Self-SimilarityA flow is said to be self similar if the prevailing velocity profiles at various streamwise stations x can be made congruent, through the use of appropriately defined independent and dependent variables. The transformation to these variables is called a similarity transformation; the transformed variables are called similarity variables. The result is a reduction, by at least one, in the number of independent variables in the flow. Thus, a two-dimensional flow can be represented in terms of a single similarity coordinate, i.e., the governing partial differential equations reduce to ordinary differential equations. The latter are much more easily solved than the former. The entire two-dimensional flow field can be re-constructed from the similarity solution. The following is a graphical and mathematical representation of this concept.
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This note was uploaded on 10/13/2010 for the course MECH 414 taught by Professor Ghia during the Winter '06 term at University of Cincinnati.