The mechanism of wrap, tilt and stretch of vorticity lines around
a
strong thin straight vortex tube of circulation Γ starting with a
vortex
filament in a simple shear flow
(U=SX2Xˆ1,
S being a shear rate) is investigated analytically. An asymptotic
expression for the vorticity field is obtained at a large Reynolds number
Γ/ν[Gt ]1, ν being the kinematic viscosity of
fluid,
and during the initial time St[Lt ]1 of evolution as well as
St[Lt ](Γ/ν)1/2. The vortex tube,
which
is inclined from the streamwise (X1) direction both
in the
vertical (X2) and spanwise (X3)
directions,
is tilted, stretched and diffused under the action of the uniform shear
and
viscosity. The simple shear
vorticity is on the other hand, wrapped and stretched around the vortex
tube by a
swirling motion, induced by it to form double spiral vortex layers of high
azimuthal
vorticity of alternating sign. The magnitude of the azimuthal vorticity
increases
up to O((Γ/ν)1/3S) at
distance
r=O((Γ/ν)1/3
(νt)1/2) from the vortex tube. The spirals induce
axial flows
of the same spiral shape with alternate sign in adjacent spirals which
in turn tilt
the simple shear vorticity toward the axial direction. As
a result, the vorticity lines wind helically around the vortex tube accompanied
by
conversion of vorticity of the simple shear to the axial direction.
The axial vorticity increases in time as S2t,
the
direction of which is opposite to that of the vortex tube at
r=O((Γ/ν)1/2
(νt)1/2) where the vorticity magnitude is strongest.
In the
near region r[Lt ](Γ/ν)1/3
(νt)1/2, on the other hand, a viscous cancellation
takes
place in tightly wrapped vorticity of alternate sign, which leads
to the disappearance of
the vorticity normal to the vortex tube. Only the axial component of the
simple
shear vorticity is left there, which is stretched by the simple shear
flow itself. As a
consequence, the vortex tube inclined toward the direction of the simple
shear vorticity (a cyclonic vortex) is intensified, while the one oriented
in the
opposite direction (an
anticyclonic vortex) is weakened. The growth rate of vorticity due to this
effect
attains a maximum (or minimum) value of
±S2/33/2 when the vortex
tube
is oriented in the direction of
Xˆ1+Xˆ2∓
Xˆ3. The present asymptotic solutions are expected
to be closely related to the flow structures around intense vortex tubes
observed
in various kinds of turbulence such as helical winding of vorticity lines
around a
vortex tube, the dominance of cyclonic vortex tubes, the appearance of
opposite-signed vorticity around streamwise vortices and a zig-zag
arrangement of streamwise vortices in homogeneous isotropic turbulence,
homogeneous
shear turbulence and near-wall turbulence.