Karman-Pohlhausen momentum integral

For turbulent flow on a rotating sphere or hemisphere, Sawatzki [53] and Chin [22] have analyzed the governing equations using the Karman-Pohlhausen momentum integral method. The turbulent boundary layer was assumed to originate at the pole of rotation, and the meridional and azimuthal velocity profiles were approximated with the one-seventh power law. Their results can be summarized by the... 

Equations (12.19), (12.22), and (12.24) for Vx, My,P are now written in terms of a single unknown variable f. Before plugging in expressions for Vx, Vy, P into x-momentum Equation (12.15), the Karman-Pohlhausen momentum integral technique is used, where pVx multiplied by continuity Equation (12.14) is added to x-momentum ... 

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