {Wagner, Gregory L. and Young, William R.},
  date = {2015-12},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {785},
  pages = {401--424},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2015.626},
  langid = {english}
}

@article{WagnerYoung_16,
  title = {A Three-Component Model for the Coupled Evolution of near-Inertial Waves, Quasi-Geostrophic Flow and the near-Inertial Second Harmonic},
  author = {Wagner, Gregory L. and Young, William R.},
  date = {2016-09},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {802},
  pages = {806--837},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2016.487},
  langid = {english}
}

@article{XieVanneste_15,
  title = {A Generalised-{{Lagrangian-mean}} Model of the Interactions between near-Inertial Waves and Mean Flow},
  author = {Xie, Jin-Han and Vanneste, J.},
  date = {2015-07-10},
  journaltitle = {Journal of Fluid Mechanics},
  shortjournal = {J. Fluid Mech.},
  volume = {774},
  pages = {143--169},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2015.251},
  langid = {english}
}

@article{Xie_20,
  title = {Downscale Transfer of Quasigeostrophic Energy Catalyzed by Near-Inertial Waves},
  author = {Xie, Jin-Han},
  date = {2020-12},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {904},
  pages = {A40},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2020.709},
  langid = {english}
}

@article{AsselinYoung_19,
  title = {An Improved Model of Near-Inertial Wave Dynamics},
  author = {Asselin, Olivier and Young, William R.},
  date = {2019-10},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {876},
  pages = {428--448},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2019.557},
  langid = {english}
}

@software{Conn_2023,
  author = {Conn, Scott},
  title = {{2DYBJ-QG}},
  url = {https://github.com/scott-conn/2DYBJ-QG},
  year = {2023}
}

@article{AscherEtAl_97,
  title = {Implicit-Explicit {{Runge-Kutta}} Methods for Time-Dependent Partial Differential Equations},
  author = {Ascher, Uri M. and Ruuth, Steven J. and Spiteri, Raymond J.},
  date = {1997-11-01},
  journaltitle = {Applied Numerical Mathematics},
  shortjournal = {Applied Numerical Mathematics},
  series = {Special {{Issue}} on {{Time Integration}}},
  volume = {25},
  number = {2},
  pages = {151--167},
  issn = {0168-9274},
  doi = {10.1016/S0168-9274(97)00056-1},
  langid = {english}
}

@article{MajdaEtAl_97,
  title = {A {{One-Dimensional Model}} for {{Dispersive Wave Turbulence}}},
  author = {Majda, A J and Mclaughlin, D W and Tabak, E G},
  date = {1997},
  journaltitle = {J. Nonlinear Sci},
  volume = {6},
  pages = {9--44},
  doi = {10.1007/BF02679124}
}

@article{PierrehumbertEtAl_94,
  title = {Spectra of Local and Nonlocal Two-Dimensional Turbulence},
  author = {Pierrehumbert, Raymond T. and Held, Isaac M. and Swanson, Kyle L.},
  date = {1994-06-01},
  journaltitle = {Chaos, Solitons \& Fractals},
  shortjournal = {Chaos, Solitons \& Fractals},
  series = {Special {{Issue}}: {{Chaos Applied}} to {{Fluid Mixing}}},
  volume = {4},
  number = {6},
  pages = {1111--1116},
  issn = {0960-0779},
  doi = {10.1016/0960-0779(94)90140-6},
  langid = {english}
}

@article{SmithEtAl_02,
  title = {Turbulent Diffusion in the Geostrophic Inverse Cascade},
  author = {Smith, K. S. and Boccaletti, G. and Henning, C. C. and Marinov, I. and Tam, C. Y. and Held, I. M. and Vallis, G. K.},
  date = {2002-10},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {469},
  pages = {13--48},
  publisher = {{Cambridge University Press}},
  issn = {1469-7645, 0022-1120},
  doi = {10.1017/S0022112002001763},
  langid = {english}
}

@article{VallgrenLindborg_11,
  title = {The Enstrophy Cascade in Forced Two-Dimensional Turbulence},
  author = {Vallgren, Andreas and Lindborg, Erik},
  date = {2011},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {671},
  pages = {168--183},
  issn = {00221120},
  doi = {10.1017/S0022112010005562},
}

@article{CalliesEtAl_16,
  title = {The Role of Mixed-Layer Instabilities in Submesoscale Turbulence},
  author = {Callies, Jörn and Flierl, Glenn and Ferrari, Raffaele and Fox-Kemper, Baylor},
  date = {2016-02-10},
  journaltitle = {Journal of Fluid Mechanics},
  shortjournal = {J. Fluid Mech.},
  volume = {788},
  pages = {5--41},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2015.700},
  langid = {english}
}

@article{Eady_49,
  title = {Long {{Waves}} and {{Cyclone Waves}}},
  author = {Eady, E. T.},
  date = {1949},
  journaltitle = {Tellus},
  volume = {1},
  number = {3},
  pages = {33--52},
  issn = {2153-3490},
  doi = {10.1111/j.2153-3490.1949.tb01265.x},
  issue = {3},
  langid = {english}
}

@article{TullochSmith_09,
  title = {A {{Note}} on the {{Numerical Representation}} of {{Surface Dynamics}} in {{Quasigeostrophic Turbulence}}: {{Application}} to the {{Nonlinear Eady Model}}},
  shorttitle = {A {{Note}} on the {{Numerical Representation}} of {{Surface Dynamics}} in {{Quasigeostrophic Turbulence}}},
  author = {Tulloch, Ross and Smith, K. Shafer},
  date = {2009-04-01},
  journaltitle = {Journal of the Atmospheric Sciences},
  volume = {66},
  number = {4},
  pages = {1063--1068},
  publisher = {{American Meteorological Society}},
  issn = {0022-4928, 1520-0469},
  doi = {10.1175/2008JAS2921.1},
  langid = {english}
}

@book{Vallis_17,
  title = {Atmospheric and {{Oceanic Fluid Dynamics}}: {{Fundamentals}} and {{Large-Scale Circulation}}},
  shorttitle = {Atmospheric and {{Oceanic Fluid Dynamics}}},
  author = {Vallis, Geoffrey K.},
  date = {2017},
  edition = {2},
  publisher = {{Cambridge University Press}},
  location = {{Cambridge}},
  doi = {10.1017/9781107588417},
  isbn = {978-1-107-06550-5}
}

@article{DuBuhler_23,
  title = {The {{Impact}} of {{Frequency Bandwidth}} on a {{One-Dimensional Model}} for {{Dispersive Wave Turbulence}}},
  author = {Dù, Ryan Shìjié and Bühler, Oliver},
  date = {2023-07-14},
  journaltitle = {Journal of Nonlinear Science},
  shortjournal = {J Nonlinear Sci},
  volume = {33},
  number = {5},
  pages = {81},
  issn = {1432-1467},
  doi = {10.1007/s00332-023-09936-8},
  langid = {english}
}

@article{HeldLarichev_96,
  title = {A Scaling Theory for Horizontally Homogeneous, Baroclinically Unstable Flow on a Beta Plane},
  author = {Held, Isaac M. and Larichev, Vitaly D.},
  date = {1996-04-01},
  journaltitle = {Journal of the Atmospheric Sciences},
  volume = {53},
  number = {7},
  pages = {946--963},
  publisher = {{American Meteorological Society}},
  issn = {00224928},
  doi = {10.1175/1520-0469(1996)053<0946:ASTFHH>2.0.CO;2},
  issue = {7}
}

@article{LarichevHeld_95,
  title = {Eddy {{Amplitudes}} and {{Fluxes}} in a {{Homogeneous Model}} of {{Fully Developed Baroclinic Instability}}},
  author = {Larichev, Vitaly D. and Held, Isaac M.},
  date = {1995-10-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {25},
  number = {10},
  pages = {2285--2297},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/1520-0485(1995)025<2285:EAAFIA>2.0.CO;2},
  langid = {english}
}

@book{Batchelor_53,
  title = {The {{Theory}} of {{Homogeneous Turbulence}}},
  author = {Batchelor, G. K.},
  date = {1953},
  publisher = {{Cambridge University Press}},
  isbn = {978-0-521-04117-1},
  langid = {english},
  pagetotal = {216}
}

@article{ShamirEtAl_23,
  title = {The {{Matsuno}}–{{Gill}} Model on the Sphere},
  author = {Shamir, Ofer and Garfinkel, Chaim I. and Gerber, Edwin P. and Paldor, Nathan},
  date = {2023-06},
  journaltitle = {Journal of Fluid Mechanics},
  volume = {964},
  pages = {A32},
  publisher = {{Cambridge University Press}},
  issn = {0022-1120, 1469-7645},
  doi = {10.1017/jfm.2023.369},
  langid = {english}
}

@article{Gill_80,
  title = {Some Simple Solutions for Heat-Induced Tropical Circulation},
  author = {Gill, A. E.},
  date = {1980},
  journaltitle = {Quarterly Journal of the Royal Meteorological Society},
  volume = {106},
  number = {449},
  pages = {447--462},
  issn = {1477-870X},
  doi = {10.1002/qj.49710644905},
  langid = {english}
}

@article{Matsuno_66,
  title = {Quasi-{{Geostrophic Motions}} in the {{Equatorial Area}}},
  author = {Matsuno, Taroh},
  date = {1966},
  journaltitle = {Journal of the Meteorological Society of Japan. Ser. II},
  volume = {44},
  number = {1},
  pages = {25--43},
  doi = {10.2151/jmsj1965.44.1_25}
}

@article{SmithYoung_02,
  title = {Conversion of the {{Barotropic Tide}}},
  author = {Llewellyn Smith, Stefan G. and Young, William R.},
  date = {2002-05-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {32},
  number = {5},
  pages = {1554--1566},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/1520-0485(2002)032<1554:COTBT>2.0.CO;2},
  langid = {english}
}

@book{Cushman-RoisinBeckers_11,
  title = {Introduction to {{Geophysical Fluid Dynamics}}: {{Physical}} and {{Numerical Aspects}}},
  shorttitle = {Introduction to {{Geophysical Fluid Dynamics}}},
  author = {Cushman-Roisin, Benoit and Beckers, Jean-Marie},
  date = {2011-09-09},
  publisher = {{Academic Press}},
  isbn = {978-0-12-088759-0},
  langid = {english},
  pagetotal = {851}
}

@article{NikurashinFerrari_10,
  title = {Radiation and {{Dissipation}} of {{Internal Waves Generated}} by {{Geostrophic Motions Impinging}} on {{Small-Scale Topography}}: {{Theory}}},
  shorttitle = {Radiation and {{Dissipation}} of {{Internal Waves Generated}} by {{Geostrophic Motions Impinging}} on {{Small-Scale Topography}}},
  author = {Nikurashin, Maxim and Ferrari, Raffaele},
  date = {2010-05-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {40},
  number = {5},
  pages = {1055--1074},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/2009JPO4199.1},
  langid = {english}
}

@article{IerleySheremet_95,
  title = {Multiple Solutions and Advection-Dominated Flows in the Wind-Driven Circulation. {{Part I}}: {{Slip}}},
  shorttitle = {Multiple Solutions and Advection-Dominated Flows in the Wind-Driven Circulation. {{Part I}}},
  author = {Ierley, Glenn R. and Sheremet, Vitalii A.},
  date = {1995-09-01},
  journaltitle = {Journal of Marine Research},
  shortjournal = {issn: 0022-2402},
  volume = {53},
  number = {5},
  pages = {703--737},
  issn = {00222402, 15439542},
  doi = {10.1357/0022240953213052},
  issue = {5},
  langid = {english}
}

@article{CessiIerley_95,
  title = {Symmetry-{{Breaking Multiple Equilibria}} in {{Quasigeostrophic}}, {{Wind-Driven Flows}}},
  author = {Cessi, Paola and Ierley, Glenn R.},
  date = {1995},
  journaltitle = {Journal of Physical Oceanography},
  volume = {25},
  number = {6},
  pages = {1196--1205},
  publisher = {{American Meteorological Society}},
  location = {{Boston MA, USA}},
  doi = {10.1175/1520-0485(1995)025<1196:SBMEIQ>2.0.CO;2},
  issue = {6}
}

@article{CapetEtAl_16,
  title = {Intensification of {{Upper-Ocean Submesoscale Turbulence}} through {{Charney Baroclinic Instability}}},
  author = {Capet, Xavier and Roullet, Guillaume and Klein, Patrice and Maze, Guillaume},
  date = {2016-11-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {46},
  number = {11},
  pages = {3365--3384},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/JPO-D-16-0050.1},
  langid = {english}
}

@article{TullochEtAl_11,
  title = {Scales, {{Growth Rates}}, and {{Spectral Fluxes}} of {{Baroclinic Instability}} in the {{Ocean}}},
  author = {Tulloch, Ross and Marshall, John and Hill, Chris and Smith, K. Shafer},
  date = {2011-06-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {41},
  number = {6},
  pages = {1057--1076},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/2011JPO4404.1},
  langid = {english}
}

@article{LuoCallies_23,
  title = {Vertical {{Exchange Induced}} by {{Mixed-Layer Instabilities}}},
  author = {Luo, Yangcheng and Callies, Jörn},
  date = {2023-10-04},
  journaltitle = {Journal of Physical Oceanography},
  volume = {-1},
  publisher = {{American Meteorological Society}},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/JPO-D-23-0059.1},
  issue = {aop},
  langid = {english}
}

@article{SmithVanneste_13,
  title = {A {{Surface-Aware Projection Basis}} for {{Quasigeostrophic Flow}}},
  author = {Smith, K. Shafer and Vanneste, Jacques},
  date = {2013-03-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {43},
  number = {3},
  pages = {548--562},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/JPO-D-12-0107.1},
  langid = {english}
}

@article{LaCasce_17,
  title = {The {{Prevalence}} of {{Oceanic Surface Modes}}},
  author = {LaCasce, J. H.},
  date = {2017},
  journaltitle = {Geophysical Research Letters},
  volume = {44},
  number = {21},
  pages = {11,097--11,105},
  issn = {1944-8007},
  doi = {10.1002/2017GL075430},
  langid = {english}
}

@article{YassinGriffies_22,
  title = {On the {{Discrete Normal Modes}} of {{Quasigeostrophic Theory}}},
  author = {Yassin, Houssam and Griffies, Stephen M.},
  date = {2022-02-01},
  journaltitle = {Journal of Physical Oceanography},
  volume = {52},
  number = {2},
  pages = {243--259},
  publisher = {American Meteorological Society},
  issn = {0022-3670, 1520-0485},
  doi = {10.1175/JPO-D-21-0199.1},
  langid = {english}
}

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