Vorticity and Jets

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Vorticity and Jets
METR 2413 12 April 2004
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Review from quiz
Review
Hydrostatic balance Vertical pressure gradient
force Scale, g 10 m/s2, vertical pgf 10
m/s2 Horizontal pressure gradient force balanced
by Coriolis force f 10-4 s-1, v 10 m/s,
Coriolis force 10-3 m/s2 ? 1 kg/m3, ?p 10
hPa 1000 Pa, ?x 1000 km 106 m
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Review from quiz
Thermal wind
In the presence of a horizontal temperature
gradient, the tilt of pressure surfaces
increases with height.
pp2
ug
?z
pp1
North
cold
warm
Zonal wind increases with height in the NH
because temperature decreases towards the pole,
giving increasing poleward height gradients.
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(No Transcript)
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Circulation and Vorticity Two primary measures
of rotation in a fluid By convention, both
circulation and vorticity are positive in the
counterclockwise direction (cyclonic in the
Northern Hemisphere) Circulation Macroscopic
measure of rotation for a finite area of the
fluid integration of the tangential component
of velocity around a closed path Vorticity The
tendency to spin about an axis Microscopic
measure of rotation at any point in the fluid
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The tighter the spin, the larger the magnitude of
the vorticity

• On Earth there is
• Vorticity from Earths spin (planetary vorticity)
• Local vorticity due to cyclonic/anticyclonic
  motion (relative vorticity)

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• Absolute vorticity (total vorticity)
• measured with respect to the fixed stars
• includes Earths rotation (planetary vorticity)
  and rotation of atmosphere relative to Earths
  surface (relative vorticity)
• angular momentum is conserved, so absolute
  vorticity is also conserved for frictionless
  motion
• ? a ? r fc constant
• where fc is the Coriolis parameter 2O sinF
  (planetary vorticity)

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• Relative vorticity
• measure of the rotation of the atmosphere about
  a vertical axis relative to Earths surface
• units of sec-1
• Synoptic scale vorticity is analyzed and plotted
  on the 500 mb chart
• 500 mb vorticity may be referred to as vertical
  vorticity (the spin is in relation to the
  vertical axis)
• The vertical component of vorticity can be
  expressed as
• ?r ?v/?x ?u/?y

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Typical magnitude of the relative vorticity for
synoptic scale flow, U 10 m/s, L 1000 km
? ?v/?x - ?u/ ?y U/L 10-5 sec-1
Typical magnitude of planetary vorticity f
10-4 s-1
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• Weve seen that relative vorticity is non-zero
  for two reasons
• Either streamlines of wind have curvature, or
• The wind field has horizontal shear (or both)

Curvature vorticity positive in troughs and
negative in ridges
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Positive and negative relative shear vorticity
can be due to variations in westerly wind speed
with latitude
slow
Positive shear vorticity
fast
fast
Negative shear vorticity
slow
Think of the above air flows as wide rivers if
you put a log oriented north-south in the flow,
the log would turn counterclockwise on the top,
and clockwise on the bottom because of the shear
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• Positive vorticity advection (PVA)
• found where air blows from regions of higher
  vorticity toward lower vorticity
• significant because main mechanism to reduce
  vorticity is divergence
• that is, in regions of PVA there tends to be
  divergence, which implies upward motions beneath
  these areas, surface convergence and surface
  pressure falls
• Negative vorticity advection (NVA)
• found where air blows from regions of lower
  vorticity towards higher vorticity
• main mechanism to increase vorticity is
  convergence
• when there is NVA in upper levels, there tends
  to be downward motion below, surface divergence
  and surface pressure rises

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Low Vorticity
Low Vorticity
Upper Level Convergence
High Vorticity
Anticyclonic Vorticity Advection - Moving from
low vorticity to high vorticity requires
convergence aloft.
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Jet streaks

• Jet streaks are localized regions of very fast
  winds embedded within the jet stream. Sometimes
  these local wind maxima reach speeds in excess of
  160 knots.
• Jet streaks are important as they are indicative
  of rising motion/falling pressures at the
  surface. The figure below represents an idealized
  jet streak.

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Height contour
Entrance Region (Rear)
Exit Region (Front)

• As air enters from the left, it must be
  accelerated as the height contours are closer
  together and the pressure gradient force is
  stronger.
• The stronger pgf causes an ageostrophic flow to
  the north, leading to convergence to the north
  and a divergence to the south. As a result, air
  sinks in the northern 'quadrant', and rises in
  the southern quadrant of a jet entrance.
• The force to accelerate the flow to the east is
  supplied by the Coriolis force as air flows from
  the south to the north near the jet entrance,
  leading to a force to the east (the right).

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• In the jet exit region, the opposite happens, as
  air flows from north to south to create the force
  necessary to decelerate the air as it leave the
  jet streak. The vertical motion resulting from
  this leads to rising air in the north quadrant
  and sinking air in the south of the jet exit.

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CONV
DIV
Exit Region (Front)
Entrance Region (Rear)

• However, not all jet streaks are straight. In
  fact, most are curved.
• The ageostrophic flow and anticyclonic vorticity
  advection cause convergence in the left entrance
  of the jet and the ageostrophic flow and the
  cyclonic vorticity advection cause divergence in
  the left exit region
• The divergence and ascent ahead of the upper
  level trough enhance the development of surface
  lows

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Summary

• Vorticity is a measure of the local rotation in a
  fluid
• Planetary vorticity due to the rotoation of the
  earth
• Relative vorticity due to the rotation of air
  relative to the surface, curvature vorticity and
  shear vorticity
• Absolute vorticity planetary vorticity
  relative vorticity is conserved in the atmosphere
• Positive (cyclonic) vorticity advection leads to
  upper level divergence, and rising motion
• Jet streaks are localized regions of very strong
  winds, with poleward motion at the jet entrance
  and equatorward flow at the jet exit
• Enhanced divergence at the left exit region of a
  cyclonic curved jet, enhances development of
  surface low