Dynamics of the Atmosphere: A Course in Theoretical Meteorology 1st Edition
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There are many books on the physics of the atmosphere. Sadly, most take the approach of rote memorization of equations that may or may not be valid models of a real atmosphere. Let the reader beware such a cook book approach to the atmosphere. Zdunkowski's book delves more deeply into fluid dynamics and its application to theoretic models. Thus he needs and applies a much deeper mathematical foundation. The mathematics quickly becomes a nightmare for people with only a background in vector calculus (like me.) But, suddenly there is a connection between the corpus of work on molecular physics (chemistry) and atmospheric motion. That alone is worth the price of a hundred of books. (Notice that I did not mention quantum mechanics. Sorry, statistical thermodynamics is not covered in theoretic meteorology here.)
Even so, you quickly see the flaws in Dyadics. The multi-linear algebra is not closed under many basic operations such as a vector product. The cross product produces a vector in the set of an orthogonal basis. The vector product produces a vector that is not in the non-orthogonal basis. Furthermore the operations explode in complexity. The reverse mappings which led to geometric topology become very important.
Let me summarize what all of this means. There are three basic approaches to mechanics. You can model a bouncing ball in a stationary room.
Or you can model a stationary ball in a bouncing room. Or you can model a bouncing ball in a bouncing room. All of the bounces are on curves instead of Cartesian vectors. Vector Calculus works well only in the first approach. This book takes you into the mathematics of the third approach
in common with many of the physicists of the past century.