## 1 Introduction  
Along with the increase in air travel, the demand for economical and environmentally friendly aircraft is also growing. In coping with this demand by minimizing environmental concerns such as carbon dioxide emissions in relation to global warming, it is vital to improve aerodynamic efficiency as well as to reduce drag. As skin friction drag constitutes more than half of all drag on an aircraft [1], reducing it is key to increasing aerodynamic performance and reducing fuel consumption rates. The boundary layer profiles play an important role in characterizing the mechanism of skin friction drag, thereby making it vital to control the boundary layer profiles. Among a number of boundary layer controlling devices such as suction [2; 3], blowing [4], synthetic jets [5], vortex generators [6], and riblets [1; 7; 8; 9; 10; 11; 12], riblets are one of the methodologies used to reduce aircraft surface drag [1; 7; 8; 9; 10; 11; 12]. Riblets are a passive means of turbulent flow control by which skin friction drag is reduced, and were first employed at the NASA Langley Research Center back in the 1970s [8; 13] in imitation of the skin structure of a shark that swims long distances at high speed. The structure of a riblet is a groove aligned in the flow direction fabricated on the wall surface that induces the streamwise vortex structure, with the aim of controlling the turbulent structure responsible for surface drag in the boundary layer, and thus reducing turbulent skin friction drag. To date, numerous studies on riblets have been conducted concerning the mechanism [8; 9; 13; 14] and effectiveness [10; 11; 12; 15] of riblets in reducing skin friction drag, and their industrial applications in wind turbine blades [10], railways [7], and aircraft [16]. Some design criteria such as the height, width and skewness of the peak shape, and detailed shape of riblets to optimize the reduction of skin friction drag for a flowfield of interest have been clarified. The 3M company demonstrated that their riblets successfully reduced skin friction drag 4-6% in the flowfield without involving any pressure gradients or angles of attack [16]. With the aid of computer simulation and highly resolved measurement techniques, the reduction of skin friction drag by riblets has been found to reach approximately 10% by optimizing the riblet geometry to cope with the flowfield of interest [17; 18; 19; 20]. With regard to an actual application of riblets on aircraft, the Airbus company has implemented wind tunnel tests for actual aircraft with riblets attached to the whole airframe surface, and consequently demonstrated the reduction of skin friction drag by approximately 2% [1; 21]. According to an estimate by Airbus, even drag reduction of 1% can reduce operation costs by more than a million dollars per aircraft on a yearly basis [1; 21]. Thus, the reduction of skin friction drag has a significant impact on economics [9]. When considering the use of riblets on actual aircraft, it is necessary to consider fabrication costs, maintainability, and sustainability in the change of environment where the riblets are exposed without a decline in aircraft performance. Additionally, it is necessary to obtain design criteria for the riblet geometry so as to optimize the reduction of skin friction drag for any locations on the aircraft (e.g., fuselage, wing), and for any change in flight conditions and attitude. The Japan Aerospace Exploration Agency (JAXA) has been investigating the effectiveness of riblets in reducing skin friction drag [22; 23] as part of their environmentally friendly aircraft research project known as Flight Investigation of skiN-friction reducing Eco-coating (FINE). The aims of the riblet study are (i) to develop paint-based riblets using aviation paint, and (ii) to optimize the riblet geometry so as to gain reduction capability of skin friction drag for JAXA's originally designed riblet [17].