Fundamentals of Turbulent Flows

Virtually all technologically relevant applications involve interactions of turbulent flows with solid walls, including flows over aircrafts and automobiles. We study these interactions using canonical wall-bounded flows, including fully developed channels, pipes, and flat-plate boundary layers, with a focus on channel flow. A common scaling may be employed in the near-wall region using the friction velocity and viscous length scale to derive the so-called wall units. In this region, which comprises the viscous sublayer, buffer layer, and overlap layer, the law of the wall governs the mean velocity profile, and the constant-stress-layer assumption is often employed. We discuss key features of the mean velocity profile, particularly the log law in the overlap region, which stands as a celebrated result in turbulence theory. Away from the wall, the outer layer scales with the boundary-layer thickness and freestream velocity. We discuss the skin friction and wake laws to describe the mean outer velocity profile and introduce the Clauser chart method. We also examine in more detail the scales and structural features of turbulence near a wall, including streaks and hairpin vortices.