## 1 Introduction  
The growing concern over energy efficiency and environmental pollution is furthering the appeal of transport vehicles, particularly aircraft, that produce less aerodynamic drag. One of the most interesting passive drag reduction techniques is the use of riblets, i.e., streamwise-aligned micro-grooves that are known to reduce turbulent skin-friction drag (see, for example, the review paper [1] and the many references therein), and are approaching usability in aeronautics. Early studies, spurred by the oil crisis of the 1970s, were performed at NASA [2], and important experiments were carried out in the Berlin oil tunnel by [PERSON] and coworkers [3, 4]. They evidenced the crucial importance of the riblet shape, their size, and--most importantly--the sharpness of their tip; optimal configurations empirically determined at the time yield up to 6-8% and possibly higher reductions in skin friction for low-_Re_ flat plate-boundary layers studied in laboratory conditions. The theoretical understanding of the riblets working mechanism is due to [PERSON] [5], who quantified the different resistance offered by a grooved wall to the parallel flow and the cross-flow. He also explained [6] how skin-friction drag reduction is equivalent to an upward shift of the logarithmic portion of the turbulent velocity profile. This important argument, later taken up again by [7], implies that it is incorrect to describe riblets performance simply as a percentage change of the skin-friction coefficient, as this simplistic figure depends on the Reynolds number of the flow. However, the value of the upward shift, once measured in viscous units, is Reynolds independent and should be used to characterize the ability of riblets (and other techniques) to reduce turbulent friction; in fact, recently this concept has been extended [8] to other strategies of skin-friction reduction. To capture, in a numerical simulation, the complex physics of the interaction between turbulence and a solid wall covered by riblets, and to properly measure friction reduction, direct numerical simulations (DNS) or wall-resolved large eddy simulations (LES) are required. Such computations are unfeasible for complex aeronautical configurations at high Reynolds numbers, where numerical simulations based on the Reynolds-Averaged Navier-Stokes equations (RANS) equipped with a turbulence model are the standard approach. Owing to their microscopic dimensions, however, riblets on an aircraft cannot be included directly in a RANS simulation. Even if they could, it is unclear to what extent a standard RANS model would be able to represent the physics of drag reduction. Bridging the gap between drag reduction by riblets in turbulent flows and the need to incorporate it into RANS-type flow solvers has led to the development of computational models for riblets. [PERSON] et al. [9] modified the Spalart-Allmaras turbulence model to account for riblets by using smooth-wall geometry. Along similar lines, [PERSON] et al. [10] introduced a modified boundary condition for the \(k-\omega\) turbulence model, and [PERSON] et al. [11] extended the Aupoix model to describe riblets locally misaligned with the mean flow, and to account for mean pressure gradients. How riblets affect a turbulent boundary layer with a non-zero pressure gradient is a debated subject [12; 13; 14]. In 2018, [PERSON] and [PERSON] [15] developed a new model based on a slip-length concept, whose results provided an interesting view on the riblets drag reduction mechanism in presence of pressure gradients. In addition to friction reduction, they found that riblets alter the pressure distribution, and may provide additional pressure drag reduction. This indirect effect was also observed for other friction-reduction devices: [PERSON] et al. [16] used spanwise forcing to reduce turbulent friction on a wall with a bump, and found in their incompressible DNS study that a reduced friction drag is accompanied by a reduced pressure drag. Similarly, using DNS, [PERSON] et al.