# Advances in Riblets Design
## 2 Physics of Riblets  
Multiple research studies have been undertaken to examine the effectiveness of various riblet geometries in reducing drag. The effectiveness of drag reduction is closely linked to the flow properties, size and configuration of riblets [23; 26; 30; 62; 63]. Some conventional shapes of riblet geometries are illustrated in Figure 1. Bladed [62], triangular [29], semi-circular [26; 64], trapezoidal [51; 65; 66; 67] and spaced triangular [68] are some of the most conventional geometries. Riblets drag reduction can be characterized by non-dimensional parameters, namely: (1) non-dimensional spacing, defined as \(s^{+}=s\cdot u_{\tau}/\
u\), in which \(\
u\) is the kinematic viscosity and \(u_{\tau}\) is the friction velocity known as a function of viscous shear stress (\(u_{\tau}=\sqrt{\tau_{0}/\rho}\)), and (2) non-dimensional height of the grooves (\(h^{+}\)). The non-dimensional parameters are generally used to compare the outcomes of using riblets with available numerical and experimental studies [6; 22; 50; 65]. In addition, by utilizing experimental data from diverse riblet configurations, the square root of non-dimensional riblet cross-section area (\(l_{g}^{+}=\sqrt{A_{g}^{+}}\)) has been introduced [57]. The goal was to determine if it could be feasible to represent drag reduction through a geometric parameter capable of encompassing the combined impact of riblet spacing and shape. This approach was implemented as another effective parameter for the characterization of riblets [69; 70]. Several researchers have dedicated their studies to investigating the effects of riblets on both boundary layers and free stream flows. Specifically, they have focused on examining the coherent structures present within the turbulent boundary layer, particularly in areas influenced by the wall. These coherent structures exhibit unique characteristics, including smaller sizes and complex three-dimensional fluctuations, which differ from the overall flow behavior [71]. These property fluctuations in the airflow over the surface of a commercial aircraft at an altitude of 12.2 km, with a Mach number (M) of 0.8 and a Reynolds number (Re) of \(10^{6}\) can be in the order of microns [32; 50]. The coherent structures are a part of the process of sweep and ejection with momentum exchange inside the turbulent boundary layer [18; 26; 72]. Momentum exchange in the turbulent boundary layer would be accrued by approaching high-speed flows to the surface (known as sweep) that is associated with positive u-component and negative v-component velocities and moving the low-speed flows from the near wall to toward freestream flow (known as ejection) that is associated with negative u-component and positive v-component velocities; this would result in shear stress effects inside the turbulent boundary layer [18; 73]. The process of sweep and ejection causes near-wall longitudinal vortices, which lead to small spanwise motions in the viscous sub-layer and then increased friction drag [73]. Riblets, like small longitudinal fences, can hamper the movements of these vortices in such a way as to control skin friction drag [32; 74; 75; 76; 35]. Research studies have been mainly focused on the viscous sublayer, the area with \(y^{+}<5\), given that 50% of turbulent energy is generated in the lower region (i.e., the lower 5% area) of the turbulent boundary layer [77]. To prevent the occurrence of sweep and injection between flow layers, riblet geometries with sizes comparable to the viscous sublayer are necessary. This size requirement ensures effective impedance of the flow interactions and promotes desired flow behavior [21]. A classical definition of drag reduction by riblet surfaces is defined by using the concept of surface-wetted area [21; 78]. Compensation of the surface wetted area is an important factor in evaluating the drag reduction performance by riblets. In this context, the level of interaction between surface and fluid flow is an indication of the shear stress and friction drag [17].