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Two-dimensional, stratified shear flow over
a ridge is considered. The finite-amplitude
disturbances are steady
and hydrostatic, and solutions
are derived from the Boussinesq from the Long's
equation. Two limiting solutions are
examined;
viz., 1) the case of marginal or neutral static
stability and 2) the case of infinite static stability
either
at or above the lower boundary. The former case
is associated with a critical point for the horizontal
flow velocity,
u=0; an infinite value of u accompanies
the latter case. The conditions for neutral static
stability that have been
derived for uniform upstream
flow conditions are shown to apply to the case when
both the upstream static stability
N¯(z¯) and the
horizontal velocity u¯(z¯) are nonuniform in the
vertical direction z¯. Upstream variations of N¯(z¯)
and u¯(z¯) cannot be specified arbitrarily if the
relative vorticity vanishes at some point either at
the ridge
or in the airstream above. An
unbound solution, u = ∞, of Long's equation will occur unless
the condition [N¯−2(u¯−2/2)z¯]z¯
< 1 is satisfied. The
physical interpretation of this constraint on the
upstream flow is provided. It is also noted
that the
same condition has been derived by Abarbanel et al. as
a sufficient condition for the nonlinear stability
of
a stratified shear flow to three-dimensional
distrurbances. However, the physical relationship
between these
two model results has not been
established.
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