in various approximate treatments of the boundary layer including the Thwaites method for laminar flows. The formal definition is given by where is the shape factor, is the displacement thickness and is the momentum thickness. Conventionally, = 2.59 (Blasius boundary layer) is typical of laminar flows, while = 1.3 - 1.4 is typical of turbulent flows near the laminar-turbulent transition. For turbulent flows near separation, 2.7. The dividing line defining laminar-transitional and transitional-turbulent values is dependent on a number of factors so it is not always a definitive parameter for differentiating laminar, transitional, or turbulent boundary layers. Moment method A relatively new method for describing the thickness and shape of the boundary layer uses the mathematical moment methodology which is commonly used to characterize statistical probability functions. The boundary layer moment method was developed from the observation that the plot of the second derivative of the Blasius boundary layer for laminar flow over a plate looks very much like a Gaussian distribution curve. The implication of the second derivative Gaussian-like shape is that the velocity profile shape for laminar flow is closely approximated as a twice integrated Gaussian function. The moment method is based on simple integrals of the velocity profile that use the entire profile, not just a few tail region data points as does . The moment method introduces four new parameters that help describe the thickness and shape of the boundary layer. These four parameters are the mean location, the boundary layer width, the velocity profile skewness, and the velocity profile excess. The skewness and excess are true shape parameters as opposed to the simple ratio parameters like the H12. Applying the moment method to the first and second derivatives of the velocity profile generates additional parameters that, for example, determine the location, shape, and thickness of the viscous forces in a turbulent boundary layer. A unique property of the moment method parameters is that it is possible to prove that many of these velocity thickness parameters are also similarity scaling parameters. That is, if similarity is present in a set of velocity profiles, then these thickness parameters must also be similarity length scaling parameters. It is straightforward to cast the properly scaled velocity profile and its first two derivatives into suitable integral kernels. The central moments based on the scaled velocity profiles are defined as where is the displacement thickness and the mean location, is given