Turbulence closure model

Chen, C. P., Studies in two-phase turbulence closure modeling, Ph.D. Thesis, Michigan State University, USA (1985). 

Aerosol production and transport over the oceans are of interest in studies concerning cloud physics, air pollution, atmospheric optics, and air-sea interactions. However, the contribution of sea spray droplets to the transfer of moisture and latent heat from the sea to the atmosphere is not well known. In an effort to investigate these phenomena, Edson et al.[12l used an interactive Eulerian-Lagrangian approach to simulate the generation, turbulent transport and evaporation of droplets. The k-e turbulence closure model was incorporated in the Eulerian-Lagrangian model to accurately simulate... 

Hanjalic, K. (1994). Advanced turbulence closure models A view of current status and future prospects. International Journal of Heat and Fluid Flow 15, 178-203. 

In an attempt to circumvent some of these problems, considerable effort has been expended to develop so-called second moment turbulent closure models in which the governing equations are closed by including terms parameterizing various turbulent correlations (see, for example, Lewellen et al., 1974 Wyngaard and Cote, 1974 Lumley and Khajeh-Nouri, 1974 Mellor and Yamada, 1974 Yamada and Mellor, 1975 Zeman and Lumley, 1976, 1979 Zeman and Tennekes, 1977 Freeman, 1977 Yamada, 1977 Manton, 1979 Binkowski, 1979). While second-order closure models are conceptually very appealing, their use in atmospheric... 

Mellor, G. L., and Yamada, T. (1974). A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791-1806. 

Chambers, T.L. and Wilcox, D.C. (1977), Critical examination of two-equation turbulence closure models for boundary layers, AIAA J., 15(6), 821. 

The more usual approach to speeding up FCM methods for multi-body flow / dispersion calculations such as this is to use the continuum approach. This requires some estimates of turbulence parameters such as mixing lengths or eddy diffusivities for the canopy (on the neighbourhood scale), but these characteristics cannot be deduced from turbulence closure models, although they may be estimated from detailed calculations of flow/dispersion around a few typical obstacles - not a straightforward or accurate process (see Moulinec et al., 2003 [436]). 

For the research or assessment mode, the models can be more sophisticated, including the large eddy simulations (LES) or other high-order turbulence closure models, down-scaling with obstacle-resolved computer fluid dynamics (CFD) tools, but such models are very expensive computationally (see e.g., Mahura et al., 2005 [389]). For the forecasting mode, the models have to be fast enough therefore, they use... 

In general CFD models show a good applicability for risk assessments in urban areas however, their results can differ depending on turbulent closure models and other assumptions (Schatzmann, 2005 [562]). For practical applications these models contain a substantial amount of empirical knowledge, not only in the turbulent closure schemes but also in the use of wall functions and in other parameterisation schemes. To cast doubt on the results is perfectly justified, as it was shown by systematic studies in which applications of the same model by different modellers to a given problem (Hall, 1997 [244]) and applications of different models by either the same or different modellers to the same problem (Ketzel et al., 2002 [332]) revealed significant differences. 

Umlauf, L., Biuchard, H, 2005, Second-order turbulence closure models for geophysical boundary layers. A review of recent work. Continental Shelf Research, 25, 795-827. 

Yamada, T. and Bunker S., 1988. Development of a nested grid, second moment turbulence-closure model and an application to the 1982 ASCOT Brush Creek data simulation, J. Atmos. Sci., Tl, pp. 562-578. 

Turbulence closure models for the unknown terms in the flux- and variance equations for single phase reactor systems are discussed extensively by Baldyga and Bourne [5] and Fox [49] [50]. However, the application of these model closures should be treated with care as most of these parameterizations are expressed in terms of the turbulent eddy and other scalar dissipation rates (and dissipation energy spectra) which are about the weakest links in turbulence modeling. The predictive capabilities of the Re3molds averaged models... 

Chen YS, S.W.Kim SW (1987) Computation of turbulent flows using an extended k-s turbulence closure model. NASA Report CR-179204 Ciofalo M, Brucato A, Grisafi F, Torraca N (1996) Turbulent Flow in Closed and Free-Surface Unbafhed Tanks Stirred by Radial Impellers. Chem Eng Sci 51(14) 3557-3573... 

The turbulence closure model. Different levels of turbulence closure are used to obtain the eddy diffusion coefficients. The turbulence models differ in the assumptions on isotropy of turbulence. 

A physical model solves essentially Navier-Stokes equation with the forcing (the wind stress, Coriolis force, and buoyancy force) under adequate approximations. In order to include the density effects, conservation equations for temperature and salinity are also solved. In order to obtain a reahstic prediction for vertical stratification, turbulent closure model is also employed. As a result, the gravitational, wind-driven, and topographically induced flows can be reproduced within... 

Chen YS, Kim SW (1987) Computation of turbulent flows using an extended k-s turbulence closure model. NASA, Report CR-179204... 

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