This talk is presented as a Zoom Webinar and requires a passcode. For anyone outside the department; If you would like to attend, email [email protected]

Connections are explored between spectral descriptions of turbulence and the mean velocity profile in wall-bounded flows using a budget for the co-spectral density. The co-spectrum is derived using a standard model for the wall normal velocity variance and a linear Rotta-like return-to-isotropy closure modified to include the isotropozition of the production for the pressure-strain effects. The approach provides a relation between well-established constants such as the von Karḿan and Kolmogorov constants, and the Rotta constant known to vary with the flow configuration.  Depending on the choices made about small-scale intermittency corrections, the logarithmic mean velocity profile or a power-law profile with an exponent that depends on the intermittency correction are derived thereby offering a new perspective on a long standing debate about the shape of the mean velocity profile in the equilibrium region.  Extensions to stably stratified flows are also discussed.