Meteo 422 – Lecture 17 – The Omega Equation Aloft

Dr. George S. Young

The derivations below generally follow those in the course text: Holton’s “An Introduction to Dynamic Meteorology”

Goal: Develop an understanding of the role of ageostrophic flow at jet stream level.

• What’s so special about the jet stream level?
• The winds are strongest at jet level, pretty much by definition.
• Mid-latitude Rossby waves (i.e. short-waves and long-waves) are typically strongest at jet level as well.
• The ageostrophic flow, including the vertical velocity, is necessary to hold a baroclinic wave (e.g. a short-wave) together is therefore strongly tied to what goes on at jet level.
• To a large extent, waves in the jet are the dog and the rest of mid-latitude weather the tail it wags.

• Why worry?
• Ageostrophic circulations caused by wind speed maxima and waves at jet level cause much of the vertical motion, cloudiness, and precipitation in the mid-latitudes.
• The interaction of the jet-induced ageostrophic motions with the overlying stratosphere can enhance surface cyclone intensification.
• The upper tropospheric fronts formed by jet-level ageostrophic circulations pose a hazard to aviation.
• Everybody’s got the bomb.

• Ageostrophic motions in the horizontal
• Horizontal map – height and geostrophic wind

· Jet streak example – sketch on blackboard

· Short-wave example – more complex –> discuss in lab

• Forcing – the equations

· The right hand term says that when the geostrophic wind advects in slower wind, the ageostrophic wind goes left of the jet in the N.H., i.e. roughly poleward.

· Likewise, when the geostrophic wind advects in faster wind, the ageostrophic wind goes left of the jet in the N.H., i.e. roughly equatorward.

· Sketch streamlines on the jet-level map.

• Forcing – the physics

· Air flowing into a region of tight pressure gradient finds itself going too slowly for Coriolis to balance the PGF, so the air accelerates towards lower pressure.

· The resulting cross-contour ageostrophic flow experiences Coriolis forcing too, acting to accelerate the along-contour flow back towards geostrophy.

· The reverse happens when air exits a region of tight pressure gradient.

• Ageostrophic motion in the vertical
• Horizontal map – convergence and divergence
• Cross section

· Entry region circulation

· Exit region circulation

· Where would you expect clouds and precipitation?

• Vertical advection of temperature

· Consider the stability of the upper troposphere

· Adiabatic heating and cooling

· Destruction of the upwind end of a jet streak

· Extension of the downwind end of a jet streak

· Ageostrophy holds the height and wind fields together to maintain some semblance of geostrophy

• Tropopause advection
• Consider the stability of the stratosphere

· Vertical advection there causes much more adiabatic heating and cooling than does similar motion in the troposphere

· So the column-average temperature and thus the surface pressure change more when the tropopause is advected up or down

· Enhanced cyclogenesis – think about why

• Tropopause folding

· Upper tropospheric fronts

· Formed by intrusions of stratospheric air into the troposphere in the entrance region of jet streaks and short-waves

· Eliminated both by mixing with tropospheric air and by retraction into the stratosphere in the exit region of jet streaks and short-waves

· Wind shear

· Strong stability and sloping inversion means strong horizontal temperature gradient

· Hence strong thermal wind

· Hence strong vertical wind shear

· If the shear becomes strong enough to overcome the stability Kelvin-Helmholtz waves form, creating dangerous turbulence

· Nuclear fallout

· Radioactive particles get rained out of the troposphere within a week

· So if someone fights a nuclear war on the other side of the world, little of that fallout reaches you.

· In contrast, radioactive particles that rise with the mushroom cloud into the stratosphere can stay there for months.

· These particles travel around the globe until they are injected into the troposphere by tropopause folds.

· The resulting fronts can carry the radiation to the surface or into storms, which rain it out.

· Creating a global fallout hazard from even local nuclear wars.