Abstract
The Mixed Spectral Finite- Difference (MSFD) model for neutrally stratified, turbulent surface-layer flow has been shown to produce accurate, computationally economical predictions of flow in complex terrain as long as certain conditions are met. Since the model is based on linearized equations, variations in the surface roughness must not be extreme and terrain slopes must, in practice, be of order 0.3 or less.
This paper summarizes modifications to the MSFD model since the original description appeared In Beljaarset al. (1987a) and Karpik (1988). A significant improvement is the formulation of the upper boundary conditions. This new approach follows from an asymptotic form of the model equations where vertical diffusion terms are neglected. The resulting differential equations have an explicit, analytically expressible solution. The asymptotic solution derived in this way is shown to match very well with the solution to the full equation set within the computational domain. We illustrate that the improved upper boundary conditions permit the use of a computational top boundary that is lower than was previously possible, thus increasing computing efficiency without sacrificing accuracy.
The paper concludes with a brief description of MSFD-PC, the personal computer version of the model, and an outline of future development plans for the MSFD model.
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References
Ayotte, K. W., Xu, D. and Taylor, P. A.: 1994, ‘The Impact of Turbulence Closure Schemes on Predictions of the Mixed Spectral Finite-Difference Model for Flow over Topography’,Boundary-Layer Meteorol. 68, 1–33.
Beljaars, A. C. M., Walmsley, J. L., and Taylor, P. A.: 1987a, ‘A Mixed Spectral Finite-Difference Model for Neutrally Stratified Boundary-Layer Flow Over Roughness Changes and Topography’,Boundary-Layer Meteorol. 38, 273–303.
Beljaars, A. C. M., Walmsley, J. L., and Taylor, P. A.: 1987b, ‘Modelling of Turbulence Over Low Hills and Varying Surface Roughness’,Boundary-Layer Meteorol. 41, 203–215.
Harlow, F. H. and Welch, J. E.: 1965, ‘Numerical Calculation of Time-Dependent Incompressible Flow of Fluid with Free Surface’,Phys. Fluids 9, 842–851.
Jackson, P. S. and Hunt, J. C. R.: 1975, ‘Turbulent Windflow over a Low Hill’,Quart. J. Roy. Meteorol. Soc. 101, 929–955.
Karpik, S. R.: 1988 ‘An Improved Method for Intergrating the Mixed Spectral Finite Difference (MSFD) Model Equations’,Boundary-Layer Meteorol. 43, 273–286.
Karpik, S. R. and Walmsley, J. L.: 1992, ‘A Linear Model for Stratified Flow in Complex Terrain’, in H. van Dop and G. Kallos (eds.),Air Pollution Modeling and Its Application,9, Plenum Press, New York, pp. 677–685.
Launder, B. E., Reece, G. J., and Rodi, W.: 1975, ‘Progress in the Development of a Reynolds-stress Turbulence Closure’,J. Fluid Mech. 68, 537–566.
Mason, P. J. and Sykes, R. I.: 1979, ‘Flow Over an Isolated Hill of Moderate Slope’,Quart. J. Roy. Meteorol. Soc. 105, 383–395.
Mellor, G. L. and Yamada, T.: 1982, ‘Development of a Turbulence Closure Model for Geophysical Fluid Problems’,Rev. Geophys. Space Phys. 20, 851–875.
Padro, J. and Walmsley, J. L.: 1990, ‘A Mixed Spectral Finite-Difference Model for Pollutant Concentrations Over a Hill’,Boundary-Layer Meteorol. 51, 343–363.
Padro, J. and Walmsley, J. L.: 1991, ‘Spatial Variations of Aerodynamic Resistance Over a Hill’, in H. van Dop and D.G. Steyn (eds.),Air Pollution Modeling and Its Application,8, Plenum Press, New York, pp. 311–319.
Taylor, P. A., Walmsley, J. L., and Salmon, J. R.: 1983, ‘A Simple Model of Neutrally Stratified Boundary-Layer Flow Over Real Terrain Incorporating Wavenumber-Dependent Scaling’,Boundary-Layer Meteorol. 26, 169–189.
Walmsley, J. L. and Padro, J.: 1990, ‘Shear Stress Results from a Mixed Spectral Finite-Difference Model: Application to the Askervein Hill Project Data’,Boundary-Layer Meteorol 51, 169–177.
Walmsley, J. L., Salmon, J. R., and Taylor, P. A.: 1982, ‘On the Application of a Model of Boundary-Layer Flow over Low Hills to Real Terrain’,Boundary-Layer Meteorol. 23, 17–46.
Walmsley, J. L., Taylor, P. A. and Keith, T.: 1986., ‘A Simple Model of Neutrally Stratified Boundary-Layer Flow over Complex Terrain with Surface Roughness Modulations (MS3DJH/3R)’,Boundary-Layer Meteorol. 36, 157–186.
Walmsley, J. L., Troen, I., Lalas, D. P., and Mason, P. J.: 1990a, ‘Surface-Layer Flow in Complex Terrain: Comparison of Models and Full-Scale Observations’,Boundary-Layer Meteorol 52, 259–281.
Walmsley, J. L., Weng, W., Karpik, S. R., Xu, D., and Taylor, P. A.: 1994, ‘Applications of the Mixed Spectral Finite-Difference (MSFD) Model and its Nonlinear Extension (NLMSFD) to Wind Flow over Blashaval Hill’, in S.-E. Gryning and M.M. Millan (eds.),Air Pollution Modelling and Its Application,10, Plenum Press, New York, pp. 263–271.
Walmsley, J. L., Woolridge, D., and Salmon, J. R.: 1990b, ‘MS-Micro/3 User's Guide’., Rep. ARD-90-008, Atmospheric Environment Service, Downsview, Ontario, Canada, 88 pp.
Xu, D. and Taylor, P. A.: 1992, ‘A Non-Linear Extension of the Mixed Spectral Finite Difference Model for Neutrally Stratified Boundary-Layer Flow Over Topography’,Boundary-Layer Meteorol. 59, 177–186.
Xu, D. and Taylor, P. A.: 1995, ‘A Note on the Constants Used inE-∈-τ Turbulence Closure’,Boundary-Layer Meteorol. 72, 205–211.
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Karpik, S.R., Walmsley, J.L. & Weng, W. The mixed spectral finite-difference (MSFD) model: Improved upper boundary conditions. Boundary-Layer Meteorol 75, 353–380 (1995). https://doi.org/10.1007/BF00712269
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DOI: https://doi.org/10.1007/BF00712269