# Turbulent Drag Reduction Characteristics of Bionic Nonsmooth Surfaces with Jets
## 1 Introduction
An average slip velocity of over 75% of the bulk velocity was obtained on a super-hydrophobic surface via DNS, and the corresponding wall shear stress reduction was found to be nearly 40% [25]. The apparent flow slip was verified with a confocal surface metrology system [26; 27]. [PERSON] et al. [28] suggested that the mean slip velocity at the wall increases the flow rate at a fixed pressure drop in turbulent pipe flow. Therefore, slip length is the key to drag reduction that is related to the flow state. In a laminar flow state, the effective slip length only depends on the surface geometry (i.e., the slip length is independent of the Reynolds number). In a turbulent flow state, the effective slip length is a function of the Reynolds number, indicating that the slip length is dependent on the flow conditions near the surface [29]. Some special flow patterns in nature also inspired new drag reduction methods. Sand dune flow is one of the most common flow patterns. Under the transport of wind, grains of sand migrate to inclined windward slopes and deposit on steep slip slopes, thereby forming dunes. [PERSON] and [PERSON] [30] pointed out that sand dunes are aerodynamic objects because their shape is adapted to allow the air flow with the least effort. [PERSON] and [PERSON] [31] also reported that the shape of dunes is directly controlled by aerodynamic processes. The drop-in velocity and shear stress at the base of a dune has been widely predicted and observed [32]. Some researchers have even applied the aerodynamic characteristics of sand dunes to practical engineering applications. [PERSON] and [PERSON] [33] proposed a new barchan dune (BD) vortex generator, which exhibited 75-80% less drag when compared with a V-gutter at the same blockage ratio. [PERSON] et al. [34] proposed a new dune-shaped combustion chamber to reduce the total pressure loss and obtain a stable trapped vortex, whose simulation results showed that there is an optimal leeward angle with small total pressure loss. Shark gills were also adapted as a bionic prototype to reduce drag. As a fast-moving marine animal, sharks can travel very fast during predation. Moreover, sharks have interesting broad gill plates located on the front of the body. Sharks inhale sea water through a half-open mouth, which flows out of the gills to exchange gas; however, the function of these gills is closely related not only to respiration, but also to drag reduction [35]. [PERSON] [36] found that fish will close the gill slits on the inside bend during turns and shunt the gill efflux into the gills on the outside bend, a separation-prone region of the body, to obviate separation drag. [PERSON] and [PERSON] [37] proposed that the orientation and placement of the gill openings are particularly well suited to the jet-blowing technique. Inspired by shark gills, [PERSON] et al. [38] studied the drag reduction characteristics of bionic jet surfaces, in which they obtained a maximum drag reduction rate of 9.51%. Similarly, [PERSON] et al. [39] studied the drag reduction characteristics of a revolving body with a bionic jet surface, in which they achieved a maximum friction reduction rate of 10.8%. A preceding study on grooved surfaces mostly focused on single V-shaped grooves parallel to the mainstream, only considering some simple morphology for nonsmooth surfaces. Moreover, the maximum drag reduction ratio reached approximately 10%, and it was hard to make further breakthroughs. The microstructures of super-hydrophobic surfaces are micron-sized, which are commonly generated via laser processing. However, from an economic point of view, super-hydrophobic surfaces are not suitable for large-scale applications in engineering fields. Based on bionics, the current study tried to provide a new drag reduction method. The study broke the limitations in a single morphology and proposed a new nonsmooth surface inspired by sand dunes. The nonsmooth surface can effectively reduce the skin friction. However, the decrease in skin friction was accompanied by a sharp increase in pressure drag.