Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 315

Figure 5.19. Adverse pressure gradient engendered by a
vortex filament in the plane y-z

In spite of its conceptual nature, the model based on the
tilting of the wall-normal vorticity introduced by Jimenez
et al. [JIM 94] is more than worthy of a mention. Consider
the tilting of a layer under the influence of the gradient ω

y

c uy , which
encompasses both the shear and velocity effects induced by
the structure (Figure 5.20). The tilted vorticity layer
approximately forms an angle

∂∂ ς Uy = and its advection by the velocity

()

( )

with the
wall at a distance y and after a period of time t . The
quantity

α ≈ arctg 1 ς t ≈ 1 ς t

()

plays the role of a strain rate. The
viscosity does not come into play when short times are at
stake, and the thickness of the vorticity layer decreases as

ς ∝

c uyy