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A Forward-in-Time Anelastic Nonhydrostatic Model in a Terrain-Following Coordinate

Ching-Yuang HuangDepartment of Atmospheric Sciences, National Central University, Chung-Li, Taiwan

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Abstract

A three-dimensional (3D) forward-in-time anelastic nonhydrostatic model in a terrain-following coordinate is developed to investigate mesoscale circulations over topography. The anelastic nonhydrostatic model utilizes the deep-continuity equation, rather than the vertical-momentum equation commonly adopted, to compute vertical velocity. Hence, the anelastic nonhydrostatic model is identical to the hydrostatic model, except that the former perturbation pressure must be solved from an elliptic equation to coincide with nondivergent wind. To enhance the efficiency of iterations for convergence, the elliptic pressure equation is transformed to an artificial parabolic form that allows semi-implicit time integration as adopted in most elastic nonhydrostatic models.

Numerical experiments using the anelastic model, the same anelastic model but employing the vertical momentum equation, and the compressible model were conducted for comparisons. The presented anelastic model is reasonably accurate as compared to linear analytical solution, and the three nonhydrostatic models show similar performances for 2D, less hydrostatic flow over a bell-shaped mountain. The anelastic approach was found to be reasonably efficient for nonlinear flow over terrain slopes somewhat less than 1, above which ill convergence for the pressure equation was observed. Simulations of 3D mountain-induced wake circulation with/without the boundary layer effects indicate that there is little difference between the downstream wake forms for the hydrostatic model and the anelastic nonhydrostatic model, a substantiation of the feasibility of the presented anelastic formulation.

Corresponding author address: Prof. Ching-Yuang Huang, Dept. of Atmospheric Sciences, National Central University, Chung-Li 32054, Taiwan.

Email: hcy@rainbow.atm.ncu.edu.tw

Abstract

A three-dimensional (3D) forward-in-time anelastic nonhydrostatic model in a terrain-following coordinate is developed to investigate mesoscale circulations over topography. The anelastic nonhydrostatic model utilizes the deep-continuity equation, rather than the vertical-momentum equation commonly adopted, to compute vertical velocity. Hence, the anelastic nonhydrostatic model is identical to the hydrostatic model, except that the former perturbation pressure must be solved from an elliptic equation to coincide with nondivergent wind. To enhance the efficiency of iterations for convergence, the elliptic pressure equation is transformed to an artificial parabolic form that allows semi-implicit time integration as adopted in most elastic nonhydrostatic models.

Numerical experiments using the anelastic model, the same anelastic model but employing the vertical momentum equation, and the compressible model were conducted for comparisons. The presented anelastic model is reasonably accurate as compared to linear analytical solution, and the three nonhydrostatic models show similar performances for 2D, less hydrostatic flow over a bell-shaped mountain. The anelastic approach was found to be reasonably efficient for nonlinear flow over terrain slopes somewhat less than 1, above which ill convergence for the pressure equation was observed. Simulations of 3D mountain-induced wake circulation with/without the boundary layer effects indicate that there is little difference between the downstream wake forms for the hydrostatic model and the anelastic nonhydrostatic model, a substantiation of the feasibility of the presented anelastic formulation.

Corresponding author address: Prof. Ching-Yuang Huang, Dept. of Atmospheric Sciences, National Central University, Chung-Li 32054, Taiwan.

Email: hcy@rainbow.atm.ncu.edu.tw

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