Dimensional analysis

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dimensional analysis

A method of determining possible relationships between meteorological variables based on their dimensions.

A systematic method called Buckingham pi theory can be used to find such relationships. The results are often expressed as dimensionless groups, called Pi groups. While Buckingham Pi theory helps to identify the appropriate dimensionless groups, it cannot indicate the relationships between the groups. Such relationships must be found empirically, based on field or laboratory measurements of the dimensionless groups. When the empirical data are plotted on graphs of one dimensionless group versus another, often data from many disparate meteorological conditions will result in one common curve, yielding a similarity relationship that may be universal. Dimensional analysis has been used extensively and successfully in studies of the atmospheric boundary layer, where turbulence precludes other more precise descriptions of the flow because exact solutions of the equations of motion are impossible to find due to the closure problem.

Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 347–404.