Interacting Mountain Waves and Boundary Layers

Abstract

Linear hydrostatic 3D mountain wave theory is extended to include a thin frictional boundary layer (BL), parameterized using two characteristic relaxation times for wind adjustment. The character of the BL is described using a “compliance coefficient,” defined as the ratio of BL thickness change to imposed pressure. In this formulation the simplest model that captures the two-way interaction between mountain waves and the boundary layer is sought. The slower BL wind speed amplifies the wind response and shifts it upstream so that the wind maxima occur in regions of favorable pressure gradient, not at points of minimum pressure. Variations in BL thickness reduce the mountain wave amplitude. The BL effect is sensitive to the wind profile convexity. The boundary layer improves the linear theory description of windy peaks. Low-level flow splitting is enhanced and wave breaking aloft is reduced. The BL also decreases the amount of upslope orographic precipitation. The wave momentum flux reduction by the BL is greater than the pressure drag reduction, indicating that part of the pressure drag is taken from BL momentum.

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

“…• No simplifying (linear) approximations applied to the model equations of motion; the most hazardous mountain wave flows are highly non-linear, e.g., rotors and hydraulic jumps/wave breaking • Realistic initial and boundary conditions, data assimilation, representation of convergence and convection; problems can occur in 3DVOM when there is significant horizontal variation in conditions and atmospheric forcing (e.g., trough or low centre within the domain), since it is initialised by a single profile • Thorough representation of moist processes (noting that the U.K. has a very moist climate with cloud and rainfall common); 3DVOM is a dry model, but in reality, reversible latent heating (cloud formation and evaporation) effects favour flow over terrain rather than blocking, also affecting wave amplitude [58]; meanwhile, irreversible latent heating effects (e.g., upslope rainfall) modify the stability profile and, hence, the wave response [59][60][61][62]; further, any orographically-triggered deep convection will negate wave activity • More sophisticated boundary layer scheme; the boundary layer is known to impact lee wave generation and downwind decay [63][64][65], while the performance of the boundary layer scheme also decides the accuracy of forecast lee wave impacts on near-surface winds [13,44] • Direct simulation of the diurnal cycle through radiation, surface and boundary layer parametrisations, including for instance nocturnal stable boundary layers; boundary layer stability strongly affects wave propagation and lee wave decay [64] • Full and contiguous coverage of the U.K. (and eventually beyond, as future computing resources allow) • Lee wave impacts become prognostic; the interplay of lee waves with the atmospheric environment in which they form, including other weather phenomena, is represented • Access to a comprehensive, standardised set of diagnostics, long-term central archiving…”

Gravity Waves and Wind-Farm Efficiency in Neutral and Stable Conditions

“…A similar approach has been used by Smith (2007Smith ( , 2010 to study the perturbation of the boundary layer by small-scale orography or constant drag forcing, representing the effect of a large wind farm. Here, we consider the boundary-layer behaviour in response to a wind-farm drag force that varies linearly with the perturbation velocity.…”

The physics of orographic gravity wave drag

“…Trapped lee wave absorption was therefore found to be maximized for stable boundary layers (in accordance with [78]). Smith [165] developed a hydrostatic 3D linear model to represent the absorption of mountain waves by boundary layers, using a bulk approach including a Rayleigh damping coefficient to represent friction. He showed that variations in the boundary layer thickness reduce the mountain wave amplitude (in agreement with [157]), the pressure drag, and even more severely the wave momentum flux, confirming that part of the pressure drag is due to boundary layer friction.…”