Numerical Analysis for Hydrostatic and Nonhydrostatic Equations of Inertial-Internal Gravity Waves

Sun, Wenbin

doi:10.1175/1520-0493(1984)112<0259:nafhan>2.0.co;2

Cited by 26 publications

(16 citation statements)

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“…The lateral eddy exchange, entrainment, vertical flux, and pressure perturbation gradient force are solved using the Forward-Backward scheme in time (Sun 1984) and using the central difference scheme in space. Vertical fluxes of rain, snow, and graupel due to downward terminal velocities are calculated with a forward scheme.…”

Section: Methodsmentioning

confidence: 99%

“…The conversion of condensate to precipitation and the cloud glaciation parameterized in their model were simplified. For the past few years, we have worked on a diagnostic one-dimensional cloud model (Haines and Sun 1994) and a new cumulus parameterization (Sun and Haines 1996), which can be incorporated into the Purdue Mesoscale Model (Haines 1992;Sun and Chern 1993;Chern 1994) to study convection and severe weather. However, the resolution of mesoscale models has been increasing, and a time dependent one-dimensional cloud model becomes required.…”

Section: Introductionmentioning

confidence: 99%

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A One-dimensional Time Dependent Cloud Model

Chen

Sun²

2002

Journal of the Meteorological Society of Japan

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483

258

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A one-dimensional prognostic cloud model has been developed for possible use in a Cumulus Parameterization Scheme (CPS). In this model, the nonhydrostatic pressure, entrainment, cloud microphysics, lateral eddy mixing and vertical eddy mixing are included, and their effects are discussed.The inclusion of the nonhydrostatic pressure can (1) weaken vertical velocities, (2) help the cloud develop sooner, (3) help maintain a longer mature stage, (4) produce a stronger overshooting cooling, and (5) approximately double the precipitation amount. The pressure perturbation consists of buoyancy pressure and dynamic pressure, and the simulation results show that both of them are important.We have compared our simulation results with those from Ogura and Takahashi's one-dimensional cloud model, and those from the three-dimensional Weather Research and Forecast (WRF) model. Our model, including detailed cloud microphysics, generates stronger maximum vertical velocity than Ogura and Takahashi's results. Furthermore, the results illustrate that this one-dimensional model is capable of reproducing the major features of a convective cloud that are produced by the three-dimensional model when there is no ambient wind shear.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A One-dimensional Time Dependent Cloud Model

Chen

Sun²

2002

Journal of the Meteorological Society of Japan

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483

258

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“…It is also noted that eigenvalue of (12) is identical to the forward-backward scheme (Sun, 1984;2010a), which becomes weakly unstable because of repeated eigenvalue at Co=1 (Sun 2010a). In addition to the physical modes of (12).…”

Section: A Original Lf Schemementioning

confidence: 97%

A modified leapfrog scheme for shallow water equations

Sun

2011

Computers & Fluids

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“…The eigenvalues and non-linear simulations of the nonhydrostatic model (NH) using the conventional forwardÁ backward scheme (FB) (Mesinger and Arakawa, 1976;Sun, 1980Sun, , 1984, the horizontal explicit and vertical implicit scheme (HEÁVI) (Klemp and Wilhelmson, 1978;Saito, 2007) and the modified non-hydrostatic model (MNH) have been discussed in Sun et al (2012), hereafter referred to as Part I. The MNH is designed to suppress highfrequency acoustic waves by multiplying the left-hand side of the continuity equation by a parameter d, where 16 ]d ]4.…”

Section: Introductionmentioning

confidence: 99%

A modified atmospheric non-hydrostatic model on low aspect ratio grids: part II

Sun

Tsuboki

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T Sun et al. (2012) proposed a modified non-hydrostatic model (MNH), in which the left-hand side of the continuity equation is multiplied by a parameter d (45d516 in the article) to suppress high-frequency acoustic waves. They showed that the MNH allows a longer time step than the original non-hydrostatic model (NH). The MNH is also more accurate and efficient than the horizontal explicit and vertical implicit scheme (HEÁVI) when the aspect ratio (Dx/Dz) is small. In addition to multiplying a parameter d, here we propose to add a smoothing on the right-hand side of the continuity equation in the MNH to damp shortest sound waves. Linear stability analysis and non-linear model simulations show that the MNH with smoothing (henceforth abbreviated as MNHS) can use twice the time interval of the MNH while maintaining the same accuracy. The MNHS is also more accurate and efficient than HEÁVI when the aspect ratio is small.

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Numerical Analysis for Hydrostatic and Nonhydrostatic Equations of Inertial-Internal Gravity Waves

Cited by 26 publications

References 0 publications

A One-dimensional Time Dependent Cloud Model

A One-dimensional Time Dependent Cloud Model

A modified leapfrog scheme for shallow water equations

A modified atmospheric non-hydrostatic model on low aspect ratio grids: part II

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