The paper by Donald Coles explores the mean-velocity profile in turbulent boundary layers, proposing a representation that combines two universal functions: the well-known law of the wall and a new function called the law of the wake. The law of the wall describes the velocity profile near the surface, while the law of the wake characterizes the profile at points of separation or reattachment. These functions are derived empirically from mean-velocity profile measurements without reference to specific turbulence mechanisms. The paper also discusses the development of turbulent boundary layers in terms of an equivalent wake profile, constrained by inertia, and modified by viscosity at the wall. The wake function is further interpreted as a manifestation of large-scale mixing processes similar to those in a wake, primarily constrained by inertia. The paper includes experimental data supporting the wake hypothesis and discusses the implications for flows approaching or recovering from separation, as well as for yawed and separated flows. The equations of mean motion derived from the mean-velocity profile are presented, and the shearing-stress field for several flows is computed and compared with experimental data.The paper by Donald Coles explores the mean-velocity profile in turbulent boundary layers, proposing a representation that combines two universal functions: the well-known law of the wall and a new function called the law of the wake. The law of the wall describes the velocity profile near the surface, while the law of the wake characterizes the profile at points of separation or reattachment. These functions are derived empirically from mean-velocity profile measurements without reference to specific turbulence mechanisms. The paper also discusses the development of turbulent boundary layers in terms of an equivalent wake profile, constrained by inertia, and modified by viscosity at the wall. The wake function is further interpreted as a manifestation of large-scale mixing processes similar to those in a wake, primarily constrained by inertia. The paper includes experimental data supporting the wake hypothesis and discusses the implications for flows approaching or recovering from separation, as well as for yawed and separated flows. The equations of mean motion derived from the mean-velocity profile are presented, and the shearing-stress field for several flows is computed and compared with experimental data.