1 IntroductionThe surface with regu

1 Introduction
The surface with regular non-smooth structure
imitating animal’s skin is called bionic non-smooth
surface (BNSS). Researches have shown that BNSS has
the ability of drag red~ction’l-~T]h.e riblet, derived from
shark skin, was considered the ideal type of non-smooth
The frictional force could be reduced by as
much as 7% to 10% in laboratory tests. Even in actual
flight test, 1 % to 2% drag reduction was also attained‘’ ‘I.
Two theories explain this drag reduction mechanism. In
the “secondary vortices theory”. Lee et al. believed that
most of the streamwise vortices stay above the riblet,
interacting with the riblet tip^'^'. The riblet tips impede
the spanwise movement of the streamwise vortices and
induce secondary vortices. The normalized root mean
square velocity fluctuation and turbulent kinetic energy
are smaller near the riblet surface compared with that
over a smooth flat plate. In the “protrusion height theory”
Bechert et al. believed that with protrusions of
height less than y+ =3-5‘12’, (where, y is perpendicular
to the wall and takes the form y+ = y .,urI u , the Reynolds
number defined with the velocity ,ur = J.o/p,
where z,is the average wall shear stress, p and ,D are
density and kinematic viscosity, respectively) ribs or
other non-smooth structures are embedded in the viscous
sublayer. In this layer, very close to the wall, any fluid
behaves in a highly viscous manner. Under viscous flow
conditions it turns out that the ribbed surface appears as
a smooth surface located at a virtual origin. However,
the location of the origin, i.e., its elevation above the
groove floor, depends on the direction of flow. For
cross-flow on the ribs, the virtual origin is closer to the
rib tips than for longitudinal flow. The difference between
these two heights, Ah, is called the “protrusion
height difference”. If a flow is generated by a fluid lump
in a plane at a height y+ above the surface, the fluid lump
experiences greater resistance if it moves laterally than if