Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth....

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Jeffrey B. Weiss University of Colorado, Boulder Geophysical Fluid Dynamics of the Earth

Transcript of Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth....

Page 1: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Jeffrey B. WeissUniversity of Colorado, Boulder

Geophysical Fluid Dynamics of the Earth

Page 2: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

The Earth is a spinning sphere• Coriolis force depends on latitude

• solar flux depends on latitude

Michael Ritter, http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/title_page.html

Page 3: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Atmosphere is turbulent• global scale forcing:

L ~ 107 m• dissipation:

νair ~ 10-5 m2/s

• jet stream velocity: U ~ 102 m/s

• Ratm= 1014

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Direct simulation impossible• Kolmogorov scale

η = 1 mm

• current global models: ~ 1o resolution ~ 100 km

• improvement needed: 108

• computer speed-up: 1032 ~ 2100

• Moore’s Law: 200 years• need to be smarter (or very patient)

Page 5: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Climate system self-organizes• layers:

troposphere• circulations

Hadley cell• spatially localized organization

ocean vortices• spatio-temporal organization

El-Niño

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Radiative forcing

IPCC

Page 7: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Atmospheric Layers• troposphere is weather layer• height governed by

radiation convection dynamics

• tropopause dynamics interesting• stratosphere stably stratified

Page 8: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

planetary boundary layer• directly feels surface• 3d turbulence• strong diurnal cycle• surface layer

lower 10% log wind profile

• free atmosphere affected by rotation/stratification

Arya, S.P. Air Pollution Meteorology and Dispersion

Page 9: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

ocean mixed layer

http://hpl.umces.edu/ocean/sml_main.htm

• directly feels atmosphere• mixed by wind• stabilized by solar heating

Page 10: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

deep ocean• thermocline

50 - 1000 m• below stably stratified• slow currents

http://www.windows.ucar.edu/tour

Page 11: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Large scale circulations• 3-cell model

trades westerlies ITCZ deserts frontal zone

• shifts seasonallyNASA JPL

Page 12: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

wind-driven ocean circulation• winds + basins = gyres

• horizontal• large geostrophic component• timescales: months

geographyalltheway.com

Page 13: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

serendipitous tracers• 1990: 20,000 Nike shoes washed into

Pacific Gyre• 1992: 29,000 bathtub toys• locations from

beachcombers

http://en.wikipedia.org/wiki/Image:Friendly_Floatees.png

Page 14: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

thermohaline circulation• density driven vertical overturning• forcing:

small scale intermittent convection uncertain vertical mixing

• timescale: 1000 yrs• large climate impact

Page 15: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

spatially localized features• Coherent structures

vortices, jets, fronts• rotation and stratification suppress

vortex stretching• inverse cascade to large scales

http://eosweb.larc.nasa.gov/HPDOCS/misr/misr_images/arctic_vortex.jpg

Page 16: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Spatio-temporal phenomena• El Niño, Monsoons, NAO, MJO, PDO, …• As records lengthen, expect to see more• can have extreme multi-scale components

NOAA

Page 17: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

Monsoon• seasonal circulation associated with land-

sea contrast• complex intermittency• experience the North American Monsoon

burst breakhttp://www.wrh.noaa.gov/fgz/science/monsoon.php?wfo=fgz

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Balances• often find balances between subset of

forces• provide insight into dynamics• departures important even if small• asymptotic analysis gives reduced

models

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Hydrostatic Balance• aspect ratio α = H/L• Froude number Fr = U/NH• non-rotating Boussinesq equations for

departures about basic state b(z)• vertical momentum eqn

• α2 Fr2 << 1 gives hydrostatic balance U2/L2 N2 << 1 tbuoy

2 << tadv2

Page 20: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• large scale troposphere N ~ 10-2/s, H ~ 10 km, L ~ 1000 km, U ~ 10 m/s Fr ~ 0.1 α ~ 0.01 α2 Fr2 ~ 10-6

fails at fronts and convection• large scale ocean

N ~ 10-2/s, H ~ 1 km, L ~ 1000 km, U ~ 0.1m/s Fr ~ 0.01 α ~ 0.001 α2 Fr2 ~ 10-10

hydrostatic down to small horizontal scales fails at deep convection sites

• preconditioning: Fr near unity• plumes: H/L large

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Geostrophic balance• Rossby number: Ro = U/ f L• horizontal momentum eqn

scaling:

• Ro << 1: geostrophy• flow along isobars• diagnostic relation

Page 22: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

upper air map

Page 23: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

thermal wind• combine geostrophic and hydrostatic• obtain wind shear

• midlatitudes heating decreases with latitude eastward wind increases with height jet intensification

Page 24: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

turbulent cascades• compare homogeneous isotropic 3d and 2d• energy injection at large scale• dissipation at small scale• intermediate: inertial scales, only depend on

energy flux ε• focus on spectra:• assume local in k and universal

Page 25: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• dimensional analysis

• T requires α = 2/3 L requires β = −5/3

Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006

Page 26: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

2d cascades• In 2d, two inviscid invariants

energy E and enstrophy Z in 3d vortex stretching creates enstrophy Z(k) = k2 E(k)

• centroid wavenumber• width• initial narrow E(k) spreads

Page 27: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• energy cascades to large scales: inverse

• similar argument: enstrophy to smallscales: direct

Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006

Page 28: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• energy inertial range to large scales• enstrophy inertial range to small scales• energy inertial ranges same scaling as 3d• need mechanism to remove energy at

large scales, e.g. Ekman drag• enstrophy flux

η ~ Z/T ~1/T3

E(k) ~ η2/3 k-3

Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006

Page 29: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

cascades on 2d β-plane• vorticity equation on 2d β-plane

f = β y

• Rossby waves

• dispersion relation

Page 30: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• scaling

• small scales advection and turbulence dominate

• crossover: Rhines scale

• large scales, β dominates waves inhibit cascades

Page 31: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

• anisotropy of Rossby waves advection freq Uk ~ Rossby wave freq ω

- 1.5 -1 . 0 -0 . 5 0.0 0.5 1.0 1.5

- 1.5

- 1.0

- 0.5

0.0

0.5

1.0

1.5

waves

turbulence

Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006

Page 32: Geophysical Fluid Dynamics of the Earth · 2008-07-14 · Geophysical Fluid Dynamics of the Earth. The Earth is a spinning sphere •Coriolis force depends on latitude •solar flux

ocean jets• zonal jets observed to populate ocean

Maximenko, et al 2005

instantaneous

18 week avg

200 week avg