PERMANENT AND TRANSIENT UPSTREAM EFFECTS IN NONLINEAR STRATIFIED FLOWOVER A RIDGE

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.