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Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves

Weller, H and Shahrokhi, A (2014) Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves. Monthly Weather Review, 142 (12). ISSN 0027-0644

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Abstract

Steep orography can cause noisy solutions and instability in models of the atmosphere.Anew technique for modeling flow over orography is introduced that guarantees curl-free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain-following grids. Curl-free gradients are achieved by using the covariant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves.
Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous.Results of gravity waves over orography are insensitive to the placement of terrain-following layers. Themodel with implicit gravity waves is stable in strongly stratified conditions, withNDt up to at least 10 (whereN is the Brunt–Väisälä frequency). A warm bubble rising over orography is simulated and the curl-free pressure gradient formulation gives much more accurate results for this test case than amodel without thismimetic property.

Item Type: Article
Uncontrolled Keywords: 0401 Atmospheric Sciences
Subjects: T Technology > TD Environmental technology. Sanitary engineering
Divisions: Maritime and Mechanical Engineering
Publisher: American Meteorological Society
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Date Deposited: 19 Feb 2019 10:40
Last Modified: 19 Feb 2019 10:45
DOI or Identification number: 10.1175/MWR-D-14-00054.1
URI: http://researchonline.ljmu.ac.uk/id/eprint/10180

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