gfdl on-line bibliography > 1988 citations
On high-drag states of nonlinear stratified flow over an obstacle
Bacmeister, J. T., and R. T. Pierrehumbert, 1988: On high-drag states
of nonlinear stratified flow over an obstacle. Journal of the Atmospheric
Sciences, 45(1), 63-80.
Abstract: We have carried out a numerical investigation of the
nature of high-drag states occurring in nonlinear stratified flow over
obstacles. In particular, we consider the relative merits of theories which
view the drag enhancement as due to linear resonance vs mechanisms which
seek to exploit analogies with nonlinear hydraulic thoery.
First we examine the behavior of the system as a function of the height
of a zero-wind line imposed in the ambient flow. The character of the high-drag
states conforms well to the predictions of the internal hydraulic analysis
of Smith, and cannot be explained in terms of linear resonance. However,
a high-drag state emerges even when the initial critical level height is
below the lowest predicted resonant height. In this case an upstream-propagating
bore is generated which adjusts conditions so as to allow a high-drag state.
Further experiment with a narrow mountain revealed that nonhydrostatic
effects do not appreciably affect the behavior for the lowest resonant
position, but considerably reduce drag at the higher order resonances.
In the second series of experiments, the numerical model is initialized
with the idealized high-drag states yielded by Smith's theory, subject
to uniform upstream wind conditions. When the mountain is high enough to
produce wavebreaking in uniform flow, an overturning region develops at
the theoretical level of no motion and a vertically propagating wave emerges
aloft; nevertheless, the flow near the ground remains substantially unaltered.
When the mountain is too low to support wavebreaking, the mixed region
in the lee collapses, and the flow reverts to a nonhydraulic Long's model
solution subject to a radiation upper boundary condition. Thus, wavebreaking
is a crucial part of the dynamics maintaining the high-drag state.
Our results expose some aspects of nonlinear gravity wave critical level
behavior that are of general interest. The long term properties of the
critical level were found to depend on the phase of the incident wave.
Of particular interest are the circumstances in which the critical level
acts as an absorber for all time. In this case the convergence of vertical
momentum flux is balanced by a divergence of horizontal momentum flux,
a state of affairs which can occur for only for a horizontally localized
wave packet incident on a horizontally unbounded critical level.