Spatio-temporal spectra in a strongly decelerated turbulent boundary layer

Spatio-temporal spectra are analysed from a direct numerical simulation of a non-equilibrium adverse pressure gradient boundary layer spanning Re$_\theta$=1500-8200. The shape factor increases from H=1.41 to 3.00. Streamwise and spanwise energy spectra are obtained in order to investigate the energy carrying structures in the inner and outer layers. Twenty probe data points at four streamwise locations (H=1.6, 2.0, 2.5 and 2.8) and 5 wall-normal locations (y/$\delta$=0.1, 0.12-0.18, 0.2, 0.5 and 0.8) are used for the temporal spectra. The spanwise spectra is available in the whole domain. Taylor's frozen turbulence hypothesis based on the local mean velocity is used to obtain the streamwise spectra. Shape, wavelength and wall-normal distance of the maximum value of the energy spectra are compared with other DNS databases based on shape factors, Re$_\theta$ and pressure gradient parameters. When the boundary layer attains a large mean velocity defect (H$>$2), the outer peak in the spectra becomes spatially localized (y/$\delta$ $\sim$ 0.40-0.60 at a spanwise wavelength of $\lambda_z/\delta$ $\sim$ 0.55-0.80 for the streamwise and spanwise velocity, and $\lambda_z/$$\delta$ $\sim$ 0.25-0.40 for the wall normal velocity.