On the Stability of a Time Dependent Boundary Layer
ICASE Report No. 93-73. Institute for Computer Applications in Science and Engineering, Hampton, Virginia, (1993)Abstract
The aim
of this
article
is to
determine
the
stability
characteristics
of a
Rayleigh
layer,
which
is known
to occur
when
the fluid
above
a flat
plate
has a
velocity
imparted
to it (parallel
to the plate).
This situation is intrinsically
unsteady, however
as a first
approximation
we consider
the instantaneous
stability
of
the
flow.
The
Orr-Sommerfeld
equation
is
found
to
govern
fixed
downstream
wavelength
linear
per-
turbations
to
the
basic
flow
profile.
By
the
solution
of
this
equation
we
can
determine
the
Reynolds
numbers
at
which
the
flow
is
neutrally
stable;
this
quasi-steady
approach
is
only
formally
applicable
for
infinite
Reynolds
numbers.
We
shall
consider
the
large
Reynolds
number
limit
of
the
original
problem
and
use
a
three
deck
mentality
to
de-
termine
the
form
of
the
modes.
The
results
of
the
two
calculations
are
compared,
and
the
linear
large
Reynolds
number
analysis
is
extended
to
consider
the
effect
of
weak
nonlinearity
in
order
to
determine
whether
the
system
is
sub
or
super
critical.