# Advances in Riblets Design
## 2 Physics of Riblets
In the riblet surfaces, turbulent flow is lifted up and interacts with riblet tips that decrease wetted area and fluid shear stress [79]. In comparison to the smooth surface, adjusting the flow vortices above the valleys of riblets results in lower values of cross-stream flow fluctuations and reduces turbulent kinetic energy near the surface [65; 79; 80]. Importantly, these adjustments also minimize pressure fluctuations in the outer layers of the flow. These alterations have the potential to influence the emitted sound in compressible fluids, especially in aviation-related contexts [51; 65]. As the reduction in wetted area is the main concept behind drag reduction, the number of indentations per unit of length should be within an optimum range [21]. The effect of non-dimensional spacing, \(s^{+}\), in drag reduction for a triangular riblet geometry with peak sharpness of \(60^{\circ}\) is illustrated in Figure 2. The figure indicates the limit of drag reduction when riblets spacing tends to be zero. Drag reduction achieves its optimum values at about \(s^{+}\approx 15\). Increasing \(s^{+}\) further would result in decreased effectiveness, causing an increase in drag more than zero, which is defined in the figure as a rough surface [35]. Figure 1: Conventional riblet geometries: (**a**) trapezoidal, (**b**) spaced triangular, (**c**) triangular, (**d**) bladed, (**e**) trapezoidal bladed, and (**f**) semi-circular. Research efforts have been dedicated to examining the aerodynamic implications of riblets on curved surfaces, particularly in the context of aircraft aerodynamics. Investigations have specifically targeted 3D applications to account for the complexities arising from variations in flow alignment experienced when airflow interacts with curved surfaces. To address these challenges, researchers have introduced curved riblet configurations featuring diverse riblet shapes, non-dimensional spacing and height. These design considerations aim to optimize drag reduction performance and effectively manage the intricate aerodynamic characteristics associated with curved surfaces [81]. Experimental and numerical studies have been conducted to investigate the impact of riblets on the structure of the boundary layer. To comprehensively understand riblet performance across different scales, a hierarchical analysis approach can be adopted. Starting at the micro-scale, detailed simulations and experiments delve into the fluid dynamics within individual riblet grooves and their interaction with the boundary layer, unveiling insights into local drag reduction mechanisms. Advancing to macro-scale, full-scale computational fluid dynamics simulations can evaluate the overall aerodynamic effect of riblets on complete aircraft systems, considering intricate flow interactions. In the experimental and numerical investigations, both viewpoints are considered separately or in a combined method. Generally speaking, these studies analyze the characteristics of the boundary layer before and after the application of riblets on flat and curved surfaces. The flow properties, including mean and fluctuating terms in the longitudinal, lateral, and vertical directions, are examined. The fluctuating terms not only influence the aerodynamic aspects but also have significant implications for the acoustical properties and generated noise [51; 62]. This paper also discusses relevant studies that explore the effects of riblets on the boundary layer and associated flow phenomena. Acknowledging the intersection of experimental and numerical research in exploring the impact of riblets on boundary layer structure, a comprehensive understanding of riblets' performance across diverse scales can be achieved through a hierarchical analysis framework. This approach entails a progression from the micro-scale, where detailed simulations and experiments illustrate the fluid dynamics within individual riblet grooves and their interaction with the boundary layer, showing localized drag reduction mechanisms.