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 9. VERTICAL MOTION 9.1 Divergence in Two and Three Dimensions The gradient symbol, encountered earlier in these notes, is really a vector operator. “Gradient” itself does not have a magnitude and direction, but the gradient of somethingdoes. A vector operator such as the gradient operator (or “del”, for short) is something that represents a mathematical operation but that can be manipulated like a vector. These manipulations always are performed using the vector components as manipulation tools. The components of the del operator in three dimensions are ⎟⎠⎞⎜⎝⎛∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂+⎟⎠⎞⎜⎝⎛∂∂=∇zyxkjiSo ⎟⎠⎞⎜⎝⎛∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂+⎟⎠⎞⎜⎝⎛∂∂=∇zTyTxTTkjiis just the vector formed when each component of del operates on temperature. Another quantity that can be created through mathematical manipulation of the gradient vector is divergence. The divergence of some vector field, or div for short, is the dot product of del with that vector field. The word divergence itself, when not followed by the ATMO 251 Chapter 9 page 1 of 22
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