---%20Introduction%20to%20Geophysical%20Fluid%20Dynamics

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--- Introduction to Geophysical Fluid Dynamics
Ch. 7 Fundamentals of Atmospheric/Ocean Modeling

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• Variables and Units
• Independent Variables
• Values are independent of each other
• x increases eastward
• y increases northward
• z increases upward
• t time
• Later we can use other coordinate systems
• p decreases upward
• latitude, longitude

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• Variables and Units
• Dependent Variables
• Values depend on other variables
• wind speeds
• u gt 0 for eastward motion
• v gt 0 for northward motion
• w gt 0 for upward motion
• Temperature T T(x,y,z,t)
• Pressure p p(x,y,z,t)
• Density ? ?(x,y,z,t)

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Part II - The International Unit System (SI)
So, for Length 1000 m 1 km 1m 1000 mm And
so forth. Much simpler!
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As of 2005, only three countries hang on to the
messy Imperial Units, Myanmar, Liberia, and the
United States.
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Part II - The International Unit System (SI)
SI prefixes -- Factor Name  Symbol 1012 tera T 10
9 giga G 106 mega M 103 kilo k 102 hecto h 101 dek
a da   Factor Name  Symbol 10-1 deci d 10-2 ce
nti c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12
pico p
 SI base units Base quantity Name Symbol length
meter m mass
kilogram    kg time
second s temperature       kelvin K
SI derived units Derived quantity Name
Symbol area square
meter m2 volume cubic
meter m3 speed, velocity meter per
second m/s acceleration meter per second
squared   m/s2 mass density kilogram per cubic
meter kg/m3 specific volume cubic meter per
kilogram m3/kg
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In meteorology/ocean, we almost always use SI
units, journals require it.
Force - Newtons (kg m/s) Pressure - We still use
millibars (mb) 1 mb 100 Pa 1 hPa (PASCALS
N/m2) (hpa hecto-pascal) Pressure force /
unit area Must use correct (SI) units in
calculations Temperatures - Always use Kelvin in
calculations T(K) T( C ) 273
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Dimensions and Units All physical quantities can
be expressed in terms of basic dimensions
Mass M (Kg) Length L (m) Time T
(s) Temperature K (K)
Velocity Distance / Time, so it has
dimensions L/T, or m/s
Acceleration Velocity / Time, so it has
dimensions L/T2, or m/s2
Force Mass x Acceleration, so it has
dimensions M LT-2, or Kg m/s2
Pressure, density
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Pressure GradientForce(PGF)

• pressure gradient high pressure ? low pressure
• pressure differences exits due to unequal
  heating of Earths surface
• spacing between isobars indicates intensity of
  gradient
• flow is perpendicular to isobars

Figure 6.7
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Pressure Gradient Force (PGF)
Figure 6.8a
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• Coriolis effect seen on a rotating platform, as 1
  person throws a ball to another person.

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Coriolis Effect

• Shell fired in N. Hem. deflects right.
• In S. Hem., it deflects left.
• Coriolis (1835) deflection due to Earths
  rotation
• Consider object moving northward in N. Hem.
• As Earth rotates, speed of surface is greatest at
  Equator and 0 at Poles.

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• Obj. A has greater eastward speed than B.
• gt When A is moved northward, it ends up at X,
  ahead of B.
• gt Appears to be a force deflecting the obj. to
  the right (Coriolis force)
• Obj. moves southward (in N.Hem.) ends up further
  west gt Coriolis deflection to right.
• Consider obj. moving eastward
• It moves faster than Earth in circular orbit
• gt incr. centrifugal force
• gt obj. pushed away from Earths spin axis.

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• Obj. moving westward is deflected poleward gt
  deflection to right (N.Hem.)
• Mathematically E-W and N-S movements can be
  treated in same way gt obj. moving in any horiz.
  direction deflects to the right in N. Hem., and
  to the left in S. Hem.
• Coriolis effect 0 at Equator, max. at Poles.
• Strength of Coriolis force proportional to speed
  of obj.

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The Coriolis Effect

• objects in the atmosphere are influenced by the
  Earths rotation
• Rotation of Earth is counter-clockwise
• results in an apparent deflection (relative to
  surface)
• deflection to the right Northern Hemisphere
  (left, S. Hemisphere)
• Greatest at the poles, 0 at the equator
• Increases with speed of moving object
• CE changes direction not speed

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Geostrophic balance

• P diff. gt pressure gradient force (PGF)
• gt air parcel moves gt Coriolis force
• Geostrophy balance between PGF Coriolis force
  .

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• Approx. geostrophic balance for large scale flow
  away from Eq.
• Q Why no geostrophic balance at Equator? A No
  Coriolis force at Eq.
• In N. Hem., geostrophic wind blow to the right of
  PGF (points from high to low P)
• In S. Hem., geostrophic wind to left of PGF.

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• Converging contours of const. pressure (isobars)
  gt faster flow gt incr. CF PGF

Get geostrophic wind pattern from isobars
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Cyclone Anticyclone

• Large low pressure cells are cyclones, (high
  pressure cells anticyclones)
• Air driven towards the centre of a cyclone by PGF
  gets deflected by Coriolis to spiral around the
  centre.

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• Difference between PGF Coriolis (CF) is the
  centripetal force needed to keep parcel in orbit.

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Convergence divergence

• Cyclone has convergence near ground but
  divergence at upper level.
• Anticyclone divergence near ground, convergence
  at upper level.

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Pressure Gradient Force Coriolis Force
Geostrophic Wind
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Upper Atmosphere Winds

• upper air moving from areas of higher to areas of
  lower pressure undergo Coriolis deflection
• air will eventually flow parallel to height
  contours as the pressure gradient force balances
  with the Coriolis force
• this geostrophic flow (wind) may only occur in
  the free atmosphere (no friction)
• stable flow with constant speed and direction

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Supergeostrophic flow
Subgeostrophic flow
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• Geostrophic flow too simplistic ? PGF is rarely
  uniform, height contours curve and vary in
  distance
• wind still flows parallel to contours HOWEVER
  continuously changing direction (and experiencing
  acceleration)
• for parallel flow to occur pressure imbalance
  must exist between the PGF and CE ? Gradient Flow
  
• Two specific types of gradient flow
• Supergeostrophic High pressure systems, CE gt PGF
  (to enable wind to turn), air accelerates
• Subgeostrophic Low pressure systems, PGF gt CE,
  air decelerates
• supergeostrophic and subgeostrophic conditions
  lead to airflow parallel to curved height
  contours

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Friction

• factor at Earths surface ? slows wind
• varies with surface texture, wind speed, time of
  day/year and atmospheric conditions
• Important for air within 1.5 km of the surface,
  the planetary boundary layer
• Because friction reduces wind speed it also
  reduces Coriolis deflection
• Friction above 1.5 km is negligible
• Above 1.5 km the free atmosphere

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Friction

• Ground friction slows wind gt CF weakens.
• CFfriction balances PGF.
• Surface wind tilted toward low p region.

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Pressure Gradient Coriolis Friction Forces
Surface Wind
Figure 6.8c
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Cyclones, Anticyclones, Troughs and Ridges

• 4 broad pressure areas in Northern hemisphere
• High pressure areas (anticyclones) ? clockwise
  airflow in the Northern Hemisphere (opposite flow
  direction in S. Hemisphere)
• Characterized by descending air which warms
  creating clear skies
• Low pressure areas (cyclones) ? counterclockwise
  airflow in N. Hemisphere (opposite flow in S.
  Hemisphere)
• Air converges toward low pressure centers,
  cyclones are characterized by ascending air which
  cools to form clouds and possibly precipitation
• In the upper atmosphere, ridges correspond to
  surface anticyclones while troughs correspond to
  surface cyclones

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Surface and upper atmosphere air flow around high
pressure systems (anticyclones)
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Surface and upper atmosphere air flow around low
pressure systems (cyclones)