Variability of Stochastically Forced Zonal Jets Laura Cope , Peter Haynes Department of Applied Mathematics and Theoretical Physics, University of Cambridge
MOTIVATION Gaseous Giant Planets Earth’s Atmosphere & Oceans What insights can we learn Credit: NASA, ESA Credit: NASA / Science Photo Library about the variability of jet streams using idealized models? Credit: NASA/JPL-Caltech/Space Science Institute Credit: https://www.nasa.gov
OBSERVATIONS Jupiter Earth’s Oceans Earth’s Atmosphere 40°S 50°S 60°S 1995 Year 1996 Voyager 1979-1980 (Sokolov, Rintoul 1996) (earth.nullschool.net) Increasing time variability
OBSERVATIONS Jupiter Earth’s Oceans Earth’s Atmosphere 40°S 50°S 60°S 1995 Year 1996 Voyager 1979-1980 (Sokolov, Rintoul 1996) (earth.nullschool.net) Cassini 2000 Increasing time variability
40°S 40°S 50°S 50°S 60°S 60°S Year 1995 1996
OVERVIEW OF IDEALIZED MODELS Planetary rotation Turbulence Friction Jets
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sha1_base64="lHfLRKj6qzQlWtG4bt8R2dg4o4s=">AB6nicdVDLSgNBEOz1GeMr6tHLYBA8LbuJYZNbwIvHiOYByRJmJ5NkyMzsMjMrhCWf4MWDIl79Im/+jZOHoKIFDUVN91dUcKZNp734aytb2xubed28rt7+weHhaPjlo5TRWiTxDxWnQhrypmkTcMp51EUSwiTtvR5Grut+p0iyWd2a0FDgkWRDRrCx0m1PpP1C0XP9UhBUfOS5tVotqJSXxCtXke96CxRhUa/8N4bxCQVBrCsdZd30tMmGFlGOF0lu+lmiaYTPCIdi2VWFAdZotTZ+jcKgM0jJUtadBC/T6RYaH1VES2U2Az1r+9ufiX103NsBpmTCapoZIsFw1TjkyM5n+jAVOUGD61BPF7K2IjLHCxNh08jaEr0/R/6RVcn2b1c1lsV5axZGDUziDC/AhgDpcQwOaQGAED/AEzw53Hp0X53XZuasZk7gB5y3T+06ji0=</latexit> IDEALIZED MODELS: MATHEMATICAL FORMULATION Equation of Motion : Vorticity Equation Stochastic Force Features 2D (barotropic) Fourier space: Planetary Stochastic Linear Hyper- Doubly periodic Rotation forcing friction viscosity Beta plane Stochastic force 𝜖𝜂 𝜖𝑢 + 𝒗 & ∇𝜂 + 𝛾𝑤 = 𝜊 − 𝜈𝜂 + 𝜉 / ∇ 0/ 𝜂 Physical space: Energy input Damping Beta, β rate,. rate, . ✏ µ
IDEALIZED MODELS: MATHEMATICAL FORMULATION Generalized Quasilinear Approximation Reference : Marston, Chini, Increasing zonal Tobias (2016) wavenumber
IDEALIZED MODELS: MATHEMATICAL FORMULATION Generalized Low modes ≤ 𝚳 Quasilinear Approximation Separation = 𝚳 Reference : High modes > 𝚳 Marston, Chini, Increasing zonal Tobias (2016) wavenumber
IDEALIZED MODELS: MATHEMATICAL FORMULATION Generalized Low modes ≤ 𝚳 Quasilinear Approximation Separation = 𝚳 Reference : High modes > 𝚳 Marston, Chini, Increasing zonal Tobias (2016) wavenumber
̅ IDEALIZED MODELS: MATHEMATICAL FORMULATION Generalized Quasilinear Approximation Overview 𝑓 ;7< = 𝑓 ;7< = Low-high mode 𝜔 7 = ? Low modes ≤ 𝚳 𝜔 = 5 𝜔 7 + 5 𝜔 + 𝜔′ decomposition: |7|89 |7|>9 Basic vorticity AB AC = ℒ 𝜂 + 𝒪[𝜂 , 𝜂 ] equation: A? B 𝜂 + H 𝒪[ ̅ 𝜂, ̅ 𝜂 ] + H 𝒪[𝜂 J , 𝜂 J ] AC = ℒ Low modes: AB L AC = ℒ 𝜂 J + 𝒪 J [ ̅ 𝜂, 𝜂 J ] +[HHNL] High modes: 𝜖𝜂 Vorticity 𝜖𝑢 + 𝒗 & ∇𝜂 + 𝛾𝑤 − HHNL = 𝜊 − 𝜈𝜂 + 𝜉 / ∇ 0/ 𝜂 equation: High modes > 𝚳
SUMMARY OF IDEALIZED MODELS Nonlinear (Λ = 𝑂) Generalized Quasilinear (Λ = 1) Quasilinear (Λ = 0) Reduction in nonlinearity
NUMERICAL SIMULATIONS – NONLINEAR (NL) MODEL Zonal mean zonal velocity Zonal velocity Zonal mean evolution in time field zonal velocity
NONLINEAR (NL) MODEL - TYPES OF VARIABILITY Randomly wandering Result 1 New type of Merging & variability nucleating found: jets migrate north and south Migrating
ALL MODELS - TYPES OF VARIABILITY NL Model (Λ = 𝑂) GQL Model (Λ = 1) QL Model (Λ = 0) Randomly wandering Merging & nucleating No clear Migrating migration
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