book11imbalance - Weather Observation and Analysis John...

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Weather Observation and Analysis John Nielsen-Gammon Course Notes These course notes are copyrighted. If you are presently registered for ATMO 251 at Texas A&M University, permission is hereby granted to download and print these course notes for your personal use. If you are not registered for ATMO 251, you may view these course notes, but you may not download or print them without the permission of the author. Redistribution of these course notes, whether done freely or for profit, is explicitly prohibited without the written permission of the author. Chapter 11. IMBALANCE AND VERTICAL MOTION 11.1 Wind-Parallel Accelerations The previous chapter discussed curved flow, and how for cyclonic curvature the wind speed had to be sub-geostrophic, and for anticyclonically curved flow the wind speed had to be super-geostrophic. Both of those situations are examples of accelerations in a direction normal (at right angles) to the wind, to the left in the first case and to the right in the second. The other type of acceleration is in the same direction as the wind: speeding up or slowing down. In the absence of friction aloft, it’s hard to imagine how that would happen. If the wind is blowing parallel to the height contours or isobars, both the pressure gradient force and the coriolis force are at right angles to the wind direction. So both of these forces would only be able to change the direction of the wind, not its speed. The solution to this paradox is in rejecting its premise. The wind simply cannot be blowing parallel to the height contours if it’s speeding up or slowing down. As long as it’s drifting slightly toward lower pressure, there’s a little bit of the pressure gradient force pointing in the along-wind direction, causing the air to speed up. And if it’s drifting slightly toward higher pressure, there’s a little bit of the pressure gradient causing it to slow down. Sure, if the wind is blowing across height contours, it must not be in geostrophic balance. But we knew that already, because we envisioned the air to be accelerating. Acceleration and exact geostrophic balance are mutually exclusive. ATMO 251 Chapter 11 page 1 of 20
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The basic rule here is easy to remember. If the air is aloft where friction has no effect, the air will be speeding up if it is drifting toward ATMO 251 Chapter 11 page 2 of 20
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lower heights or lower pressures, and the air will be slowing down if it is drifting toward higher heights or higher pressures. Somewhere buried in here is a basic rule for accelerations versus departures from geostrophic balance. Imagine a vector that represents the difference between what the wind is actually and what the wind would be if it was in perfect geostrophic balance. This vector, called the ageostrophic wind vector and written a v r , can be computed (or eyeballed) from straightforward vector subtraction: g a v v v r r r = Let’s see what the ageostrophic wind vector would be in certain prototypical situations. In the case of an anticyclone, the air is curving
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This note was uploaded on 04/02/2008 for the course ATMO 251-501/50 taught by Professor Alcorn during the Fall '07 term at Texas A&M.

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book11imbalance - Weather Observation and Analysis John...

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