Permanent and Transient Upstream Effects in Nonlinear Stratified Flow over a Ridge

Abstract

The ?high drag? state of stratified flow over isolated terrain is still an impediment to theoretical and experimental estimation of topographic wave drag and mean-flow modification. Linear theory misses the transition to the asymmetrical configuration that produces the enhanced drag. Steady-state nonlinear models rely on an ad hoc upstream condition like Long's hypothesis and can, as a result, be inconsistent with the 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, especially as regards its permanence. A time-dependent numerical model with open boundaries is used in an effort to distinguish between permanent and transient upstream flow changes and to relate these to developments near the mountain. A nonrotating atmosphere with initially uniform wind and static stability is assumed. It is found that permanent alterations are primarily due to an initial surge not directly related to wave breaking. Indeed, there are no obvious parameter thresholds in the time-mean upstream state until ?orographic adjustment? (deep blocking) commences. Wave breaking, in addition to establishing the downstream shooting flow, generates a persistent, quasi-periodic, up-stream transience, which apparently involves the ducting properties of the downslope mixed region. This transience is slow enough to be easily confused with permanent changes. To understand the inflow alteration and transience, the energy and momentum budgets are examined in regions near the mountain. High drag conditions require permanent changes in flow force difference across the mountain and, consequently, an ongoing horizontal flux of energy and negative momentum. The source of the upstream transience is localized at the head of the mixed region. Blocking allows the total drag to exceed the saturation value by more than an order of magnitude. The implications for nonlinear steady-state models and wave drag parameterization are discussed.