On the use of a coordinate transformation for the solution of the Navier-Stokes equations

Gal-Chen, Tzvi; Somerville, Richard C. J.

doi:10.1016/0021-9991(75)90037-6

Cited by 580 publications

(264 citation statements)

References 23 publications

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“…[14] ARPS uses a terrain-following coordinate system to solve the nonhydrostatic, compressible Navier-Stokes equations [Gal-Chen and Somerville, 1975]. In the ARPS implementation, the vertical coordinates and the associated Jacobians are defined numerically and can thus be arbitrary and time-dependent [Fiedler and Trapp, 1993;Fiedler et al, 1998].…”

Section: Arps Modelmentioning

confidence: 99%

Fine‐scale modeling of the boundary layer wind field over steep topography

Raderschall

Lehning

Schär

2008

Water Resources Research

105

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[1] This paper describes the adaptation of wind fields to steep and complex terrain using fine-scale numerical modeling. The work is motivated by the need of high-resolution flow fields to predict snow transport and snow cover development for avalanche warning purposes. Applying the nonhydrostatic and compressible atmospheric prediction model Advanced Regional Prediction System (ARPS) to steep alpine topography, the boundary layer flow was simulated and evaluated against measurements. The adaptation of the wind field to steep terrain for specific initial and boundary conditions was simulated. The topography used in our study has a length scale of 500 m, a typical height of 150 m, and maximum slopes of 45°. Numerical experiments with idealized triangular ridges were conducted to find an adequate model configuration. This analysis indicates that a highresolution grid with horizontal spacing of at least 25 m and vertical spacing of 3 m near the surface is necessary to reproduce small-scale flow features such as speed-up, separation, and recirculation. The onset of flow separation is highly sensitive to initial and boundary conditions, slope angle, and surface roughness. The results of the comparison between the model simulations and measurements on our experimental site show that typical wind field characteristics are well reproduced. The simulated wind fields have been used to drive a numerical three-dimensional snow drift model, which is presented in a companion paper by Lehning et al. (2008).

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Section: Arps Modelmentioning

confidence: 99%

Fine‐scale modeling of the boundary layer wind field over steep topography

Raderschall

Lehning

Schär

2008

Water Resources Research

105

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“…Besides the above-mentioned deficiency in the cloud microphysical scheme (Smith et al, 2003), the freeatmosphere temperature and wind fields were found to be heavily disturbed by grid-scale numerical noise over the Alps despite heavy smoothing of the model topography. Schär et al (2002) suggested that numerical errors related to the terrain-following coordinate system (Gal-Chen and Somerville, 1975) were responsible for these undesirable noisy structures. These numerical errors were found to be roughly proportional to the steepness of the coordinate surfaces and to severely reduce the numerical accuracy of horizontal advection.…”

Section: Model Improvements Triggered By Mapmentioning

confidence: 99%

Quantitative precipitation forecasting in the Alps: The advances achieved by the Mesoscale Alpine Programme

Richard

Buzzi

Zängl³

2007

Quart J Royal Meteoro Soc

104

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ABSTRACT:The improvement of Quantitative Precipitation Forecasting (QPF) in mountainous regions was a major supporting objective of the Mesoscale Alpine Programme (MAP) project P1 devoted to the study of orographic precipitation. This paper reviews the main MAP-related achievements regarding QPF improvement and highlights the MAP impact on developing QPF research and planning future operational strategies. Recent results based on MAP case-studies, on data analysis and assimilation, on quantification of model uncertainties, and on model intercomparison and verification substantiate the progress made in recent years in improving model performance in relation to short-range, high-resolution forecasting in complex topography regions, well represented by the European Alps.

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“…The same model configuration as in Lebeaupin et al (2006) and Lebeaupin Brossier et al (2008) is used, with two interactive nested grids running at horizontal resolutions of 9.5 km and 2.4 km, respectively. The vertical grid is described by the generalized coordinates from Gal-Chen and Somerville (1975) with a stretched grid of 40 levels with interlevel spaces ranging from 75 m at low levels to 900 m at the model top. The MESO-NH time steps are 20 s and 5 s for the 9.5 km and 2.4 km domains, respectively.…”

Section: The Meso-nh Modelmentioning

confidence: 99%

Two‐way one‐dimensional high‐resolution air–sea coupled modelling applied to Mediterranean heavy rain events

Brossier

Ducrocq

Giordani

2008

Quart J Royal Meteoro Soc

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South-eastern France is prone to heavy rain events during the autumn. For these extreme precipitation events, the Mediterranean Sea fuels the atmospheric boundary layer in heat and moisture and sometimes contributes to flooding, owing to the large swell and waves produced in these situations. The aim of this study is to examine how the severe atmospheric conditions over the sea associated with these events alter the ocean mixed layer, and what feedback the ocean contributes to the precipitation events.To address these questions, a high-resolution air-sea coupled system is developed between the atmospheric MESO-NH model and a one-dimensional ocean model. It is applied for short range (24 h) and high-resolution (2-3 km) simulations of three representative torrential rainfall events: 12-13 November 1999 (Aude case), 8-9 September 2002 (Gard case) and 3 December 2003 (Hérault case). In those meteorological situations characterized by moderate to intense low-level winds, the Mediterranean Sea globally loses energy, to the benefit of the convective precipitating systems. The result is an overall decrease of the thermal content all along the simulation of the events. Significant cooling and deepening of the ocean mixed layer are found in the areas of intense low-level winds. A notable result of the study concerns the impact of the torrential rainfall on the ocean mixed layer. The most important disturbances of the ocean mixed layer are indeed found underneath the heavy precipitation. The salt content is decreased all along the ocean mixed layer depth, but more significantly in the first ten metres near the air-sea interface, with the formation of a salt barrier.By performing both two-way and one-way coupled simulations, it is found that the interactive coupling tends to moderate both the atmospheric and ocean responses compared with the one-way mode. The differences between the two-way and one-way coupled simulations are, however, found to be relatively small considering the atmospheric short-range forecast.

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On the use of a coordinate transformation for the solution of the Navier-Stokes equations

Cited by 580 publications

References 23 publications

Fine‐scale modeling of the boundary layer wind field over steep topography

Fine‐scale modeling of the boundary layer wind field over steep topography

Quantitative precipitation forecasting in the Alps: The advances achieved by the Mesoscale Alpine Programme

Two‐way one‐dimensional high‐resolution air–sea coupled modelling applied to Mediterranean heavy rain events

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