The Origin of the Log Law Region for Wall-bounded Turbulent Boundary Layer Flows

The origin of the Log Law behavior of a wall-bounded turbulent boundary layer is outlined. The new theory of the origin of the Log Law starts with previous experimental observations that show that the turbulent boundary layer fluid undergoes rapid changes in the wall shear stress at any point on the wall. The main insight provided herein is that this rapid change in the wall shear stress corresponds to a rapid, quantifiable change in the location of the viscous sublayer toward and away from the wall in the velocity boundary layer. When this viscous layer is then spatially averaged, we theorize that the normal exponential-like decay of the viscous shear is stretched out in the tail region. The next step is to use various experimental results from the literature to show that the viscous sublayer, which is directly proportional to the second derivative of the velocity profile, extends much deeper into the boundary layer than previously thought. In fact it is shown that the viscosity effects extend all the way into the Log Law region where the spatially-averaged tail region begins to show a oneover- distance-from-the-wall-squared behavior. Hence, when the spatially-averaged second derivative profile is twice integrated to obtain the velocity profile perpendicular to the wall, one obtains the classic logarithmic profile behavior of the Log Law region of the turbulent boundary layer.