Resolvent analysis of a turbulent self-similar adverse pressure gradient turbulent boundary layer at the verge of separation*

There has been much theoretical, experimental and numerical research into turbulent boundary layers (TBLs) with the vast majority focused on the zero-pressure-gradient case. Concerning its adverse pressure gradient (APG) counterpart, however, many aspects of their scaling, structure and stability remain unresolved. The study of a canonical APG-TBL is, therefore, of the utmost importance. The self-similar (SS-APG-TBL) is arguably the most appropriate canonical form to study as a canonical APG-TBL. This SS-APG-TBL exists at the verge of separation, where the mean wall-shear stress is zero and the non-dimensional pressure parameter β → ∞. A DNS of a SS-ABG-TBL with a momentum thickness-based Reynolds number range from 570 to 13,800, and a self-similar region with momentum thickness-based Reynolds number range of 10,000 to 12,300 has been undertaken. This DNS has been used as the basis for a bi-global resolvent analysis to provide insight into the linear amplification from linearised Navier-Stokes equations that uses only the mean flow field of this flow. A bi-global resolvent analysis sweep over a range of temporal frequencies and spanwise waveumbers has been undertaken. The results reveal that the maximum gain and its resolvent velocity response mode are closely associated with structures that correspond to intense u'v' structures, as well as to the location of maximum turbulence intensity that is located at one displacement thickness from the wall with a spanwise length scale of approximately 1.5 displacement thicknesses.