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Dale R. Durran
,
Ming-Jen Yang
,
Donald N. Slinn
, and
Randy G. Brown

Abstract

This paper investigates several fundamental aspects of wave-permeable, or “radiation,” lateral boundary conditions. Orlanski (1976) proposed that approximate wave-permeable boundary conditions could be constructed by advecting disturbances out of the domain at a phase speed c *, which was to be calculated from the values of the prognostic variable near the boundary. Rigorous justification for this approach is possible for one-dimensional shallow-water flow. It is shown, however, that the floating c * approach gives poor results in the one-dimensional shallow-water problem because all accuracy in the c * calculations is eventually destroyed by the positive feedback between errors in c * and (initially small) errors in the prognostic fields at the boundary. Better results were achieved by using fixed values of c *. In our test cases, an externally specified c * could deviate from the true phase speed U + c by 40%–60% and still yield better results than schemes in which c * was calculated at the boundary.

In order to examine the effects of wave dispersion on the question of whether c * should be fixed or calculated, tests were conducted with a two-level shallow-water model. Once again, the simulations with fixed c * were distinctly superior to those in which c * was calculated at the boundary. A reasonable, though nonoptimal, value for the fixed c * was the phase speed of the fastest wave.

Wave dispersion is, however, not the only factor that makes it difficult to specify wave-permeable boundary conditions. Two-dimensional shallow-water waves are nondispersive, but their trace velocities along the x and y axes are functions of wavenumber. As a consequence, the simple radiation boundary condition appropriate for one-dimensional shallow-water flow is just an approximation for two-dimensional flow. Engquist and Majda ( 1977) developed improved boundary conditions for the two-dimensional problem by constructing approximate “one-way equations.” In this paper, the approach of Engquist and Majda is used to construct second-order one-way wave equations for situations with nonzero mean flow. The new boundary condition is tested against several alternative schemes and found to give the best results. The new boundary condition is particularly recommended for situations where waves strike the boundary at nonnormal angles of incidence.

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Daniel J. Kirshbaum
,
George H. Bryan
,
Richard Rotunno
, and
Dale R. Durran

Abstract

The triggering of convective orographic rainbands by small-scale topographic features is investigated through observations of a banded precipitation event over the Oregon Coastal Range and simulations using a cloud-resolving numerical model. A quasi-idealized simulation of the observed event reproduces the bands in the radar observations, indicating the model’s ability to capture the physics of the band-formation process. Additional idealized simulations reinforce that the bands are triggered by lee waves past small-scale topographic obstacles just upstream of the nominal leading edge of the orographic cloud. Whether a topographic obstacle in this region is able to trigger a strong rainband depends on the phase of its lee wave at cloud entry. Convective growth only occurs downstream of obstacles that give rise to lee-wave-induced displacements that create positive vertical velocity anomalies wc and nearly zero buoyancy anomalies bc as air parcels undergo saturation. This relationship is quantified through a simple analytic condition involving wc , bc , and the static stability N2 m of the cloud mass. Once convection is triggered, horizontal buoyancy gradients in the cross-flow direction generate circulations that align the bands parallel to the flow direction.

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Jeffrey D. Kelley
,
David M. Schultz
,
Russ S. Schumacher
, and
Dale R. Durran

Abstract

On 25 December 2016, a 984-hPa cyclone departed Colorado and moved onto the northern plains, drawing a nearby Arctic front into the circulation and wrapping it cyclonically around the equatorward side of the cyclone. A 130-km-wide and 850-km-long swath of surface winds exceeding 25 m s−1 originated underneath the comma head of the lee cyclone and followed the track of the Arctic front from Colorado to Minnesota. These strong winds formed in association with a downslope windstorm and mountain wave over Colorado and Wyoming, producing an elevated jet of strong winds. Central to the distribution of winds in this case is the Arctic air mass, which both shielded the elevated winds from surface friction behind the front and facilitated the mixing of the elevated jet down to the surface just behind the Arctic front, due to steep lapse rates associated with cold-air advection. The intense circulation south of the cyclone center transported the Arctic front and the elevated jet away from the mountains and out across Great Plains. This case is compared to an otherwise similar cyclone that occurred on 28–29 February 2012 in which a downslope windstorm occurred, but no surface mesoscale wind maximum formed due to the absence of a well-defined Arctic front and postfrontal stable layer. Despite the superficial similarities of this surface wind maximum to a sting jet (e.g., origin in the midtroposphere within the comma head of the cyclone, descent evaporating the comma head, acceleration to the top of the boundary layer, and an existence separate from the cold conveyor belt), this swath of winds was not caused by a sting jet.

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