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Abstract
The viscous wall region of a fully developed turbulent pipe flow is investigated using a nonlinear, time-dependent, three-dimensional model. In the model, the velocity field is assumed to satisfy periodic boundary conditions in the longitudinal and spanwise directions, the velocity vanishes at the pipe wall, the velocity fluctuations are assumed to vanish at large distances from the wall, and a law of the wall profile is imposed on the longitudinal and spanwise average of the longitudinal component of velocity outside the viscous wall region. The model equations are solved using pseudospectral methods and the computed mean velocity profile, fluctuation intensities, and turbulence production rate are found to be in good agreement with experiment in the viscous wall region. It is found that the bulk of turbulence production is generated by length scales larger than 40 in the spanwise direction and 200 in the longitudinal direction.