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Connections between the “−5/3” spectral and “−7/3” cospectral scaling exponents characterizing the inertial subranges of the wall-normal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of high-Reynolds number turbulent boundary layers. Previous laboratory experiments and field measurements featured here in the atmospheric boundary layer show that the “−7/3” scaling in the momentum flux cospectrum Fuw(k) commences at lower wavenumbers (around kz = 3) than the “−5/3” scaling in the wall-normal energy spectrum Eww(k) (around kz = 6), where k is the streamwise wavenumber and z is the distance from the surface. A satisfactory explanation as to why Fuw(k) attains its “−7/3” inertial subrange scaling earlier than Eww(k) in wavenumber space remains elusive. A cospectral budget (CSB) model subject to several simplifications and closure schemes offers one viewpoint. In its simplest form, the CSB model assumes a balance at all k between the production term and a Rotta...

On the linkage between the k−5/3 spectral and k−7/3 cospectral scaling in high-Reynolds number turbulent boundary layers