A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

• Published in: Acta geophysica Vol. 59; no. 6; pp. 1109 - 1134
• Main Authors: Smolarkiewicz, Piotr K., Szmelter, Joanna
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Versita 01.12.2011; Versita; Springer Nature B.V
• Subjects: Anelasticity; Asymptotic properties; Atmospheric models; Computer simulation; Construction; Differential equations; Discretization; Earth and Environmental Science; Earth Sciences; Fluid mechanics; Geophysics; Geophysics/Geodesy; Geotechnical Engineering & Applied Earth Sciences; Gravity; Gravity waves; Internal waves; Mathematical models; mountain waves; nonoscillatory forward-in-time schemes; soundproof equations; Structural Geology; unstructured mesh models; atmospheric models; nonoscillatory forward-in-time schemes; soundproof equations; unstructured mesh models; mountain waves
• ISSN: 1895-6572; 1895-7455
• DOI: 10.2478/s11600-011-0043-z

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudoincompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech. , 663 , 120–147)].