SelfSimilarity
A 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 twodimensional 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 twodimensional flow field can be reconstructed 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.
 Winter '06
 Ghia

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