ABSTRACT
In the first paper,
the development of Crow instability in
a homogeneous field of turbulence is studied.
The Crow instability becomes well developed in
most atmospheric turbulence levels, but in strong turbulence the vortex pair
deforms more irregularily due to turbulence advection.
The maximum Crow instability
wavelength decreases with increasing nondimensional turbulence
intensity (
), while it increases with increasing turbulence
integral length scale.
The vortex lifespan
is controlled primarily by and decreases with
increasing , while the effect of integral scale of turbulence
on vortex lifespan is
of minor importance. The lifespan of vortex in our numerical simulations
is estimated to be about 40
larger than
the theoretically predicted value.
This larger lifespan compared with an analytic theory agrees very well
with the data from laboratory experiments
and is caused
by slower growth in the middle of the vortex lifespan.
The maximum deviation in lifespan from the average value
due to ambient turbulence alone
is about 
of the mean for small and
about 
of the mean
for large , showing much less scatter in lifespan
compared with atmospheric observations.
The larger scatter of lifespans in atmospheric observations
appears to result from other factors such as stratification,
wind shear, and inhomogeneous ambient turbulence.
In the second paper,
the vortex decay and descent in
a homogeneous field of turbulence is investigated.
The decay rate of the vortex circulation increases clearly with
increasing ambient turbulence level but
decreases with increasing radial distance, which
is consistent with field observations.
Simple vortex decay
models are proposed as functions of
and radial distance.
A Gaussian type of vortex decay model
can be applied at larger radial distances,
while
an exponential type of vortex decay model can be applied at smaller
radial distances near the core,
but the latter can be extended up to a radial distance
of about
half of the initial vortex separation distance (b0)
for strong turbulence.
The circulation averaged over radial distances
from 
(rc is the initial core radius) to 
,which is related to the rolling moment of an encountering aircraft,
shows
a Gaussian decay for weak and moderate turbulence and
an exponential decay for strong turbulence.
A model for the vortex descent
based on the vortex decay model
is also proposed as a function of and dimensionless time.
The model predictions for the decay of the average circulation
appear to be in reasonable agreement with
observation data which have a large scatter, as long as the theoretical
circulation is used as the initial value.
However, the decay rates of observed circulations
are much larger than those obtained from our numerical simulations,
impling that besides ambient turbulence there are some additional factors
enhancing the vortex decay.
In particular, the effect of
ambient stratification on the enhancement of the vortex decay
appears to be significant.