Dynamics of rotor formation in uniformly stratified two‐dimensional flow over a mountain

Abstract

The coupling between mountain waves in the free atmosphere and rotors in the boundary layer is investigated using a two-dimensional numerical model and linear wave theory. Uniformly stratified flow past a single mountain is examined.Depending on background stratification and mountain width, different wave regimes are simulated, from weakly to strongly nonlinear and from hydrostatic to non-hydrostatic. Acting in conjunction with surface friction, mountain waves cause the boundary layer to separate from the ground, causing the development of atmospheric rotors in the majority of the simulated flows.The rotors with largest vertical extent and strongest reverse flow near the ground are found to develop when the wave field is nonlinear and moderately non-hydrostatic, in line with linear theory predictions showing that the largest wave amplitudes develop in such conditions. In contrast, in near-hydrostatic flows boundary-layer rotors form even if the wave amplitude predicted by linear theory is relatively small. In such cases, rotors appear to be decoupled from the wave field aloft by low-level wave breaking. In fact, rotor formation is caused by short-wavelength modes propagating horizontally along an elevated and stably stratified jet below the neutrally stratified wave-breaking region. Once formed, atmospheric rotors trigger non-hydrostatic wave modes that can penetrate through the finite-depth neutral layer above the jet and propagate into the free atmosphere.In all simulated cases, non-hydrostatic effects -i.e. sharp vertical accelerations -appear to be essential for rotor formation, regardless of the degree of hydrostaticity in the primary wave field.

Synoptic‐flow interaction with valley cold‐air pools and effects on cold‐air pool persistence: Influence of valley size and atmospheric stability

“…Sachsperger et al . () find a maximum in wave amplitude around NH / U = 1 for such moderately non‐hydrostatic cases, H / L p = 0.1–0.2, with weaker waves for more and less hydrostatic cases. They also find that rotor trains accompany wave breaking, similar to those evident here in Figure , which are also larger and more vigorous in the same H / L p range.…”

Mountain Waves in High Resolution Forecast Models: Automated Diagnostics of Wave Severity and Impact on Surface Winds

“…Mountain waves, induced by stable tropospheric flow over terrain, are a well-known source of aviation hazards, such as strong up-and down-drafts, downslope windstorms [1][2][3][4], clear air turbulence (CAT) associated with tropospheric wave breaking [5][6][7][8][9][10], low-level turbulence and 'rotors' associated with wave-induced boundary layer separation [11][12][13][14][15][16][17] and hydraulic jump-like flows [12,18], as well as hazards to surface transport [19], such as very strong or gusty winds [20].…”

On the Boundary Conditions in the Numerical Simulation of Stably Stratified Fluids Flows

“…3. This choice seems to be a little bit counter intuitive, because the density ρ is governed by the transport equation (11) or (9), where the classical choice is to prescribe the values of the transported quantity at the inlet boundary. Here we should keep in mind that the transported quantity (ρ or ρ ′ ) is not a passive scalar.…”

“…Here we should keep in mind that the transported quantity (ρ or ρ ′ ) is not a passive scalar. The equation (11) or (9) is a part of the governing system, where the density ρ (or its perturbation ρ ′ ) plays an active role in the buoyancy force in the equation (12) or (10). In the steady case, the equation (11) should rather be understood as a geometrical constraint to the density and velocity field, specifying that u · ∇ρ = 0, i.e.…”

“…This is often combined with the use of the damping/buffer/sponge zones approach adopted close to the external artificial boundaries, as it can be seen e.g. in Sachsperger et al [11], Gatti-Bono and Colella [9], Ford [8], Slinn and Riley [12], Bauer et al [1], Wan and Porté-Agel [16] etc. .…”