Macroturbulent cascades of energy and enstrophy in models and observations of planetary atmospheres
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1 Macroturbulent cascades of energy and enstrophy in models and observations of planetary atmospheres Peter Read + Roland Young + Fachreddin Tabataba-Vakili + Yixiong Wang [Dept. of Physics, University of Oxford] With thanks to Pierre Augier & Erik Lindborg KTH and LEGI, Grenoble 8/18/2016 GTP Boulder 1
2 Geostrophic turbulence (Charney 1971; Salmon 1978, 1980) Q: How does this work (given Gage & Nastrom; Cho & Lindborg )? - k -5/3 at mesoscales - Downscale KE Q: what about nonlocal transfers & zonal flows? 8/18/2016 GTP Boulder 2
3 Cascades & Waterfalls in large-scale atmospheric & oceanic turbulence? Classical (incremental) cascades Local in spectral space Interacting eddies are close in scale Inertial ranges (where spectral fluxes ~ independent of scale)?? Nonlocal cascades or waterfalls Direct interactions between very different scales Non-local in spectral terms Anisotropic? [E.g. eddy-zonal flow interactions] Diagnostics: Spectral fluxes of enstrophy, KE, APE and TE in simple GCMs Diagnostics of Earth-like circulations as fn of Ω Geostrophic or inertio-stratified turbulence? Observed Cascades & Waterfalls in Jupiter s atmosphere Analysis of cloud-track wind measurements from Cassini Spectral fluxes [and Structure functions] 8/18/2016 GTP Boulder 3
4 CIRCULATION REGIMES The rotating annulus laboratory experiment Q Regime Diagram Flow patterns [Pfeffer et al. - FSU] 8/18/2016 GTP Boulder 4
5 Exploring parameter space with a simple [3D] climate model [Wang et al. 2014, 2016] Pseudo-spectral dynamical core - PUMA [Univ. of Hamburg] Spherical harmonics in horizontal, FD in vertical T21-T170 [7.5 o x7.5 o 1 o x1 o ], 10 levels Flat surface (no topography) Simple radiative forcing Linear relaxation to specified T(,z) Linear drag at/near surface Time constant fr Vary, rad or fr Vary Q and F r or Ta Run to equilibrium [~20 Earth yrs] [Cf Earth in Perpetual equinox] [Yixiong Wang 2014] 8/18/2016 GTP Boulder 5
6 Key planetary parameters defining circulation regimes? Thermal Rossby number where U = g(dq y /q 0 )H WR (scale height) and L = R, H = R m T g Damping/dissipation parameters [ Taylor numbers?] 2 F (rad, fr) = 4W 2 (t 2 rad,t fr t rad» c p p S 3 s gt eff æ t fr» t drag ç è H h BL 2 ); [cf Ta = 4W 2 t visc ] ; radiative time constant ö ; "spin-down" timescale ø
7 Key planetary parameters defining circulation regimes? Thermal Rossby number Ro T = U ΩL gδθ yh Ω 2 R 2 θ 0 where U = g(dq y /q 0 )H WR (scale height) and L = R, H = R m T g Damping/dissipation parameters [ Taylor numbers?] F (rad,fr) = 2Ω τ rad, τ fr 4 ; [cf Ta = ( 2ΩτEkman ) 4 ] τ rad c pp s σgt eff 3 ; radiative time constant τ fr τ drag H h BL ; [ spin-down timescale (Valdes & Hoskins 1988)] 8/18/2016 GTP Boulder 7
8 Schematic regime diagram? T Super-rotating circulation Thermal Rossby number Axisymmetric circulation Regular baroclinic waves M E Irregular baroclinic waves Multiple jets U N Neptune J Frictional Taylor number 8/18/2016 GTP Boulder 8
9 KE Spectra 8/18/2016 GTP Boulder 9
10 How to measure turbulent cascades? Spectral fluxes Nonlinear enstrophy tendency Energy interaction tendency [rotational] Spectral fluxes [enstrophy (H), KE (F)] 8/18/2016 GTP Boulder 10
11 Enstrophy Spectral fluxes Ω* = 1/16 Ω* = 1/8 Ω* = 1/4 Ω* = 1/2 Ω* = 1 Ω* = 2 Ω* = 4 Ω* = 8 8/18/2016 GTP Boulder 11
12 Full spectral energy budget (Augier & Lindborg 2013) The energy budget can be written wrt spherical harmonic components Conversion APE -> KE Where Vertical fluxes Nonlinear terms 8/18/2016 GTP Boulder 12
13 Full spectral energy budget (Augier & Lindborg 2013) Conversion and flux terms APE -> KE conversion Nonlinear tendencies Spectral flux obtained by summing (integrating) over wavenumber (and height) e.g. for KE 8/18/2016 GTP Boulder 13
14 Full spectral energy budget (Augier & Lindborg 2013) 8/18/2016 GTP Boulder 14
15 Ω* = 1 Ro T = /18/2016 GTP Boulder 15
16 Ω* = 1 Ro T = /18/2016 GTP Boulder 16
17 Ω* = 1 Ro T = 0.08 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 17
18 Ω* = ½ Ro T = 0.32 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 18
19 LOCAL APE-KE Tendency Ω* = ¼ Ro T = /18/2016 GTP Boulder 19
20 LOCAL APE-KE Tendency Ω* = ¼ Ro T = 1.28 Eddy-eddy Zonal-zonal and Zonal-eddy 8/18/2016 GTP Boulder 20
21 Ω* = 1/16 Ro T = 20.5 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 21
22 Ω* = 1 Ro T = 0.08 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 22
23 Ω* = 2 Ro T = 0.02 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 23
24 Ω* = 4 Ro T = LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 24
25 Ω* = 8 Ro T = LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 25
26 Ω* = 8 Ro T = n jets? NB Forward cascade mostly In rotational components LOCAL +ve APE-KE Tendency 8/18/2016 GTP Boulder 26
27 Cassini cloud motion tracking 8/18/2016 GTP Boulder 27
28 Jupiter: relative vorticity (Cassini ISS images - Galperin et al 2014) 8/18/2016 GTP Boulder 28
29 Jupiter: KE spectrum & spectral fluxes? ~n -5/3? Zonostrophy index R b = L R /L b 5 ~n jets ~n -5 -> non-local energy transfers 8/18/2016 GTP Boulder 29
30 Jupiter: KE spectrum & spectral fluxes? [Rotational flow: Boer & Shepherd 1987] KE Forward cascade? Enstrophy Inverse cascade ~n jets ~n D? ~n jets ~n D? 8/18/2016 GTP Boulder 30
31 Jupiter: Zonal-eddy transfer function [Rotational flow: Boer & Shepherd 1987] n jets n jets 8/18/2016 GTP Boulder 31
32 Discussion: Geostrophic turbulence (Revised paradigm [low-moderate Ro T ]: Earth & Mars?) Mainly divergent components: stratified turbulence & internal waves?? K jets Non-local: Mainly rotational components 8/18/2016 GTP Boulder 32
33 Discussion: Geostrophic turbulence (Revised paradigm [low Ro T ]: Jupiter, Saturn..[oceans]?) Mainly rotational components: geostrophic (balanced) Rossby waves? K jets Non-local: Mainly rotational components 8/18/2016 GTP Boulder 33
34 Discussion: Inertio-stratified turbulence? (New paradigm for high Ro T : Titan, Venus.) Thermal forcing Baroclinic energy Hadley Cell Divergent flow Barotropic energy Excitation of 3D turbulence Boundary Layer friction K 0 K D Wavenumber K 8/18/2016 GTP Boulder 34
35 Many open questions.? Nature of inertio-stratified cascade? IG wave turbulence? Does a real atmosphere behave like the GCMs in exhibiting these cascades and waterfalls in spectral transfers of energy & enstrophy? Are all GCMs consistent in representing cascades? Apparently not? (Augier & Lindborg 2013) Depends substantially on sub-grid parameterizations. How to measure large-scale turbulent cascades/waterfalls from observations? Role of reanalyses...? Role of baroclinic instability on Jupiter/Saturn? Role of thermal tides on Venus...? 8/18/2016 GTP Boulder 35
36 Cascades In-verse Image credit: Stephen Conlin Small whorls grow greater whorls by keeping their vorticity, Collide and merge, grow bigger yet, towards waves and anisotropy. Waves great and small feed zonal jets by keeping their zonostrophy, Till unstable they grow, meander and break, returning to viscosity. PLR (2016). 8/18/2016 GTP Boulder 36
37 Jupiter: Measured velocity fields 8/18/2016 GTP Boulder 37
38 Zonostrophy index R b = L R /L b 5 ( ) ( ) Shallowing slope (~ n -5/3?) - Upscale or downscale cascade? E Z = C Z b 2 (n / a) -5 (1) E R = C R e 2/3 (n / a) -5/3 (2) ~n -5 -> non-local energy transfers e» W kg -1» ( )C(K E, K Z ) See Galperin et al. (2014) 8/18/2016 GTP Boulder 38
39 Energy transfers on Jupiter? - Structure functions s LLL ~ -er [For inertial range] + for inverse cascade - for forward cascade. 8/18/2016 GTP Boulder 39
40 Ω* = 1 Ro T = /18/2016 GTP Boulder 40
41 Ω* = 1 Ro T = 0.08 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 41
42 Ω* = ½ Ro T = 0.32 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 42
43 Ω* = 1/8 Ro T = 5.13 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 43
44 Ω* = 1/16 Ro T = 20.5 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 44
45 Ω* = 1 Ro T = 0.08 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 45
46 Ω* = 2 Ro T = 0.02 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 46
47 Ω* = 4 Ro T = LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 47
48 Ω* = 8 Ro T = LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 48
49 Ω* = 1/8 Ro T = 5.13 LOCAL APE-KE Tendency 8/18/2016 GTP Boulder 49
50 Image credit: Stephen Conlin L. F. Richardson & turbulence Big whorls have little whorls Which feed on their velocity, And little whorls have lesser whorls And so on to viscosity - [in the molecular sense] L. F. Richardson (1922). 8/18/2016 GTP Boulder 50
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