# Turbulent Drag Reduction Characteristics of Bionic Nonsmooth Surfaces with Jets
## 1 Introduction  
Flow control and drag reduction are important research focuses that should be fully considered in a range of engineering fields. High efficiency of drag reduction can improve propulsion efficiency and reduce fuel consumption [1]. Turbulence is a common flow state in most situations, and the skin friction on the turbulent wall is much greater than that on the laminar wall [2; 3]. Therefore, the study of drag reduction in wall turbulence has important practical significance. To control the flow, a variety of methods have been proposed. Changing the wall conditions by the super-hydrophobic wall was considered as an effective method [4; 5]. Changing the fluid properties by adding polymers also achieved control effects [6]. Moreover, the application of external motions and forces to the original wall to generate controllable disturbance and achieve the flow control was also studied [7; 8; 9]. These methods have achieved certain effects in specific working conditions. Taking inspiration from nature, researchers started to study the turbulent drag reduction on grooved surfaces, which was inspired by the nonsmooth structures on shark skin. Most studies focused on drag reduction characteristics and its mechanisms [10]. The shape and size of the groove structure were shown to have significant impacts on drag reduction characteristics. Simulations and physical experiments showed that the groove surface can achieve a maximum drag reduction ratio of 10% when the dimensionless spacing (S\({}^{+}\)) was between 16 and 20 and the dimensionless height (H/S) was between 0.5 and 0.8 [11; 12]. A study of an airfoil model with longitudinal microgrooves also showedthat the drag reduction effect can be obtained by setting the scale of the micro-groove equal to the scale of the turbulent vortex near the wall [13]. The decrease in the exchange of flow momentum is one of the main causes of drag reduction. [PERSON] et al. [11] found that the existence of the groove can inhibit the frequency of momentum exchange along the spreading direction. Although the existence of the groove will increase the surface area, the spikes can destroy the streamwise vortex and restrain the spreading motion, thereby restraining the formation of low-speed strips and reducing the turbulent kinetic energy exchange. Moreover, the fluid in the groove valley can be maintained at a low-speed state, and the shear stress in the trough can be greatly reduced, resulting in a net reduction in skin friction [14; 15]. Therefore, the drag reduction enhancement mechanism of microgrooves can be considered as the restriction effect [16]. Direct numerical simulations intended to study the relationship between vortices at the bottom of the trench and energy dissipation also confirmed the above conclusions [17]. The existence of the groove will also affect the transition process, which can be a two-dimensional linear process or a three-dimensional process [18]. In recent years, another natural phenomenon, named a \"super-hydrophobic surface\", has attracted increasing research interest. This type of surface has significant effects on drag reduction [19; 20; 21]; so much so that the drag reduction ratio even approached 50% in some experiments with low speed [22]. There are two ways to obtain a super-hydrophobic surface: (1) by modifying a high-surface-energy rough surface with low-surface-energy materials and (2) by constructing a micro-rough structure on a low-surface-energy surface. One of the important ways to study drag reduction characteristics is via direct numerical simulation (DNS). In such simulations, a hydrophobic surface is always represented by a slip boundary condition. When the slip boundary condition was used in the streamwise direction, the skin friction drag decreased. However, when the slip boundary condition was used in the spanwise direction, the drag increased [23; 24]. The flow slip on the wall is considered to be the main cause of drag reduction.