Constraints on the wall layer in turbulent pipe flow

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Dynamical constraints on the wall layer in turbulent pipe flow imply both a narrow peak in the streamwise component of the turbulent Lamb vector near the wall, and a scaling of the wall layer depth proportional to the depth of the viscous sublayer. An approximation of the Lamb vector distribution, which equates to the gradient of Reynolds stress, is proposed. Hence the equation for streamwise mean flow may be integrated to obtain an expression for the velocity profile in the wall layer.