St. Garner, PERMANENT AND TRANSIENT UPSTREAM EFFECTS IN NONLINEAR STRATIFIED FLOWOVER A RIDGE, Journal of the atmospheric sciences, 52(2), 1995, pp. 227-246
The ''high drag'' state of stratified how over isolated terrain is sti
ll an impediment to theoretical and experimental estimation of topogra
phic wave drag and mean-flow modification. Linear theory misses the tr
ansition to the asymmetrical configuration that produces the enhanced
drag. Steady-state nonlinear models rely on an ad hoc upstream conditi
on like Long's hypothesis and can, as a result, be inconsistent with t
he flow established naturally by transients, especially if blocking is
involved. Numerical solutions of the stratified initial Value problem
have left considerable uncertainty about the upstream alteration, esp
ecially as regards its permanence. A time-dependent numerical model wi
th open boundaries is used in an effort to distinguish between permane
nt and transient upstream flow changes and to relate these to developm
ents near the mountain. A nonrotating atmosphere with initially unifor
m wind and static stability is assumed. It is found that permanent alt
erations are primarily due to an initial surge not directly related to
wave breaking. Indeed, there are no obvious parameter thresholds in t
he time-mean upstream state until ''orographic adjustment'' (deep bloc
king) commences. Wave breaking, in addition to establishing the downst
ream shooting how, generates a persistent, quasi-periodic, upstream tr
ansience, which apparently involves the ducting properties of the down
slope mixed region. This transience is slow enough to be easily confus
ed with permanent changes. To understand the inflow alteration and tra
nsience, the energy and momentum budgets are examined in regions near
the mountain. High drag conditions require permanent changes in Row fo
rce difference across the mountain and, consequently, an ongoing horiz
ontal flux of energy and negative momentum. The source of the upstream
transience is localized at the head of the mixed region. Blocking all
ows the total drag to exceed the saturation value by more than an orde
r of magnitude. The implications for nonlinear steady-state models and
wave drag parameterization are discussed.